1492 lines
47 KiB
Fortran
1492 lines
47 KiB
Fortran
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!
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!=======================================================================
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!
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MODULE CALCULATORS_3
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!
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USE ACCURACY_REAL
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!
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! This module contains the subroutines allowing to compute
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! various properties of the electron/plasma liquids:
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!
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! * local field corrections : CALC_LFC
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! * I(q) function : CALC_IQF
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! * structure factor : CALC_SFC
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! * pair correlation function : CALC_PCF
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!
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! * pair distribution function : CALC_PDF
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! * vertex function : CALC_VTX
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! * plasmon damping coefficient: CALC_DMP
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!
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! * q bounds : CALC_QBD
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! * relaxation time : CALC_RLX
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! * screening wave number : CALC_SCR
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! * omega = q * v_F : CALC_QVF
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!
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! * moments of Im[epsilon] : CALC_MEP
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! * moments of S(q,omega) : CALC_MSF
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! * moments of loss function : CALC_MLO
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!
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! * zeros of Re [epsilon] : CALC_RE0
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!
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! * inelastic mean free path : CALC_MFP
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!
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! * Fourier-space Nevalinna : CALC_NEV
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! * time-space memory function : CALC_MEM
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!
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CONTAINS
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!
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!=======================================================================
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!
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SUBROUTINE CALC_LFC(X)
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!
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! This subroutine computes the local field correction G(q, omega)
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!
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!
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! Input parameters:
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!
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! * X : dimensionless factor --> X = q / (2 * k_F)
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!
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!
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! Intermediate parameters:
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!
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature in SI
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!
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!
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! Output parameters:
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!
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! * E : energy array
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! * LFCR : real part of local field correction
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! * LFCI : imaginary part of local field correction
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!
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!
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 3 Dec 2020
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!
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USE DIMENSION_CODE, ONLY : NSIZE
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USE REAL_NUMBERS, ONLY : ZERO
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USE MATERIAL_PROP, ONLY : RS
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USE EXT_FIELDS, ONLY : T
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USE LF_VALUES, ONLY : GSTDY,GQ_TYPE,GQO_TYPE
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USE SF_VALUES, ONLY : SQ_TYPE
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!
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USE E_GRID
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!
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USE LOCAL_FIELD_STATIC
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USE LOCAL_FIELD_STATIC_2
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USE LOCAL_FIELD_DYNAMIC
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!
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USE OUT_VALUES_3, ONLY : I_LF
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USE PRINT_FILES, ONLY : IO_LF
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!
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IMPLICIT NONE
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!
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REAL (WP) :: X
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REAL (WP) :: LFCR(NSIZE),LFCI(NSIZE),E(NSIZE)
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REAL (WP) :: RLFC,ILFC
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REAL (WP) :: EN,ETA
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REAL (WP) :: Y
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!
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INTEGER :: IE,LOGF
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!
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LOGF = 6 !
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!
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Y = X + X ! q/k_F
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!
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IF(GSTDY == ' STATIC') THEN !
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!
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! Static local field correction:
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!
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! 1) G(q) not based on S(q)
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!
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IF(GQ_TYPE /= 'HNCA' .AND. GQ_TYPE /= 'IKPA') THEN !
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CALL LFIELD_STATIC(X,RS,T,GQ_TYPE,RLFC) !
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ELSE
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!
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! 1) G(q) based on S(q)
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!
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IF(SQ_TYPE /= 'GEA' .AND. SQ_TYPE /= 'ICH' .AND. & !
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SQ_TYPE /= 'PKA' .AND. SQ_TYPE /= 'SIN' .AND. & !
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SQ_TYPE /= 'SPA') THEN !
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CALL LFIELD_STATIC_2(X,RS,T,GQ_TYPE,RLFC) !
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ELSE !
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WRITE(LOGF,10) !
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STOP !
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END IF !
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!
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END IF !
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!
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LFCR(1) = RLFC !
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LFCI(1) = ZERO !
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!
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IF(I_LF == 1) THEN ! writing to
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WRITE(IO_LF,*) Y,ZERO,RLFC,ZERO ! file
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END IF !
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!
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ELSE !
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!
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! Dynamic local field correction
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!
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CALL LFIELD_DYNAMIC(X,RS,E_MIN,E_MAX,N_E,T,ETA, & !
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GQO_TYPE,E,LFCR,LFCI) !
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!
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IF(I_LF == 1) THEN !
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DO IE = 1, N_E ! writing to
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WRITE(IO_LF,*) Y,E(IE),LFCR(IE),LFCI(IE) ! file
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END DO !
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END IF !
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!
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END IF !
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!
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! Format:
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!
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10 FORMAT(//,10X,'<<<<< ERROR IN CALCULATOR_3 :: CALC_LFC >>>>>', &
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/,10X,'<<<<< WRONG CHOICE OF GQ_TYPE :: SQ_TYPE >>>>>', &
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//,10X,' --> G(q) choice uses S(q) which uses G(q) <--',//)
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!
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END SUBROUTINE CALC_LFC
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!
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!=======================================================================
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!
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SUBROUTINE CALC_IQF(X)
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!
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! This subroutine computes the local field correction I(q) = G(q,inf)
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!
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!
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! Input parameters:
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!
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! * X : dimensionless factor --> X = q / (2 * k_F)
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!
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!
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! Intermediate parameters:
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!
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature in SI
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!
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!
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! Output parameters:
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!
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! * IQR : real part of I(q)
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! * IQI : imaginary of I(q)
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!
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!
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 15 Sep 2020
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!
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USE MATERIAL_PROP, ONLY : RS,DMN
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USE EXT_FIELDS, ONLY : T
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!
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USE REAL_NUMBERS, ONLY : ZERO
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USE LF_VALUES, ONLY : GQ_TYPE,IQ_TYPE
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USE SF_VALUES, ONLY : SQ_TYPE
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USE ENERGIES, ONLY : EC_TYPE
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USE IQ_FUNCTIONS_1
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!
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USE OUT_VALUES_3, ONLY : I_IQ
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USE PRINT_FILES, ONLY : IO_IQ
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP) :: IQ
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REAL (WP) :: Y
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!
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Y = X + X ! q/k_F
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!
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IF(DMN == '3D') THEN !
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CALL IQ_3D(X,RS,IQ_TYPE,IQ) !
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ELSE IF(DMN == '2D') THEN !
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CONTINUE ! not implemented yet
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ELSE IF(DMN == '1D') THEN !
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CONTINUE ! not implemented yet
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END IF !
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!
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IF(I_IQ == 1) THEN ! writing to
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WRITE(IO_IQ,*) Y,IQ ! file
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END IF !
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!
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END SUBROUTINE CALC_IQF
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!
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!=======================================================================
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!
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SUBROUTINE CALC_SFC(X)
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!
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! This subroutine computes the structure factor S(q, omega)
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!
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!
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! Input parameters:
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!
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! * X : dimensionless factor --> X = q / (2 * k_F)
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!
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!
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! Intermediate parameters:
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!
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature in SI
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!
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!
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! Output parameters:
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!
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! * E : energy array
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! * SFCR : real part of the structure factor
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! * SFCI : imaginary part of structure factor
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!
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!
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! Note: as S(q,omega) is proportional to the inverse of a
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! frequency, we renormalize it by multiplicating it
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! by E_F / h_bar to obtain a dimensionless quantity
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!
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 21 Dec 2020
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!
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USE DIMENSION_CODE, ONLY : NSIZE
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!
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USE MATERIAL_PROP, ONLY : DMN,RS
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USE EXT_FIELDS, ONLY : T
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!
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USE REAL_NUMBERS, ONLY : ZERO,ONE,FOURTH
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USE CONSTANTS_P1, ONLY : H_BAR
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USE FERMI_SI, ONLY : EF_SI
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!
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USE E_GRID
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!
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USE LF_VALUES, ONLY : GQ_TYPE,IQ_TYPE
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USE SF_VALUES
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USE STRUCTURE_FACTOR_STATIC
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USE STRUCTURE_FACTOR_STATIC_2
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USE STRUCTURE_FACTOR_DYNAMIC
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USE STRUCTURE_FACTOR_DYNAMIC_2
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!
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USE UTIC_VALUES
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USE RELAXATION_TIME_STATIC
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USE PLASMON_ENE_SI
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USE PLASMON_DISP_REAL
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USE DECAY_RATE
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USE UTIC_PARAMETERS
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!
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USE OUT_VALUES_3, ONLY : I_SF
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USE PRINT_FILES, ONLY : IO_SF
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!
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IMPLICIT NONE
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!
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REAL (WP) :: X
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REAL (WP) :: RSFC,ISFC
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REAL (WP) :: Z,EN,SQ,SQ_RN
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REAL (WP) :: Y
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REAL (WP) :: HOM_Q
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REAL (WP) :: E1,E2,E3,E4,E5,E6
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!
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REAL (WP) :: FLOAT
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!
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INTEGER :: IE,LOGF
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!
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LOGF = 6 !
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!
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Y = X + X ! q/k_F
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!
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! Storing the omega-independent UTIC parameters whenever necessary
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!
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IF(SQO_TYPE == 'UTI') THEN !
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IF(DMN == '3D') THEN !
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TAU_Q = UTIC_RT_3D(X,RS,T,SQ_TYPE,GQ_TYPE) ! tau(q)
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CALL PLASMON_DISP_3D_2(X,RS,T,'UTI_MOD',HOM_Q) !
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OM_Q = HOM_Q / H_BAR ! omega(q)
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GAM_Q = UTIC_DR_3D(X,RS,T,SQ_TYPE,GQ_TYPE,IQ_TYPE) ! gamma(q)
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CALL UTIC_PARAM(X,RS,T,MO_Q,MO_0) ! Omega(q), Omega(0)
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!
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E1 = H_BAR / (TAU_Q * EF_SI) !
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E2 = ENE_P_SI / EF_SI !
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E3 = H_BAR * OM_Q / EF_SI !
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E4 = ABS(H_BAR * GAM_Q / EF_SI) !
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E5 = H_BAR * MO_Q / EF_SI !
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E6 = H_BAR * MO_0 / EF_SI !
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!
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WRITE(1,*) Y,E1,E2,E3,E4,E5,E6 !
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END IF
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END IF !
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!
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IF(SSTDY == ' STATIC') THEN !
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!
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! Static structure factor
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!
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! 1) S(q) not based on G(q)
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!
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IF(SQ_TYPE /= 'GEA' .AND. SQ_TYPE /= 'ICH' .AND. & !
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SQ_TYPE /= 'PKA' .AND. SQ_TYPE /= 'SIN' .AND. & !
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SQ_TYPE /= 'SPA') THEN !
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CALL STFACT_STATIC(X,RS,T,SQ_TYPE,RSFC) !
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!
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! 2) S(q) based on G(q)
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!
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ELSE !
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!
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IF(GQ_TYPE /= 'HNCA' .AND. GQ_TYPE /= 'IKPA') THEN !
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CALL STFACT_STATIC_2(X,RS,T,SQ_TYPE,RSFC) !
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ELSE
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WRITE(LOGF,10) !
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STOP !
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END IF !
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!
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END IF !
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IF(I_SF == 1) THEN ! writing to
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WRITE(IO_SF,*) Y,ZERO,RSFC,ZERO ! file
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END IF !
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!
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ELSE !
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!
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! Dynamic structure factor
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!
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DO IE = 1, N_E ! energy loop
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!
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EN = E_MIN + FLOAT(IE - 1) * E_STEP ! E = hbar omega / E_F
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!
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Z = FOURTH * EN / (X * X) ! Z = omega / omega_q
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!
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IF(SQO_TYPE /= 'EPS') THEN !
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CALL STFACT_DYNAMIC(X,Z,RS,T,SQO_TYPE,SQ_TYPE,SQ) !
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ELSE
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CALL STFACT_DYNAMIC_FROM_EPS(X,Z,RS,T,SQ) !
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END IF !
|
||
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!
|
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SQ_RN = SQ * EF_SI / H_BAR ! renormalized S(q,omega)
|
||
|
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!
|
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|
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IF(I_SF == 1) THEN ! writing to
|
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WRITE(IO_SF,*) Y,EN,SQ_RN,ZERO ! file
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END IF !
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!
|
||
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END DO !
|
||
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!
|
||
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END IF !
|
||
|
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!
|
||
|
|
! Format:
|
||
|
|
!
|
||
|
|
10 FORMAT(//,10X,'<<<<< ERROR IN CALCULATOR_3 :: CALC_SFC >>>>>', &
|
||
|
|
/,10X,'<<<<< WRONG CHOICE OF SQ_TYPE :: GQ_TYPE >>>>>', &
|
||
|
|
//,10X,' --> S(q) choice uses G(q) which uses S(q) <--',//)
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_SFC
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_PCF
|
||
|
|
!
|
||
|
|
! This subroutine computes the pair correlation function g(r)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Intermediate parameters:
|
||
|
|
!
|
||
|
|
! * RS : Wigner-Seitz radius (in units of a_0)
|
||
|
|
! * T : temperature in SI
|
||
|
|
! * DMN : problem dimension
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * GR : g(r) ar r
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 29 Jul 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE MATERIAL_PROP, ONLY : RS,DMN
|
||
|
|
USE EXT_FIELDS, ONLY : T
|
||
|
|
USE PC_VALUES, ONLY : GR_TYPE
|
||
|
|
USE PD_VALUES, ONLY : RH_TYPE
|
||
|
|
USE PAIR_CORRELATION
|
||
|
|
!
|
||
|
|
USE R_GRID
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_PC
|
||
|
|
USE PRINT_FILES, ONLY : IO_PC
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
REAL (WP) :: R,GR
|
||
|
|
!
|
||
|
|
REAL (WP) :: FLOAT
|
||
|
|
!
|
||
|
|
INTEGER :: IR
|
||
|
|
!
|
||
|
|
DO IR = 1, N_R ! r loop
|
||
|
|
!
|
||
|
|
R = R_MIN + FLOAT(IR - 1) * R_STEP ! r/a0 point
|
||
|
|
!
|
||
|
|
IF(DMN == '3D') THEN !
|
||
|
|
CALL PAIR_CORRELATION_3D(R,RS,T,GR_TYPE,RH_TYPE,GR) !
|
||
|
|
ELSE IF(DMN == '2D') THEN !
|
||
|
|
CONTINUE !
|
||
|
|
ELSE IF(DMN == '1D') THEN !
|
||
|
|
CONTINUE !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
IF(I_PC == 1) THEN !
|
||
|
|
WRITE(IO_PC,*) R,GR !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
ENDDO !
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_PCF
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_PDF
|
||
|
|
!
|
||
|
|
! This subroutine computes the pair distribution function rho2(r)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Intermediate parameters:
|
||
|
|
!
|
||
|
|
! * RS : Wigner-Seitz radius (in units of a_0)
|
||
|
|
! * T : temperature in SI
|
||
|
|
! * DMN : problem dimension
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * R2 : rho2(r) ar r
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 29 Jul 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE MATERIAL_PROP, ONLY : RS,DMN
|
||
|
|
USE EXT_FIELDS, ONLY : T
|
||
|
|
USE PD_VALUES, ONLY : RH_TYPE
|
||
|
|
USE PAIR_DISTRIBUTION
|
||
|
|
!
|
||
|
|
USE R_GRID
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_P2
|
||
|
|
USE PRINT_FILES, ONLY : IO_P2
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
REAL (WP) :: R,R2
|
||
|
|
!
|
||
|
|
REAL (WP) :: FLOAT
|
||
|
|
!
|
||
|
|
INTEGER :: IR
|
||
|
|
!
|
||
|
|
DO IR = 1, N_R ! r loop
|
||
|
|
!
|
||
|
|
R = R_MIN + FLOAT(IR - 1) * R_STEP ! r/a0 point
|
||
|
|
!
|
||
|
|
IF(DMN == '3D') THEN !
|
||
|
|
CALL PAIR_DISTRIBUTION_3D(R,RS,T,RH_TYPE,R2) !
|
||
|
|
ELSE IF(DMN == '2D') THEN !
|
||
|
|
CONTINUE !
|
||
|
|
ELSE IF(DMN == '1D') THEN !
|
||
|
|
CONTINUE !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
IF(I_P2 == 1) THEN !
|
||
|
|
WRITE(IO_P2,*) R,R2 !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END DO !
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_PDF
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_VTX(X)
|
||
|
|
!
|
||
|
|
! This subroutine computes the vertex function Gamma(q, omega)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Input parameters:
|
||
|
|
!
|
||
|
|
! * X : dimensionless factor --> X = q / (2 * k_F)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Intermediate parameters:
|
||
|
|
!
|
||
|
|
! * RS : Wigner-Seitz radius (in units of a_0)
|
||
|
|
! * T : temperature in SI
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * E : energy array
|
||
|
|
! * VTXR : real part of vertex function
|
||
|
|
! * VTXI : imaginary part vertex function
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 30 Apr 2020
|
||
|
|
!
|
||
|
|
USE DIMENSION_CODE, ONLY : NSIZE
|
||
|
|
USE REAL_NUMBERS, ONLY : ZERO,ONE,FOURTH,SMALL,INF
|
||
|
|
USE COMPLEX_NUMBERS, ONLY : IC
|
||
|
|
USE MATERIAL_PROP, ONLY : DMN,RS
|
||
|
|
USE EXT_FIELDS, ONLY : T,H
|
||
|
|
USE LF_VALUES, ONLY : GSTDY,GQ_TYPE,GQO_TYPE
|
||
|
|
USE DF_VALUES, ONLY : ESTDY,EPS_T,D_FUNC
|
||
|
|
!
|
||
|
|
USE E_GRID
|
||
|
|
!
|
||
|
|
USE SCREENING_TYPE
|
||
|
|
USE SCREENING_VEC
|
||
|
|
!
|
||
|
|
USE LOCAL_FIELD_STATIC
|
||
|
|
USE LOCAL_FIELD_DYNAMIC
|
||
|
|
USE DFUNC_STATIC
|
||
|
|
USE DFUNCT_STAN_DYNAMIC
|
||
|
|
USE DFUNCL_STAN_DYNAMIC
|
||
|
|
USE DFUNCL_MAGN_DYNAMIC
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_VX
|
||
|
|
USE PRINT_FILES, ONLY : IO_VX
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
CHARACTER (LEN = 4) :: D_FUNCL,D_FUNCT
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: X
|
||
|
|
REAL (WP) :: E(NSIZE)
|
||
|
|
REAL (WP) :: LFCR(NSIZE),LFCI(NSIZE)
|
||
|
|
REAL (WP) :: EPSR(NSIZE),EPSI(NSIZE)
|
||
|
|
REAL (WP) :: VTXR,VTXI
|
||
|
|
REAL (WP) :: RLFC,ILFC
|
||
|
|
REAL (WP) :: REPS,IEPS
|
||
|
|
REAL (WP) :: ETA
|
||
|
|
REAL (WP) :: Z,EN
|
||
|
|
REAL (WP) :: Y
|
||
|
|
!
|
||
|
|
REAL (WP) :: A,NU,KS_SI
|
||
|
|
!
|
||
|
|
REAL (WP) :: FLOAT
|
||
|
|
!
|
||
|
|
COMPLEX (WP) :: EPS,LFC,VTX
|
||
|
|
!
|
||
|
|
INTEGER :: IE
|
||
|
|
!
|
||
|
|
A = ZERO ! temporary
|
||
|
|
NU = ZERO !
|
||
|
|
!
|
||
|
|
Y = X + X ! q / k_F
|
||
|
|
!
|
||
|
|
! Computing the screening wave vector
|
||
|
|
!
|
||
|
|
CALL SCREENING_VECTOR(SC_TYPE,DMN,X,RS,T,KS_SI)
|
||
|
|
!
|
||
|
|
! 1) Computing the local field correction
|
||
|
|
!
|
||
|
|
IF(GSTDY == ' STATIC') THEN !
|
||
|
|
!
|
||
|
|
! Static local field correction
|
||
|
|
!
|
||
|
|
CALL LFIELD_STATIC(X,RS,T,GQ_TYPE,RLFC) !
|
||
|
|
!
|
||
|
|
LFCR(1) = RLFC !
|
||
|
|
LFCI(1) = ZERO !
|
||
|
|
!
|
||
|
|
ELSE !
|
||
|
|
!
|
||
|
|
! Dynamic local field correction
|
||
|
|
!
|
||
|
|
CALL LFIELD_DYNAMIC(X,RS,E_MIN,E_MAX,N_E,T,ETA, & !
|
||
|
|
GQO_TYPE,E,LFCR,LFCI) !
|
||
|
|
!
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
! 2) Computing the dielectric function
|
||
|
|
!
|
||
|
|
IF(ESTDY == ' STATIC') THEN !
|
||
|
|
!
|
||
|
|
! Static dielectric function
|
||
|
|
!
|
||
|
|
IF(EPS_T == 'LONG') THEN !
|
||
|
|
!
|
||
|
|
D_FUNCL = 'RPA1' !
|
||
|
|
CALL DFUNCL_STATIC(X,D_FUNCL,REPS,IEPS) ! longitudinal eps
|
||
|
|
EPSR(1) = REPS !
|
||
|
|
EPSI(1) = IEPS !
|
||
|
|
!
|
||
|
|
ELSE !
|
||
|
|
D_FUNCT = D_FUNC !
|
||
|
|
CONTINUE ! transverse eps
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
ELSE !
|
||
|
|
!
|
||
|
|
! Dynamic dielectric function
|
||
|
|
!
|
||
|
|
DO IE = 1, N_E ! energy loop
|
||
|
|
!
|
||
|
|
EN = E_MIN + FLOAT(IE - 1) * E_STEP ! EN = hbar omega / E_F
|
||
|
|
!
|
||
|
|
Z = FOURTH * EN / (X * X) ! Z = omega / omega_q
|
||
|
|
!
|
||
|
|
IF(EPS_T == 'LONG') THEN ! longitudinal eps
|
||
|
|
!
|
||
|
|
D_FUNCL = 'RPA1' !
|
||
|
|
IF(H < SMALL) THEN !
|
||
|
|
CALL DFUNCL_DYNAMIC(X,Z,RS,T,D_FUNCL,IE,REPS,IEPS) ! no magnetic field
|
||
|
|
ELSE !
|
||
|
|
CALL DFUNCL_DYNAMIC_M(X,Z,KS_SI,A,NU,D_FUNCL,REPS,IEPS) ! magnetic field
|
||
|
|
END IF !
|
||
|
|
ELSE ! transverse eps
|
||
|
|
D_FUNCT = D_FUNC !
|
||
|
|
IF(H < SMALL) THEN !
|
||
|
|
CALL DFUNCT_DYNAMIC(X,Z,D_FUNCT,REPS,IEPS) ! no magnetic field
|
||
|
|
ELSE !
|
||
|
|
CONTINUE ! magnetic field
|
||
|
|
END IF !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
EPSR(IE) = REPS !
|
||
|
|
EPSI(IE) = IEPS !
|
||
|
|
E(IE) = EN !
|
||
|
|
!
|
||
|
|
END DO ! end of energy loop
|
||
|
|
!
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
! 3) Computing the vertex function and writing to file
|
||
|
|
!
|
||
|
|
! As we have chosen D_FUNCL='RPA1', PI = PI0 and the
|
||
|
|
! vertex function is:
|
||
|
|
!
|
||
|
|
! 1
|
||
|
|
! ---------------------
|
||
|
|
! 1 + LFC * (EPS - 1)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
IF(I_VX == 1) THEN !
|
||
|
|
DO IE = 1, N_E !
|
||
|
|
!
|
||
|
|
LFC = LFCR(IE) + IC * LFCI(IE) !
|
||
|
|
EPS = EPSR(IE) + IC * EPSI(IE) !
|
||
|
|
VTX = ONE / (ONE + LFC * (EPS - ONE)) !
|
||
|
|
VTXR = REAL(VTX,KIND=WP) !
|
||
|
|
VTXI = AIMAG(VTX) !
|
||
|
|
|
||
|
|
WRITE(IO_VX,*) Y,E(IE),VTXR,VTXI !
|
||
|
|
!
|
||
|
|
END DO !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_VTX
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_DMP(IX,X)
|
||
|
|
!
|
||
|
|
! This subroutine computes the plasmon damping coefficient gamma_q
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Im[ epsilon ] |
|
||
|
|
! gamma_q = - _______________ |
|
||
|
|
! |
|
||
|
|
! d Re[ epsilon ]/d omega | omega=Omega_q
|
||
|
|
!
|
||
|
|
! where epsilon is the dielectric function.
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Input parameters:
|
||
|
|
!
|
||
|
|
! * IX : index of X-point
|
||
|
|
! * X : dimensionless factor --> X = q / (2 * k_F)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Intermediate parameters:
|
||
|
|
!
|
||
|
|
! * RS : Wigner-Seitz radius (in units of a_0)
|
||
|
|
! * T : temperature in SI
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * E : energy array
|
||
|
|
! * VTXR : real part of vertex function
|
||
|
|
! * VTXI : imaginary part vertex function
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 30 Apr 2021
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE DIMENSION_CODE, ONLY : NSIZE
|
||
|
|
USE MATERIAL_PROP, ONLY : RS
|
||
|
|
USE EXT_FIELDS, ONLY : T
|
||
|
|
!
|
||
|
|
USE REAL_NUMBERS, ONLY : ZERO,TWO,FOURTH,TTINY,INF
|
||
|
|
USE FERMI_SI, ONLY : KF_SI
|
||
|
|
!
|
||
|
|
USE E_GRID
|
||
|
|
!
|
||
|
|
USE DF_VALUES, ONLY : D_FUNC
|
||
|
|
!
|
||
|
|
USE INTEGRATION, ONLY : INTEGR_L
|
||
|
|
USE DFUNCL_STAN_DYNAMIC
|
||
|
|
!
|
||
|
|
USE FIND_ZERO, ONLY : FIND_ZERO_FUNC
|
||
|
|
USE PLASMON_DAMPING, ONLY : EXACT_DAMPING
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_DC
|
||
|
|
USE PRINT_FILES, ONLY : IO_DC
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
INTEGER,INTENT(IN) :: IX
|
||
|
|
INTEGER :: IE
|
||
|
|
INTEGER :: IDERIV
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: X
|
||
|
|
REAL (WP) :: D,TAU
|
||
|
|
REAL (WP) :: Y,E,V,Z
|
||
|
|
REAL (WP) :: REPS,IEPS
|
||
|
|
REAL (WP) :: EN(NSIZE)
|
||
|
|
REAL (WP) :: EPSR(NSIZE),EPSI(NSIZE)
|
||
|
|
REAL (WP) :: ZEROF,GAMMA_Q
|
||
|
|
!
|
||
|
|
REAL (WP) :: FLOAT
|
||
|
|
!
|
||
|
|
IDERIV = 5 !
|
||
|
|
!
|
||
|
|
Y = X + X ! q/k_F
|
||
|
|
!
|
||
|
|
! Constructing the e-grid
|
||
|
|
!
|
||
|
|
DO IE = 1, N_E ! E_F
|
||
|
|
!
|
||
|
|
E = E_MIN + FLOAT(IE - 1) * E_STEP ! in units of
|
||
|
|
V = E ! hbar * omega / E_F
|
||
|
|
Z = FOURTH * V / (X * X) ! omega / omega_q
|
||
|
|
!
|
||
|
|
! Computing the dielectric function epsilon(q,E)
|
||
|
|
!
|
||
|
|
CALL DFUNCL_DYNAMIC(X,Z,RS,T,D_FUNC,IE,REPS,IEPS) !
|
||
|
|
!
|
||
|
|
EN(IE) = E !
|
||
|
|
EPSR(IE) = REPS !
|
||
|
|
EPSI(IE) = IEPS !
|
||
|
|
!
|
||
|
|
END DO !
|
||
|
|
!
|
||
|
|
! Computing the plasmon energy at q:
|
||
|
|
! Only the highest energy zero is kept
|
||
|
|
!
|
||
|
|
CALL FIND_ZERO_FUNC(EN,EPSR,N_E,ZEROF) !
|
||
|
|
!
|
||
|
|
! Computing the damping coefficient
|
||
|
|
!
|
||
|
|
CALL EXACT_DAMPING(IX,IDERIV,N_E,EN,EPSR,EPSI,ZEROF,GAMMA_Q) !
|
||
|
|
!
|
||
|
|
IF(I_DC == 1) THEN !
|
||
|
|
WRITE(IO_DC,*) Y,GAMMA_Q !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_DMP
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_QBD
|
||
|
|
!
|
||
|
|
! This subroutine computes the plasmon q-bounds
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * Q_MIN : plasmon lower q-bound
|
||
|
|
! * Q_MAX : plasmon upper q-bound
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 6 Oct 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE Q_BOUNDS
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_QC
|
||
|
|
USE PRINT_FILES, ONLY : IO_QC
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
REAL (WP) :: Q_MIN,Q_MAX
|
||
|
|
!
|
||
|
|
CALL QBOUNDS(Q_MIN,Q_MAX)
|
||
|
|
!
|
||
|
|
IF(I_QC == 1) THEN !
|
||
|
|
WRITE(IO_QC,*) Q_MIN,Q_MAX !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_QBD
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_RLX(X)
|
||
|
|
!
|
||
|
|
! This subroutine computes the relaxation time
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Input parameters:
|
||
|
|
!
|
||
|
|
! * X : dimensionless factor --> X = q / (2 * k_F)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * TAU : relaxation time
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 7 Oct 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE MATERIAL_PROP, ONLY : DMN,RS
|
||
|
|
USE EXT_FIELDS, ONLY : T
|
||
|
|
USE PLASMA, ONLY : ZION
|
||
|
|
!
|
||
|
|
USE SCREENING_VEC, ONLY : DEBYE_VECTOR
|
||
|
|
USE DAMPING_VALUES, ONLY : VI_TYPE
|
||
|
|
USE RELAXATION_TIME_STATIC
|
||
|
|
USE VISCOSITY
|
||
|
|
!
|
||
|
|
USE EL_PHO_INTER
|
||
|
|
!
|
||
|
|
USE REAL_NUMBERS, ONLY : ZERO
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_RL
|
||
|
|
USE PRINT_FILES, ONLY : IO_RL
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: X
|
||
|
|
REAL (WP) :: Y,ETA,KD_SI,TAU
|
||
|
|
REAL (WP) :: LR,S_L
|
||
|
|
!
|
||
|
|
Y = X + X ! q/k_F
|
||
|
|
!
|
||
|
|
LR = ZERO ! residual mfp (temporary)
|
||
|
|
S_L = ZERO ! scattering length (temporary)
|
||
|
|
!
|
||
|
|
! Computing the Debye momentum
|
||
|
|
!
|
||
|
|
CALL DEBYE_VECTOR('3D',T,RS,KD_SI) !
|
||
|
|
!
|
||
|
|
! Computation of the viscosity
|
||
|
|
!
|
||
|
|
IF(DMN == '3D') THEN !
|
||
|
|
CALL VISCOSITY_3D(RS,T,ZION,KD_SI,X,ZERO,NA,MA,RA, & !
|
||
|
|
DEBYE_T,EP_C,LR,VI_TYPE,ETA) !
|
||
|
|
ELSE IF(DMN == '2D') THEN !
|
||
|
|
CALL VISCOSITY_2D(T,S_L,VI_TYPE,ETA) !
|
||
|
|
ELSE IF(DMN == '1D') THEN !
|
||
|
|
ETA = ZERO ! not yet implemented
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
! Computing the relaxation time
|
||
|
|
!
|
||
|
|
CALL RELAXATION_TIME(X,TAU) !
|
||
|
|
!
|
||
|
|
IF(I_RL == 1) THEN !
|
||
|
|
WRITE(IO_RL,*) Y,TAU !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_RLX
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_SCR(X)
|
||
|
|
!
|
||
|
|
! This subroutine computes the screening wave number
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Input parameters:
|
||
|
|
!
|
||
|
|
! * X : dimensionless factor --> X = q / (2 * k_F)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * KS : screening wave number
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 13 Oct 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE MATERIAL_PROP, ONLY : DMN,RS
|
||
|
|
USE EXT_FIELDS, ONLY : T
|
||
|
|
!
|
||
|
|
USE CONSTANTS_P1, ONLY : BOHR
|
||
|
|
USE SCREENING_TYPE
|
||
|
|
USE SCREENING_VEC
|
||
|
|
USE SCREENING_VEC2
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_KS
|
||
|
|
USE PRINT_FILES, ONLY : IO_KS
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: X
|
||
|
|
REAL (WP) :: Y
|
||
|
|
REAL (WP) :: KS_SI,KS
|
||
|
|
!
|
||
|
|
Y = X + X ! q / k_F
|
||
|
|
!
|
||
|
|
IF(SC_TYPE == 'DH' .OR. SC_TYPE == 'TF') THEN !
|
||
|
|
CALL SCREENING_VECTOR(SC_TYPE,DMN,X,RS,T,KS_SI) !
|
||
|
|
ELSE !
|
||
|
|
CALL SCREENING_VECTOR2(SC_TYPE,DMN,X,RS,T,KS_SI) !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
KS = KS_SI * BOHR ! KS in units of a_0
|
||
|
|
!
|
||
|
|
IF(I_KS == 1) THEN !
|
||
|
|
WRITE(IO_KS,*) Y,KS !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_SCR
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_QVF(X)
|
||
|
|
!
|
||
|
|
! This subroutine computes the omega = q * v_F (U = 1) equation, as well
|
||
|
|
! as U + X = 1 and U - X = 1
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Input parameters:
|
||
|
|
!
|
||
|
|
! * X : dimensionless factor --> X = q / (2 * k_F)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * OM : omega
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! hbar omega
|
||
|
|
! Note: We use here the fact that V = ------------ = 4 * U * X
|
||
|
|
! E_F
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Therefore U = 1 <==> V = 4 * X
|
||
|
|
! U + X = 1 <==> V = 4 * (1 - X) * X
|
||
|
|
! U - X = 1 <==> V = 4 * (1 + X) * X
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 25 Nox 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE REAL_NUMBERS, ONLY : ONE,FOUR
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_OQ
|
||
|
|
USE PRINT_FILES, ONLY : IO_OQ
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: X
|
||
|
|
REAL (WP) :: Y,OM0,OM1,OM2
|
||
|
|
!
|
||
|
|
Y = X + X ! q / k_F
|
||
|
|
!
|
||
|
|
OM0 = FOUR * X !
|
||
|
|
OM1 = FOUR * (ONE - X) * X !
|
||
|
|
OM2 = FOUR * (ONE + X) * X !
|
||
|
|
!
|
||
|
|
IF(I_OQ == 1) THEN !
|
||
|
|
WRITE(IO_OQ,*) Y,OM0,OM1,OM2 !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_QVF
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_MEP(X)
|
||
|
|
!
|
||
|
|
! This subroutine computes the moments of the
|
||
|
|
! imaginary part of the dielectric function
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Input parameters:
|
||
|
|
!
|
||
|
|
! * X : dimensionless factor --> X = q / (2 * k_F)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * MEP : moment of S(q,omega) function in reduced units
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 21 Oct 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE MOMENTS
|
||
|
|
USE MOMENTS_CALC
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_ME
|
||
|
|
USE PRINT_FILES, ONLY : IO_ME
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: X
|
||
|
|
REAL (WP) :: Y,MEP
|
||
|
|
!
|
||
|
|
Y = X + X ! q/k_F
|
||
|
|
!
|
||
|
|
CALL MOMENTS_EPSILON(X,N_M,MEP) !
|
||
|
|
!
|
||
|
|
IF(I_ME == 1) THEN ! writing to
|
||
|
|
WRITE(IO_ME,*) Y,MEP ! file
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_MEP
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_MSF(X)
|
||
|
|
!
|
||
|
|
! This subroutine computes the moments of the
|
||
|
|
! dynamical structure factor
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Input parameters:
|
||
|
|
!
|
||
|
|
! * X : dimensionless factor --> X = q / (2 * k_F)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * MSF : moment of S(q,omega) function in reduced units
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 20 Oct 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE MOMENTS
|
||
|
|
USE MOMENTS_CALC
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_MS
|
||
|
|
USE PRINT_FILES, ONLY : IO_MS
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: X
|
||
|
|
REAL (WP) :: Y,MSF
|
||
|
|
!
|
||
|
|
Y = X + X ! q/k_F
|
||
|
|
!
|
||
|
|
CALL MOMENTS_STRUCT_FACTOR(X,N_M,MSF) !
|
||
|
|
!
|
||
|
|
IF(I_MS == 1) THEN ! writing to
|
||
|
|
WRITE(IO_MS,*) Y,MSF ! file
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_MSF
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_MLO(X)
|
||
|
|
!
|
||
|
|
! This subroutine computes the moments of the loss function
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Input parameters:
|
||
|
|
!
|
||
|
|
! * X : dimensionless factor --> X = q / (2 * k_F)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * MLO : moment of loss function in reduced units
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 20 Oct 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE MOMENTS
|
||
|
|
USE MOMENTS_CALC
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_ML
|
||
|
|
USE PRINT_FILES, ONLY : IO_ML
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: X
|
||
|
|
REAL (WP) :: Y,MLO
|
||
|
|
!
|
||
|
|
Y = X + X ! q/k_F
|
||
|
|
!
|
||
|
|
CALL MOMENTS_LOSS_FUNCTION(X,N_M,MLO) !
|
||
|
|
!
|
||
|
|
IF(I_ML == 1) THEN ! writing to
|
||
|
|
WRITE(IO_ML,*) Y,MLO ! file
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_MLO
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_RE0(X)
|
||
|
|
!
|
||
|
|
! This subroutine computes the zeros of the real part of
|
||
|
|
! the dielectric function: Re[ epsilon(q,omega) ]
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Input parameters:
|
||
|
|
!
|
||
|
|
! * X : dimensionless factor --> X = q / (2 * k_F)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Intermediate parameters:
|
||
|
|
!
|
||
|
|
! * RS : Wigner-Seitz radius (in units of a_0)
|
||
|
|
! * T : temperature in SI
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * Y : q / k_F
|
||
|
|
! * RE0 : zeros of real part dielectric function
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Note: By setting a non-zero value to variable SHF, the subroutine
|
||
|
|
! will solve Re[ epsilon(q,omega) ] = - SHF
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 30 Apr 2021
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE MATERIAL_PROP, ONLY : DMN,RS
|
||
|
|
USE EXT_FIELDS, ONLY : T,H
|
||
|
|
USE DF_VALUES, ONLY : ESTDY,EPS_T,D_FUNC
|
||
|
|
!
|
||
|
|
USE DIMENSION_CODE, ONLY : NSIZE
|
||
|
|
USE REAL_NUMBERS, ONLY : ZERO,FOURTH,SMALL,INF
|
||
|
|
!
|
||
|
|
USE E_GRID
|
||
|
|
!
|
||
|
|
USE SCREENING_TYPE
|
||
|
|
USE SCREENING_VEC
|
||
|
|
!
|
||
|
|
USE DFUNC_STATIC
|
||
|
|
USE DFUNCT_STAN_DYNAMIC
|
||
|
|
USE DFUNCL_STAN_DYNAMIC
|
||
|
|
USE DFUNCL_MAGN_DYNAMIC
|
||
|
|
!
|
||
|
|
USE FIND_ZERO
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_ZE
|
||
|
|
USE PRINT_FILES, ONLY : IO_ZE
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
CHARACTER (LEN = 4) :: D_FUNCL,D_FUNCT
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: X
|
||
|
|
REAL (WP) :: EN
|
||
|
|
REAL (WP) :: Y,Z
|
||
|
|
REAL (WP) :: REPS,IEPS
|
||
|
|
REAL (WP) :: E(NSIZE)
|
||
|
|
REAL (WP) :: EPSR(NSIZE)
|
||
|
|
REAL (WP) :: ZEROF
|
||
|
|
!
|
||
|
|
REAL (WP) :: A,NU,KS_SI
|
||
|
|
REAL (WP) :: LFT,TAU,DR,D,ETA
|
||
|
|
!
|
||
|
|
REAL (WP), PARAMETER :: SHF = 0.0E0_WP
|
||
|
|
!
|
||
|
|
REAL (WP) :: FLOAT
|
||
|
|
!
|
||
|
|
INTEGER :: IE
|
||
|
|
!
|
||
|
|
A = ZERO ! temporary
|
||
|
|
NU = ZERO !
|
||
|
|
!
|
||
|
|
Y = X + X ! q / k_F
|
||
|
|
!
|
||
|
|
! Computing the screening wave vector
|
||
|
|
!
|
||
|
|
CALL SCREENING_VECTOR(SC_TYPE,DMN,X,RS,T,KS_SI)
|
||
|
|
!
|
||
|
|
! Computing the dynamic dielectric function
|
||
|
|
!
|
||
|
|
DO IE = 1, N_E ! energy loop
|
||
|
|
!
|
||
|
|
EN = E_MIN + FLOAT(IE - 1) * E_STEP ! EN = hbar omega / E_F
|
||
|
|
!
|
||
|
|
Z = FOURTH * EN / (X * X) ! Z = omega / omega_q
|
||
|
|
!
|
||
|
|
IF(EPS_T == 'LONG') THEN ! longitudinal eps
|
||
|
|
!
|
||
|
|
D_FUNCL = D_FUNC !
|
||
|
|
IF(H < SMALL) THEN !
|
||
|
|
CALL DFUNCL_DYNAMIC(X,Z,RS,T,D_FUNCL,IE,REPS,IEPS) ! no magnetic field
|
||
|
|
ELSE !
|
||
|
|
CALL DFUNCL_DYNAMIC_M(X,Z,KS_SI,A,NU,D_FUNCL,REPS,IEPS) ! magnetic field
|
||
|
|
END IF !
|
||
|
|
ELSE ! transverse eps
|
||
|
|
D_FUNCT = D_FUNC !
|
||
|
|
IF(H < SMALL) THEN !
|
||
|
|
CALL DFUNCT_DYNAMIC(X,Z,D_FUNCT,REPS,IEPS) ! no magnetic field
|
||
|
|
ELSE !
|
||
|
|
CONTINUE ! magnetic field
|
||
|
|
END IF !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
EPSR(IE) = REPS + SHF !
|
||
|
|
E(IE) = EN !
|
||
|
|
!
|
||
|
|
END DO ! end of energy loop
|
||
|
|
!
|
||
|
|
! Computing the zeros of EPSR
|
||
|
|
!
|
||
|
|
IF(I_ZE == 1) THEN !
|
||
|
|
CALL PRINT_ZERO_FUNC(Y,E,EPSR,N_E) !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_RE0
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_MFP
|
||
|
|
!
|
||
|
|
! This subroutine computes the inelastic mean free path
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 19 Oct 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE REAL_NUMBERS, ONLY : SMALL
|
||
|
|
USE FERMI_SI, ONLY : EF_SI
|
||
|
|
USE ENE_CHANGE, ONLY : EV,ANG
|
||
|
|
!
|
||
|
|
USE ELECTRON_MEAN_FREE_PATH
|
||
|
|
USE IMFP
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_MF
|
||
|
|
USE PRINT_FILES, ONLY : IO_MF
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
INTEGER :: IE
|
||
|
|
INTEGER, PARAMETER :: NE_MAX = 1480 ! max. number of energy points
|
||
|
|
!
|
||
|
|
REAL (WP) :: LAMBDA
|
||
|
|
REAL (WP) :: E_STEP
|
||
|
|
REAL (WP) :: E,EK
|
||
|
|
REAL (WP) :: E_MIN,E_MAX
|
||
|
|
!
|
||
|
|
REAL (WP) :: FLOAT
|
||
|
|
!
|
||
|
|
E_MIN = EK_INI ! lower value in eV
|
||
|
|
E_MAX = EK_FIN ! upper value in eV
|
||
|
|
!
|
||
|
|
E_STEP = (E_MAX - E_MIN) / FLOAT(NE_MAX - 1) ! e-step in eV
|
||
|
|
!
|
||
|
|
DO IE = 1, NE_MAX !
|
||
|
|
!
|
||
|
|
E = E_MIN + FLOAT(IE - 1) * E_STEP ! E in eV
|
||
|
|
EK = E * EV ! E in SI
|
||
|
|
!
|
||
|
|
CALL MEAN_FREE_PATH(EK,LAMBDA) ! IMFP in SI
|
||
|
|
LAMBDA = LAMBDA / ANG ! IMFP in Angström
|
||
|
|
!
|
||
|
|
IF(I_MF == 1) THEN !
|
||
|
|
WRITE(IO_MF,*) E,LAMBDA !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END DO ! end of energy loop
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_MFP
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_NEV(X)
|
||
|
|
!
|
||
|
|
! This subroutine computes the Fourier space Nevalinna/memory function
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 28 Jan 2021
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE MATERIAL_PROP, ONLY : RS
|
||
|
|
USE EXT_FIELDS, ONLY : T
|
||
|
|
!
|
||
|
|
USE E_GRID
|
||
|
|
!
|
||
|
|
USE REAL_NUMBERS, ONLY : FOURTH
|
||
|
|
!
|
||
|
|
USE RELAXATION_TIME_STATIC
|
||
|
|
USE MEMORY_FUNCTIONS_F
|
||
|
|
USE NEVALINNA_FUNCTIONS
|
||
|
|
!
|
||
|
|
USE DF_VALUES, ONLY : D_FUNC,NEV_TYPE,MEM_TYPE,ALPHA,BETA
|
||
|
|
USE DAMPING_SI
|
||
|
|
USE DAMPING_VALUES, ONLY : PCT
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_NV
|
||
|
|
USE PRINT_FILES, ONLY : IO_NV
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
INTEGER :: IE,I_F
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: X
|
||
|
|
!
|
||
|
|
REAL (WP) :: Y,Z
|
||
|
|
REAL (WP) :: E
|
||
|
|
REAL (WP) :: NEVR,NEVI
|
||
|
|
!
|
||
|
|
REAL (WP) :: FLOAT,REAL,AIMAG
|
||
|
|
!
|
||
|
|
COMPLEX (WP) :: FUNC
|
||
|
|
!
|
||
|
|
Y = X + X ! q / k_F
|
||
|
|
!
|
||
|
|
! Check for Nevanlinna or memory function --> switch I_F
|
||
|
|
!
|
||
|
|
IF(D_FUNC(1:3) == 'NEV') THEN !
|
||
|
|
I_F = 1 !
|
||
|
|
ELSE IF(D_FUNC(1:3) == 'MEM') THEN !
|
||
|
|
I_F = 2 !
|
||
|
|
ELSE !
|
||
|
|
I_F = 0 !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
DO IE = 1, N_E ! energy loop
|
||
|
|
!
|
||
|
|
E = E_MIN + FLOAT(IE - 1) * E_STEP ! E = hbar omega / E_F
|
||
|
|
!
|
||
|
|
Z = FOURTH * E / (X * X) ! Z = omega / omega_q
|
||
|
|
!
|
||
|
|
IF(I_F == 1) THEN !
|
||
|
|
FUNC = NEVAN2(X,Z,RS,T,TAU,NEV_TYPE) !
|
||
|
|
ELSE IF(I_F == 2) THEN !
|
||
|
|
FUNC = MEMORY_F(E,TAU,TAU2,PCT,ALPHA,BETA,MEM_TYPE) !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
NEVR = REAL(FUNC,KIND=WP) !
|
||
|
|
NEVI = AIMAG(FUNC) !
|
||
|
|
!
|
||
|
|
IF(I_NV == 1) THEN !
|
||
|
|
WRITE(IO_NV,*) Y,E,NEVR,NEVI !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END DO ! end of energy loop
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_NEV
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE CALC_MEM
|
||
|
|
!
|
||
|
|
! This subroutine computes the time-domain memory function
|
||
|
|
! as a function of t / tau
|
||
|
|
!
|
||
|
|
! When tau is q-dependent, the only vamue considered is the first one
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 28 Jan 2021
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE REAL_NUMBERS, ONLY : ZERO,TEN,HALF
|
||
|
|
!
|
||
|
|
USE Q_GRID, ONLY : Q_MIN
|
||
|
|
!
|
||
|
|
USE DF_VALUES, ONLY : ALPHA,BETA,MEM_TYPE
|
||
|
|
USE DAMPING_SI
|
||
|
|
USE DAMPING_VALUES, ONLY : PCT
|
||
|
|
!
|
||
|
|
USE RELAXATION_TIME_STATIC
|
||
|
|
USE MEMORY_FUNCTIONS_T
|
||
|
|
!
|
||
|
|
USE OUT_VALUES_3, ONLY : I_MT
|
||
|
|
USE PRINT_FILES, ONLY : IO_MT
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
INTEGER :: IT
|
||
|
|
INTEGER, PARAMETER :: NT_MAX = 200 ! max. number of time points
|
||
|
|
!
|
||
|
|
REAL (WP) :: MEMR
|
||
|
|
REAL (WP) :: T ! t / tau
|
||
|
|
REAL (WP) :: T1 ! t
|
||
|
|
REAL (WP) :: T_MIN,T_MAX,T_STEP
|
||
|
|
REAL (WP) :: X
|
||
|
|
!
|
||
|
|
REAL (WP) :: FLOAT
|
||
|
|
!
|
||
|
|
T_MIN = ZERO ! lower time value
|
||
|
|
T_MAX = TEN ! upper time value
|
||
|
|
X = Q_MIN * HALF ! initial value of q / 2 k_F
|
||
|
|
!
|
||
|
|
T_STEP = (T_MAX - T_MIN) / FLOAT(NT_MAX - 1) ! t-step in units of tau
|
||
|
|
!
|
||
|
|
DO IT = 1, NT_MAX !
|
||
|
|
!
|
||
|
|
T = T_MIN + FLOAT(IT - 1) * T_STEP ! t in units of tau
|
||
|
|
!
|
||
|
|
T1 = T * TAU ! time is SI
|
||
|
|
!
|
||
|
|
MEMR = MEMORY_T(T1,TAU,TAU2,PCT,ALPHA,BETA,MEM_TYPE) * & !
|
||
|
|
TAU * TAU ! in units of 1 / tau^2
|
||
|
|
!
|
||
|
|
IF(I_MT == 1) THEN !
|
||
|
|
WRITE(IO_MT,*) T,MEMR !
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
END DO ! end of time loop
|
||
|
|
!
|
||
|
|
END SUBROUTINE CALC_MEM
|
||
|
|
!
|
||
|
|
END MODULE CALCULATORS_3
|