367 lines
11 KiB
Fortran
367 lines
11 KiB
Fortran
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!=======================================================================
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MODULE MOMENTS_CALC
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!
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USE ACCURACY_REAL
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!
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! This module provides the functions/subroutines to compute
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! the moments of different functions
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!
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!
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!
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CONTAINS
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!=======================================================================
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!
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SUBROUTINE MOMENTS_LOSS_FUNCTION(X,N,MLO)
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!
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! This module computes the moments of the loss function
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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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! * N : moment order
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!
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!
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! Output variables :
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!
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! * MLO : moment
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!
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!
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!
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! The moments are defined by
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! _ _
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! / + INF | |
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! | n | - 1 |
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! < omega^n> = 2 | omega Im | ------------- | d omega
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! | | eps(q,omega) |
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! / 0 |_ _|
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!
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!
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!
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! Author : D. Sébilleau
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! Last modified : 30 Apr 2021
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!
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!
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USE DIMENSION_CODE, ONLY : NSIZE
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USE MATERIAL_PROP, ONLY : RS
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USE EXT_FIELDS, ONLY : T
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!
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USE REAL_NUMBERS, ONLY : ZERO,TWO,FOURTH,TTINY,INF
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USE FERMI_SI, ONLY : KF_SI
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!
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USE E_GRID
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!
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USE DF_VALUES, ONLY : D_FUNC
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!
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USE INTEGRATION, ONLY : INTEGR_L
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USE DFUNCL_STAN_DYNAMIC
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!
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IMPLICIT NONE
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!
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INTEGER,INTENT(IN) :: N
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INTEGER :: IE
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INTEGER :: ID
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INTEGER :: I_ZE
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP), INTENT(OUT):: MLO
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REAL (WP) :: E,V,Z
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REAL (WP) :: EPSR,EPSI
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REAL (WP) :: ELF(NSIZE)
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REAL (WP) :: A
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!
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IF(MOD(N,2) == 0 .AND. N /= 0) THEN !
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MLO = ZERO !
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RETURN !
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END IF !
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!
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I_ZE = 0 ! switch for integrand = 0
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!
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! Constructing the e-grid
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!
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DO IE = 1, N_E ! E_F
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!
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E = E_MIN + FLOAT(IE - 1) * E_STEP ! in units of
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V = E ! hbar * omega / E_F
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Z = FOURTH * V / (X * X) ! omega / omega_q
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!
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! Computing the dielectric function epsilon(q,E)
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!
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CALL DFUNCL_DYNAMIC(X,Z,RS,T,D_FUNC,IE,EPSR,EPSI) !
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!
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! Computing the loss function ELF = Im [ -1 / epsilon(q,E) ]
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!
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ELF(IE) = E**N * EPSI / ( (EPSR * EPSR + EPSI * EPSI) ) ! integrand function
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!
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IF(ABS(ELF(IE)) >= TTINY) I_ZE = IE !
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!
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END DO !
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!
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IF(I_ZE > 0) THEN !
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!
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! Performing the e-integration with respect to E
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!
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ID = 1 !
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CALL INTEGR_L(ELF,E_STEP,NSIZE,N_E,A,ID) !
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!
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MLO = TWO * A !
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!
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ELSE ! IN always = 0
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!
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MLO = ZERO !
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!
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END IF !
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!
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END SUBROUTINE MOMENTS_LOSS_FUNCTION
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!
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!=======================================================================
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!
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SUBROUTINE MOMENTS_STRUCT_FACTOR(X,N,MSF)
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!
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! This module computes the moments of the dynamical structure factor
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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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! * N : moment order
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!
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!
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! Output variables :
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!
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! * MLO : moment
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!
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!
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!
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! The moments are defined by
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!
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! / + INF
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! | n
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! < omega^n> = 2 | omega S(q,omega) d omega
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! |
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! / 0
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!
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!
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! Note: in the calculation of the moments of the loss function, q and omega
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! are respectively in units of k_F and E_F
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!
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! --> we write the coefficient COEF in units of 1/ E_F
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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 Oct 2020
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!
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!
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USE DIMENSION_CODE, ONLY : NSIZE
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USE MATERIAL_PROP, ONLY : RS
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USE EXT_FIELDS, ONLY : T
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!
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USE REAL_NUMBERS, ONLY : ZERO,TWO,HALF,FOURTH,TTINY,INF
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USE CONSTANTS_P1, ONLY : H_BAR,M_E
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USE FERMI_SI, ONLY : EF_SI,KF_SI
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USE PI_ETC, ONLY : PI_INV
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!
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USE E_GRID
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!
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USE PLASMON_ENE_SI
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USE SF_VALUES
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USE STRUCTURE_FACTOR_DYNAMIC
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USE MOMENTS, ONLY : M_TYPE
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USE INTEGRATION, ONLY : INTEGR_L
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!
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IMPLICIT NONE
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!
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INTEGER,INTENT(IN) :: N
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INTEGER :: IE
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INTEGER :: ID
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INTEGER :: I_ZE
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INTEGER :: LOGF
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP), INTENT(OUT):: MSF
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!
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REAL (WP) :: Q_SI,EQ_SI
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REAL (WP) :: COEF,MLO
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REAL (WP) :: E,V,Z
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REAL (WP) :: SQM(NSIZE)
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REAL (WP) :: SQO,A
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!
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LOGF = 6 ! log file unit
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!
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IF(M_TYPE == 'EPS') THEN
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!
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Q_SI = TWO * KF_SI * X ! q in SI
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!
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EQ_SI = HALF * H_BAR * H_BAR * Q_SI * Q_SI / M_E ! h_bar omega_q in SI
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COEF = TWO * PI_INV * (EQ_SI / ENE_P_SI) * EF_SI / ENE_P_SI! coefficient in units of 1/E_F
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!
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! Computing the moments of the loss function
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!
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CALL MOMENTS_LOSS_FUNCTION(X,N,MLO) !
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!
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MSF = COEF * MLO !
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!
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ELSE IF(M_TYPE == 'SQO') THEN !
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!
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IF(SSTDY == ' STATIC') THEN ! pathological case
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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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! Constructing the e-grid
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!
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DO IE = 1, N_E !
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!
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E = E_MIN + FLOAT(IE - 1) * E_STEP ! in units of
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V = E ! hbar * omega / E_F
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Z = FOURTH * V / (X * X) ! omega / omega_q
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!
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! Computing the dynamical structure factor
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!
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CALL STFACT_DYNAMIC(X,Z,RS,T,SQO_TYPE,SQ_TYPE,SQO) !
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!
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SQM(IE) = E**N * SQO ! integrand function
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!
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IF(ABS(SQM(IE)) >= TTINY) I_ZE = IE !
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!
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END DO !
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!
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IF(I_ZE > 0) THEN !
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!
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! Performing the e-integration with respect to E
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!
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ID = 1 !
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CALL INTEGR_L(SQM,E_STEP,NSIZE,N_E,A,ID) !
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!
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MSF = TWO * A !
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!
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ELSE ! IN always = 0
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!
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MSF = ZERO !
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!
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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,'<<<<< SSTDY PARAMETER WRONG >>>>>',/ &
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10X,'<<<<< CHANGE IN INPUT FILE >>>>>',//)
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!
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END SUBROUTINE MOMENTS_STRUCT_FACTOR
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!
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!=======================================================================
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!
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SUBROUTINE MOMENTS_EPSILON(X,N,MEP)
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!
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! This module computes the moments of the dynamical structure factor
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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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! * N : moment order
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!
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!
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! Output variables :
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!
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! * MEP : moment
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!
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!
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!
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! The moments are defined by
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!
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! / + INF _ _
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! | n | |
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! < omega^n> = 2 | omega Im | eps(q,omega) | d omega
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! | |_ _|
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! / 0
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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 : 30 Apr 2021
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!
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!
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!
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USE DIMENSION_CODE, ONLY : NSIZE
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USE MATERIAL_PROP, ONLY : RS
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USE EXT_FIELDS, ONLY : T
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!
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USE REAL_NUMBERS, ONLY : ZERO,TWO,FOURTH,TTINY,INF
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USE FERMI_SI, ONLY : KF_SI
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!
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USE E_GRID
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!
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USE DF_VALUES, ONLY : D_FUNC
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!
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USE INTEGRATION, ONLY : INTEGR_L
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USE INTEGRATION4
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USE DFUNCL_STAN_DYNAMIC
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!
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IMPLICIT NONE
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!
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INTEGER,INTENT(IN) :: N
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INTEGER :: IE
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INTEGER :: ID
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INTEGER :: I_ZE
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP), INTENT(OUT):: MEP
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REAL (WP) :: E,V,Z
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REAL (WP) :: EPSR,EPSI
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REAL (WP) :: ELF(NSIZE)
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REAL (WP) :: A
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!
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IF(MOD(N,2) == 0 .AND. N /= 0) THEN !
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MEP = ZERO !
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RETURN !
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END IF !
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!
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I_ZE = 0 ! switch for integrand = 0
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!
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! Constructing the e-grid
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!
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DO IE = 1, N_E ! E_F
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!
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E = E_MIN + FLOAT(IE - 1) * E_STEP ! in units of
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V = E ! hbar * omega / E_F
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Z = FOURTH * V / (X * X) ! omega / omega_q
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!
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! Computing the dielectric function epsilon(q,E)
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!
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CALL DFUNCL_DYNAMIC(X,Z,RS,T,D_FUNC,IE,EPSR,EPSI) !
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!
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! Computing the loss function ELF = Im [ -1 / epsilon(q,E) ]
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!
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ELF(IE) = E**N * EPSI ! integrand function
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!
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IF(ABS(ELF(IE)) >= TTINY) I_ZE = IE !
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!
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END DO !
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!
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IF(I_ZE > 0) THEN !
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!
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! Performing the e-integration with respect to E
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!
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ID = 1 !
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CALL INTEGR_L(ELF,E_STEP,NSIZE,N_E,A,ID) !
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!
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MEP = TWO * A !
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!
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ELSE ! IN always = 0
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!
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MEP = ZERO !
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!
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END IF !
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!
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END SUBROUTINE MOMENTS_EPSILON
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!
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END MODULE MOMENTS_CALC
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