120 lines
3.8 KiB
Fortran
120 lines
3.8 KiB
Fortran
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
MODULE LOSS_MOMENTS
|
||
|
|
!
|
||
|
|
USE ACCURACY_REAL
|
||
|
|
!
|
||
|
|
!
|
||
|
|
CONTAINS
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE LOSS_MOMENTS_AN(X,C0,C2,C4)
|
||
|
|
!
|
||
|
|
! This subroutine computes "analytically" the first three moments
|
||
|
|
! of the loss function.
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! References: (1) Yu. V. Arkhipov et al, EPL, 104, 35003 (2013)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Warning: This subroutine makes us of the Arkhipov et al definition
|
||
|
|
! of the loss function
|
||
|
|
!
|
||
|
|
! / + INF _ _
|
||
|
|
! 1 | n-1 | 1 |
|
||
|
|
! C_n = ---- | omega Im | - --------- | d omega
|
||
|
|
! pi | |_ epsilon _|
|
||
|
|
! / - INF
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Input parameters:
|
||
|
|
!
|
||
|
|
! * X : dimensionless factor --> X = q / (2 * k_F)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Outpu parameters:
|
||
|
|
!
|
||
|
|
! * C0 : \
|
||
|
|
! * C2 : > moments of the loss function
|
||
|
|
! * C4 : /
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 23 Nov 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE MATERIAL_PROP, ONLY : DMN,RS
|
||
|
|
USE LF_VALUES, ONLY : IQ_TYPE
|
||
|
|
!
|
||
|
|
USE REAL_NUMBERS, ONLY : ONE,TWO,FOUR,HALF
|
||
|
|
USE CONSTANTS_P1, ONLY : H_BAR,M_E
|
||
|
|
USE FERMI_SI, ONLY : KF_SI,EF_SI
|
||
|
|
USE PLASMON_ENE_SI
|
||
|
|
USE DFUNC_STATIC, ONLY : RPA1_EPS_S_LG
|
||
|
|
USE UTILITIES_1, ONLY : D
|
||
|
|
USE IQ_FUNCTIONS_1
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: X
|
||
|
|
REAL (WP), INTENT(OUT) :: C0,C2,C4
|
||
|
|
!
|
||
|
|
REAL (WP) :: Q_SI
|
||
|
|
REAL (WP) :: OMP,OMQ
|
||
|
|
REAL (WP) :: OMP2,OMQ2
|
||
|
|
REAL (WP) :: EPSR,EPSI
|
||
|
|
REAL (WP) :: DIME,AV_KE,IQ
|
||
|
|
!
|
||
|
|
! Computing the plasmon frequency
|
||
|
|
!
|
||
|
|
OMP = ENE_P_SI / H_BAR ! omega_p
|
||
|
|
!
|
||
|
|
! Computing the plasmon kinetic frequency
|
||
|
|
!
|
||
|
|
Q_SI = TWO * X * KF_SI ! q in SI
|
||
|
|
OMQ = HALF * H_BAR * Q_SI * Q_SI / M_E ! omega_q in SI
|
||
|
|
!
|
||
|
|
OMP2 = OMP * OMP !
|
||
|
|
OMQ2 = OMQ * OMQ !
|
||
|
|
!
|
||
|
|
! Computing the dimensionality
|
||
|
|
!
|
||
|
|
DIME = D(DMN) !
|
||
|
|
!
|
||
|
|
! Computing the static RPA dielectric function
|
||
|
|
!
|
||
|
|
CALL RPA1_EPS_S_LG(X,DMN,EPSR,EPSI) !
|
||
|
|
!
|
||
|
|
! Computing I(q)
|
||
|
|
!
|
||
|
|
IF(DMN == '3D') THEN !
|
||
|
|
CALL IQ_3D(X,RS,IQ_TYPE,IQ) !
|
||
|
|
ELSE IF(DMN == '2D') THEN !
|
||
|
|
CONTINUE ! not implemented yet
|
||
|
|
ELSE IF(DMN == '1D') THEN !
|
||
|
|
CONTINUE ! not implemented yet
|
||
|
|
END IF !
|
||
|
|
!
|
||
|
|
! Computing the average ground state kinetic energy :
|
||
|
|
!
|
||
|
|
! d
|
||
|
|
! <t> = --------- E_F
|
||
|
|
! 0 (d + 2)
|
||
|
|
!
|
||
|
|
AV_KE = DIME * EF_SI / (DIME + TWO) ! <t>_0 in SI
|
||
|
|
!
|
||
|
|
! Getting the moments in SI
|
||
|
|
!
|
||
|
|
C0 = ONE - ONE / EPSR ! \
|
||
|
|
C2 = OMP2 ! |
|
||
|
|
C4 = OMP2 * ( FOUR * AV_KE * OMQ / H_BAR + & ! |> ref. (1) eq. (3)-(4)
|
||
|
|
OMQ2 + OMP2 * (ONE - IQ) & ! |
|
||
|
|
) ! /
|
||
|
|
!
|
||
|
|
END SUBROUTINE LOSS_MOMENTS_AN
|
||
|
|
!
|
||
|
|
END MODULE LOSS_MOMENTS
|