propagator_m Module

This module defines a type 'propagator' which represents a propagator (also known as a Green's function) for a given position and energy. The equilibrium parts (i.e. retarded and advanced) are represented via the Riccati parameters γ, γ~ and their derivatives, while the nonequilibrium part (i.e. Keldysh part) is represented by the traces of the distribution function and its derivatives. These are together sufficient to reconstruct the full 8×8 propagator and its derivatives, and can be used to calculate the associated physical quantities such as the density of states, charge currents, spin currents, and so on.


Uses


Interfaces

public interface propagator

  • private pure function propagator_construct_vacuum() result(this)

    Construct a vacuum propagator, i.e. a propagator which satisfies G=0.

    Arguments

    None

    Return Value type(propagator)

    Constructed object

  • private pure function propagator_construct_riccati(g, gt, dg, dgt) result(this)

    Construct an arbitrary state by explicitly providing Riccati parameters. Unspecified Riccati parameters default to zero due to spin constructors. The distribution function defaults to equilibrium at zero temperature.

    Arguments

    Type IntentOptional Attributes Name
    type(spin), intent(in) :: g

    Riccati parameter γ
    type(spin), intent(in) :: gt

    Riccati parameter γ~
    type(spin), intent(in), optional :: dg

    Riccati parameter ∇γ
    type(spin), intent(in), optional :: dgt

    Riccati parameter ∇γ~

    Return Value type(propagator)

    Constructed object

  • private pure function propagator_construct_bcs(energy, gap) result(this)

    Constructs the state of a a BCS superconductor at a given energy, which may have an imaginary term representing inelastic scattering. The second argument 'gap' is used to provide the superconducting order parameter Δ. The distribution function defaults to equilibrium at zero temperature.

    Arguments

    Type IntentOptional Attributes Name
    complex(kind=wp), intent(in) :: energy

    Quasiparticle energy
    complex(kind=wp), intent(in) :: gap

    Order parameter

    Return Value type(propagator)

    Constructed object


Derived Types

type, public ::  propagator

Components

Type Visibility Attributes Name Initial
type(spin), public :: g

Riccati parameter γ
type(spin), public :: gt

Riccati parameter γ~
type(spin), public :: dg

Riccati parameter ∇γ
type(spin), public :: dgt

Riccati parameter ∇γ~
type(spin), public :: d2g

Riccati parameter ∇²γ
type(spin), public :: d2gt

Riccati parameter ∇²γ~
type(spin), public :: N

Riccati normalization N
type(spin), public :: Nt

Riccati normalization N~
real(kind=wp), public, dimension(0:7) :: h = [1, 0, 0, 0, 0, 0, 0, 0]

Distribution trace H
real(kind=wp), public, dimension(0:7) :: dh = [0, 0, 0, 0, 0, 0, 0, 0]

Distribution trace ∇H
real(kind=wp), public, dimension(0:7) :: d2h = [0, 0, 0, 0, 0, 0, 0, 0]

Distribution trace ∇²H

Constructor

private pure function propagator_construct_vacuum ()

Construct a vacuum propagator, i.e. a propagator which satisfies G=0.
private pure function propagator_construct_riccati (g, gt, dg, dgt)

Construct an arbitrary state by explicitly providing Riccati parameters. Unspecified Riccati parameters default to zero due to spin constructors. The distribution function defaults to equilibrium at zero temperature.
private pure function propagator_construct_bcs (energy, gap)

Constructs the state of a a BCS superconductor at a given energy, which may have an imaginary term representing inelastic scattering. The second argument 'gap' is used to provide the superconducting order parameter Δ. The distribution function defaults to equilibrium at zero temperature.

Type-Bound Procedures

procedure, public :: retarded => propagator_retarded ../../

Retarded propagator Gᴿ
procedure, public :: retarded_gradient => propagator_retarded_gradient ../../

Retarded propagator ∇Gᴿ
procedure, public :: retarded_laplacian => propagator_retarded_laplacian ../../

Retarded propagator ∇²Gᴿ
procedure, public :: advanced => propagator_advanced ../../

Advanced propagator Gᴬ
procedure, public :: advanced_gradient => propagator_advanced_gradient ../../

Advanced propagator ∇Gᴬ
procedure, public :: advanced_laplacian => propagator_advanced_laplacian ../../

Advanced propagator ∇²Gᴬ
procedure, public :: keldysh => propagator_keldysh ../../

Keldysh propagator Gᴷ
procedure, public :: keldysh_gradient => propagator_keldysh_gradient ../../

Keldysh propagator ∇Gᴷ
procedure, public :: distribution => propagator_distribution ../../

Distribution matrix H
procedure, public :: distribution_gradient => propagator_distribution_gradient ../../

Distribution matrix ∇H
procedure, public :: dissipation => propagator_dissipation ../../

Dissipation matrix M
procedure, public :: dissipation_gradient => propagator_dissipation_gradient ../../

Dissipation matrix ∇M
procedure, public :: condensate => propagator_condensate ../../

Condensate matrix Q
procedure, public :: condensate_gradient => propagator_condensate_gradient ../../

Condensate matrix ∇Q
procedure, public :: selfenergy1 => propagator_selfenergy1 ../../

Self-energy matrix R₁
procedure, public :: selfenergy2 => propagator_selfenergy2 ../../

Self-energy matrix R₂
procedure, public :: supercurrent => propagator_supercurrent ../../

Spectral super currents
procedure, public :: lossycurrent => propagator_lossycurrent ../../

Spectral lossy currents
procedure, public :: accumulation => propagator_accumulation ../../

Spectral accumulations
procedure, public :: correlation => propagator_correlation ../../

Spectral correlations
procedure, public :: density => propagator_density ../../

Local density of states
procedure, public :: save => propagator_save ../../

Export Riccati parameters
procedure, public :: load => propagator_load ../../

Import Riccati parameters