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Quantum Correlation Functions using Path Integrals

API

QuantumDynamics.ComplexTNPI.A_of_t — Function
A_of_t(; Hamiltonian::AbstractMatrix{ComplexF64}, β::Real, t::Real, N::Int, Jw::AbstractVector{<:SpectralDensities.SpectralDensity}, svec::AbstractMatrix{<:Real}, A, B, extraargs::Utilities.TensorNetworkArgs=Utilities.TensorNetworkArgs())

Calculates $Tr_{env}(U(t) exp(-β H/2) A exp(-β H/2) U^{-1}(t))$ for a system interacting with an environment at a time-point t using the tensor network path integral method. This can be used for thermodynamics or for calculating correlation functions.

Arguments:

  • Hamiltonian: system Hamiltonian
  • Jw: array of spectral densities
  • svec: diagonal elements of system operators through which the corresponding baths interact. QuAPI currently only works for baths with diagonal coupling to the system.
  • β: inverse temperature
  • t: time at which the function is evaluated
  • N: number of path integral discretizations
  • A: system operator to be evaluated
  • extraargs: extra arguments for the tensor network algorithm. Contains the cutoff threshold for SVD filtration, the maximum bond dimension, maxdim, and the algorithm of applying an MPO to an MPS.
source
QuantumDynamics.ComplexTNPI.complex_correlation_function — Function
complex_correlation_function(; Hamiltonian::AbstractMatrix{ComplexF64}, β::Real, tfinal::Real, dt::Real, N::Int, Jw::AbstractVector{<:SpectralDensities.SpectralDensity}, svec::AbstractMatrix{<:Real}, A, B, Z::Real, extraargs::Utilities.TensorNetworkArgs=Utilities.TensorNetworkArgs(), verbose::Bool=false, output::Union{Nothing,HDF5.Group}=nothing, exec=ThreadedEx())

Calculates the $<A(0) B(t_c)> / Z$ correlation function for a system interacting with an environment upto a maximum time of tfinal with a time-step of dt using the tensor network path integral method.

Arguments:

  • Hamiltonian: system Hamiltonian
  • Jw: array of spectral densities
  • svec: diagonal elements of system operators through which the corresponding baths interact. QuAPI currently only works for baths with diagonal coupling to the system.
  • β: inverse temperature
  • tfinal: maximum time till which the correlation function is evaluated
  • dt: time-step for evaluating correlation function
  • N: number of path integral discretizations
  • A: system operator evaluated at time zero
  • B: array of system operators evaluated at time t
  • Z: partition function for normalization
  • extraargs: extra arguments for the tensor network algorithm. Contains the cutoff threshold for SVD filtration, the maximum bond dimension, maxdim, and the algorithm of applying an MPO to an MPS.
  • verbose: verbosity
  • output: output HDF5 file for storage of results
  • exec: FLoops.jl execution policy
source
QuantumDynamics.ComplexQuAPI.A_of_t — Function
A_of_t(; Hamiltonian::AbstractMatrix{ComplexF64}, β::Float64, t::Float64, N::Int64, Jw::AbstractVector{<:SpectralDensities.SpectralDensity}, svec::AbstractMatrix{Float64}, A, extraargs::QuAPI.QuAPIArgs=QuAPI.QuAPIArgs(), exec=FLoops.ThreadedEx())

Calculates $Tr_{env}(U(t) exp(-β H/2) A exp(-β H/2) U^{-1}(t))$ for a system interacting with an environment at a time-point t using the tensor network path integral method. This can be used for thermodynamics or for calculating correlation functions.

Arguments:

  • Hamiltonian: system Hamiltonian
  • Jw: array of spectral densities
  • svec: diagonal elements of system operators through which the corresponding baths interact. QuAPI currently only works for baths with diagonal coupling to the system.
  • β: inverse temperature
  • t: time at which the function is evaluated
  • N: number of path integral discretizations
  • A: system operator to be evaluated
  • extraargs: extra arguments for the tensor network algorithm. Contains the cutoff threshold for SVD filtration, the maximum bond dimension, maxdim, and the algorithm of applying an MPO to an MPS.
  • exec: FLoops.jl execution policy
source
QuantumDynamics.ComplexQuAPI.complex_correlation_function — Function
complex_correlation_function(; Hamiltonian::AbstractMatrix{ComplexF64}, β::Real, tfinal::Real, dt::Real, N::Int, Jw::AbstractVector{<:SpectralDensities.SpectralDensity}, svec::AbstractMatrix{<:Real}, A, B, Z::Real, extraargs::QuAPI.QuAPIArgs=QuAPI.QuAPIArgs(), verbose::Bool=false, output::Union{Nothing,HDF5.Group}=nothing, exec=ThreadedEx())

Calculates the $<B(t_c) A(0)> / Z$ correlation function for a system interacting with an environment upto a maximum time of tfinal with a time-step of dt using the tensor network path integral method.

Arguments:

  • Hamiltonian: system Hamiltonian
  • Jw: array of spectral densities
  • svec: diagonal elements of system operators through which the corresponding baths interact. QuAPI currently only works for baths with diagonal coupling to the system.
  • β: inverse temperature
  • tfinal: maximum time till which the correlation function is evaluated
  • dt: time-step for evaluating correlation function
  • N: number of path integral discretizations
  • A: system operator evaluated at time zero
  • B: system operator evaluated at time t
  • Z: partition function for normalization
  • extraargs: extra arguments for the tensor network algorithm. Contains the cutoff threshold for SVD filtration, the maximum bond dimension, maxdim, and the algorithm of applying an MPO to an MPS.
  • verbose: verbosity
  • output: output HDF5 file for storage of results
  • exec: FLoops.jl execution policy
source