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Influence Functional Coefficients

The influence functional coefficients are discretizations of the bath correlation function required for simulations using the QuAPI influence functionals or QCPI with harmonic backreaction. QuantumDynamics provides facilities for generating these coefficients and storing them in a way that utilizes the limited time-translational symmetry that they demonstrate. These coefficients have been listed in many papers, the first being QuAPI1.

API

QuantumDynamics.EtaCoefficients.EtaCoeffs — Type

EtaCoefficients holds the various discretized η-coefficients required for a QuAPI-based simulation. These are the minimum number of coefficients required, stored using time-translational symmetry wherever possible.

The values are stored as follows:

  • η00: The self-interaction of the two terminal time points.
  • ηmm: The self-interaction of all intermediate points.
  • η0m: The interaction between a terminal and an intermediate point at different time separations.
  • ηmn: The interaction between two intermediate points at different time separations.
  • η0e: The interaction between the two terminal points at different time separations.
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QuantumDynamics.EtaCoefficients.calculate_η — Function
calculate_η(specdens::SpectralDensities.ContinuousSpectralDensity; β::Real, dt::Real, kmax::Int, imaginary_only=false)

Calculates the η-coefficients from an analytic spectral density and returns them as an object of the structure EtaCoeffs. The integrations involved are done using trapezoidal integration

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calculate_η(specdens::SpectralDensity.DiscreteOscillators; β::Real, dt::Real, kmax::Int, classical::Bool=false, imaginary_only=false)

Calculates the η-coefficients from a discretized set of harmonic modes and returns them as an object of the structure EtaCoeffs. The integrations involved are converted to sums over frequency modes.

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QuantumDynamics.EtaCoefficients.ZetaCoeffs — Type

ZetaCoefficients holds the various discretized ζ-coefficients required for a QCPI-HBR-based simulation. These are the minimum number of coefficients required, stored using time-translational symmetry wherever possible.

The values are stored as follows:

  • ζ00: The self-interaction of the two terminal time points.
  • ζmm: The self-interaction of all intermediate points.
  • ζ0m: The interaction between a terminal and an intermediate point at different time separations.
  • ζmn: The interaction between two intermediate points at different time separations.
  • ζ0e: The interaction between the two terminal points at different time separations.
source
QuantumDynamics.EtaCoefficients.calculate_ζ — Function
calculate_ζ(specdens::SpectralDensities.ContinuousSpectralDensity; dt::Real, kmax::Int)

Calculates the ζ-coefficients from an analytic spectral density and returns them as an object of the structure EtaCoeffs. The integrations involved are done using trapezoidal integration

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calculate_ζ(specdens::SpectralDensity.DiscreteOscillators; dt::Real, kmax::Int)

Calculates the ζ-coefficients from a discretized set of harmonic modes and returns them as an object of the structure EtaCoeffs. The integrations involved are converted to sums over frequency modes.

source