SpectralDensities.jl
This package implements commonly used spectral densities for Open Quantum Systems and typical operations on them.
Features
Features of SpectralDensities.jl include:
- Definition of most widely used spectral densities: Ohmic, Sub-Ohmic, Supra-Ohmic, Lorentzian (Underdamped), Debye (Overdamped)
- Flexibility to choose desidred cutoff functions: hard cutoffs, exponential cutoff, gaussian cutoff.
- Calculation of the correlation function of a given spectral density (with specialised methods for the pre-defined types)
- Calculation of reorganisation energy of a given spectral density (with specialised methods for the pre-defined types)
- Calculation of the memory kernel of a given spectral density, both in the time domain, and the imaginary part in the Fourier domain (with specialised methods for some of the pre-defined types)
- Methods to compute the spectral density integrals that appear in the weak coupling (2nd order expansion), both for the dynamics (see e.g. H. Breuer, F. Petruccione, "The Theory of Open Quantum Systems"), and the equilibrium mean-force state (see e.g. J.D. Cresser, J. Anders, Phys. Rev. Lett. 127, 250601 (2021)).
Quick start
The desired spectral density can be constructed by simply passing the desired parameters to their respective constructor. For example, for an Ohmic spectral density $J(\omega) = 3\omega$ we have
Johmic = OhmicSD(3)To add a ctuoff to a base spectral density, one simply passes it to the cutoff constructor. For example, to add an exponential cutoff $e^{-\omega/7}$ we can do
Jc = ExponentialCutoffSD(Johmic, 7)Defining custom spectral densities
The base AbstractSD can be easily extended by the user. To do so, one must create a new sub-type for which at least one of the methods sd (the spectral density itself $J(\omega)$) or sdoverω (the spectral density divided by frequency $J(\omega)/\omega$) must be defined. It is strongly recommended to define, if possible, sdoverω since it typically makes it simpler to numerically handle potential singularities.
This is the only requirement, and all other methods will automatically work on the new subtype. Of course, as is typical of Julia's super flexible multiple-dispatch system, the user should consider providing custom functions on the new type for the reorganisation energy, etc.