Analytic Representations of Bath Correlation Functions for Ohmic and Superohmic Spectral Densities Using Simple Poles

TL;DR

This paper introduces a method to analytically represent bath correlation functions for various spectral densities using simple poles, aiding open quantum system modeling and emphasizing the importance of low-frequency behavior.

Contribution

It presents a novel class of fit functions enabling analytic calculation of bath correlation functions for ohmic and superohmic spectral densities using pole expansions.

Findings

Effective fitting of spectral densities for photosynthetic complexes.

Analytic expressions for bath correlation functions derived.

Proper low-frequency behavior is crucial for accurate spectral fits.

Abstract

We present a scheme to express a bath correlation function (BCF) corresponding to a given spectral density (SD) as a sum of damped harmonic oscillations. Such a representation is needed, for example, in many open quantum system approaches. To this end we introduce a class of fit functions that enables us to model ohmic as well as superohmic behavior. We show that these functions allow for an analytic calculation of the BCF using pole expansions of the temperature dependent hyperbolic cotangent. We demonstrate how to use these functions to fit spectral densities exemplarily for cases encountered in the description of photosynthetic light harvesting complexes. Finally, we compare absorption spectra obtained for different fits with exact spectra and show that it is crucial to take properly into account the behavior at small frequencies when fitting a given SD.