Related papers: A Dyson equation approach for averaging of classical and quantum observables on multiple realizations of Markov processes

A Dyson equation approach for averaging of classical and quantum observables on multiple realizations of Markov processes

URL: http://arxiv.org/abs/2004.01183v3
Date: Thu, 6 May 2021 11:29:22 GMT
Title: A Dyson equation approach for averaging of classical and quantum observables on multiple realizations of Markov processes
Authors: Simone Sturniolo
Abstract summary: Time dependent signals are often the result of an ensemble average over many microscopical dynamical processes. We present a numerical approach that can potentially be used to solve such time evolution problems. We benchmark it against a Monte Carlo simulations of the same problems.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Time dependent signals in experimental techniques such as Nuclear Magnetic Resonance (NMR) and Muon Spin Relaxation (muSR) are often the result of an ensemble average over many microscopical dynamical processes. While there are a number of functions used to fit these signals, they are often valid only in specific regimes, and almost never properly describe the "spectral diffusion" regime, in which the dynamics happen on time scales comparable to the characteristic frequencies of the system. Full treatment of these problems would require one to carry out a path integral over all possible realizations of the dynamics of the time dependent Hamiltonian. In this paper we present a numerical approach that can potentially be used to solve such time evolution problems, and we benchmark it against a Monte Carlo simulations of the same problems. The approach can be used for any sort of dynamics, but is especially powerful for any dynamics that can be approximated as Markov processes, in which the dynamics at each step only depend on the previous state of the system. The approach is used to average both classical and quantum observables; in the latter case, a formalism making use of Liouvillians and density matrices is used.

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