Nonperturbative Treatment of non-Markovian Dynamics of Open Quantum Systems

Abstract

We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments-one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (nonunitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, nonperturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open-system dynamics.

Non-Markovian quantum processes: Complete framework and efficient characterization

“…This is reassuring, since the description should not be more complex than the corresponding OQE. Even though the environment dimension could be large, there is always a consistent OQE with d E ≤ d 3 k −1 , and we expect the effective bond dimension to be much smaller than this in practice; often only part of the environment interacts with the system at any given time and, in practice, even an infinite-dimensional environment can be approximated by a finite one [49,50]. This comprises a significantly more efficient representation for processes with many time steps, and opens up the possibility to use singular value truncation and other techniques [46,47,51,52] to meaningfully approximate the dynamics by pruning low-probability branches of the MPS description.…”

A trapped-ion simulator for spin-boson models with structured environments

“…In this regime, the Lindblad oscillator produces the same reservoir correlation function and thus influence functional as the Ohmic oscillator. According to the equivalence theorem in [35], in this regime the Lindblad oscillator acts as an effective macroscopic reservoir with Lorentzian spectral density as given inequation (7) above.…”

Precursors of non-Markovianity

“…Our work paves the way for considering the relevance of such precursors in a variety of settings which allow for the systematic introduction of environmental degrees of freedom, e.g. within the framework of reaction coordinate models or chain mappings [35][36][37][38][39][40][41].…”