Non-perturbative treatment of open-system multi-time expectation values in Gaussian bosonic environments

Abstract

We determine the conditions for the equivalence between the multi-time expectation values of a general finite-dimensional open quantum system when interacting with, respectively, an environment undergoing a free unitary evolution or a discrete environment under a free evolution fixed by a proper Gorini-Kossakowski-Lindblad-Sudarshan generator. We prove that the equivalence holds if both environments are bosonic and Gaussian and if the one- and two-time correlation functions of the corresponding interaction operators are the same at all times. This result leads to a non-perturbative evaluation of the multi-time expectation values of operators and maps of open quantum systems interacting with a continuous set of bosonic modes by means of a limited number of damped modes, thus setting the ground for the investigation of open-system multi-time quantities in fully general regimes.

16 pages, 1 figure. Submission to a special issue of 'Open Systems and Information Dynamics' devoted to the memory of Prof. Andrzej Kossakowski

References in corpus (9)

• Non-perturbative treatment of non-Markovian dynamics of open quantum systems
• Quantum regression theorem and non-Markovianity of quantum dynamics
• Vanishing quantum discord is not necessary for completely-positive maps
• Non-Markovian finite-temperature two-time correlation functions of system operators: beyond the quantum regression theorem
• Fingerprint and universal Markovian closure of structured bosonic environments
• Extension of the Nakajima-Zwanzig approach to multitime correlation functions of open systems
• The quantum regression theorem for out-of-time-ordered correlation functions
• Quantum regression beyond the Born-Markov approximation for generalized spin-boson models
• Quantum regression in dephasing phenomena

Cited by in corpus (6)

• Non-Hermitian Pseudomodes for Strongly Coupled Open Quantum Systems: Unravelings, Correlations and Thermodynamics
• Understanding gravitationally induced decoherence parameters in neutrino oscillations using a microscopic quantum mechanical model
• Pseudomode treatment of strong-coupling quantum thermodynamics
• Thermal cycle and polaron formation in structured bosonic environments
• Quantum Cramer-Rao Precision Limit of Noisy Continuous Sensing
• Testing bath correlation functions for open quantum dynamics simulations