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Title: Non-Markovian reduced propagator, multiple-time correlation functions, and master equations with general initial conditions in the weak-coupling limit

Abstract

In this paper we derive the evolution equation for the reduced propagator, an object that evolves vectors of the Hilbert space of a system S interacting with an environment B in a non-Markovian way. This evolution is conditioned to certain initial and final states of the environment. Once an average over these environmental states is made, reduced propagators permit the evaluation of multiple-time correlation functions of system observables. When this average is done stochastically the reduced propagator evolves according to a stochastic Schroedinger equation. In addition, it is possible to obtain the evolution equations of the multiple-time correlation functions which generalize the well-known quantum regression theorem to the non-Markovian case. Here, both methods, stochastic and evolution equations, are described by assuming a weak coupling between system and environment. Finally, we show that reduced propagators can be used to obtain a master equation with general initial conditions, and not necessarily an initial vacuum state for the environment. We illustrate the theory with several examples.

Authors:
 [1];  [2]
  1. Departamento de Fisica Fundamental II, Universidad de La Laguna, La Laguna 38203, Tenerife (Spain)
  2. Departamento de Fisica Fundamental y Experimental, Electronica y Sistemas, Universidad de La Laguna, La Laguna 38203, Tenerife (Spain)
Publication Date:
OSTI Identifier:
20974505
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.73.022102; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATION FUNCTIONS; COUPLING; EQUATIONS; HILBERT SPACE; MARKOV PROCESS; PROPAGATOR; SCHROEDINGER EQUATION; VACUUM STATES; VECTORS; WEAK-COUPLING MODEL

Citation Formats

Vega, Ines de, and Alonso, Daniel. Non-Markovian reduced propagator, multiple-time correlation functions, and master equations with general initial conditions in the weak-coupling limit. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.022102.
Vega, Ines de, & Alonso, Daniel. Non-Markovian reduced propagator, multiple-time correlation functions, and master equations with general initial conditions in the weak-coupling limit. United States. https://doi.org/10.1103/PHYSREVA.73.022102
Vega, Ines de, and Alonso, Daniel. 2006. "Non-Markovian reduced propagator, multiple-time correlation functions, and master equations with general initial conditions in the weak-coupling limit". United States. https://doi.org/10.1103/PHYSREVA.73.022102.
@article{osti_20974505,
title = {Non-Markovian reduced propagator, multiple-time correlation functions, and master equations with general initial conditions in the weak-coupling limit},
author = {Vega, Ines de and Alonso, Daniel},
abstractNote = {In this paper we derive the evolution equation for the reduced propagator, an object that evolves vectors of the Hilbert space of a system S interacting with an environment B in a non-Markovian way. This evolution is conditioned to certain initial and final states of the environment. Once an average over these environmental states is made, reduced propagators permit the evaluation of multiple-time correlation functions of system observables. When this average is done stochastically the reduced propagator evolves according to a stochastic Schroedinger equation. In addition, it is possible to obtain the evolution equations of the multiple-time correlation functions which generalize the well-known quantum regression theorem to the non-Markovian case. Here, both methods, stochastic and evolution equations, are described by assuming a weak coupling between system and environment. Finally, we show that reduced propagators can be used to obtain a master equation with general initial conditions, and not necessarily an initial vacuum state for the environment. We illustrate the theory with several examples.},
doi = {10.1103/PHYSREVA.73.022102},
url = {https://www.osti.gov/biblio/20974505}, journal = {Physical Review. A},
issn = {1050-2947},
number = 2,
volume = 73,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}