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Title: Non-stochastic matrix Schrödinger equation for open systems

Abstract

We propose an extension of the Schrödinger equation for a quantum system interacting with environment. This extension describes dynamics of a collection of auxiliary wavefunctions organized as a matrix m, from which the system density matrix can be reconstructed as ρ{sup ^}=mm{sup †}. We formulate a compatibility condition, which ensures that the reconstructed density satisfies a given quantum master equation for the system density. The resulting non-stochastic evolution equation preserves positive-definiteness of the system density and is applicable to both Markovian and non-Markovian system-bath treatments. Our formalism also resolves a long-standing problem of energy loss in the time-dependent variational principle applied to mixed states of closed systems.

Authors:
; ;  [1];  [2]
  1. Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4 (Canada)
  2. (Canada)
Publication Date:
OSTI Identifier:
22413328
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 23; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY; DENSITY MATRIX; ENERGY LOSSES; MARKOV PROCESS; MIXED STATE; MIXED STATES; QUANTUM SYSTEMS; SCHROEDINGER EQUATION; TIME DEPENDENCE; VARIATIONAL METHODS; WAVE FUNCTIONS

Citation Formats

Joubert-Doriol, Loïc, Ryabinkin, Ilya G., Izmaylov, Artur F., E-mail: artur.izmaylov@utoronto.ca, and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6. Non-stochastic matrix Schrödinger equation for open systems. United States: N. p., 2014. Web. doi:10.1063/1.4903829.
Joubert-Doriol, Loïc, Ryabinkin, Ilya G., Izmaylov, Artur F., E-mail: artur.izmaylov@utoronto.ca, & Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6. Non-stochastic matrix Schrödinger equation for open systems. United States. doi:10.1063/1.4903829.
Joubert-Doriol, Loïc, Ryabinkin, Ilya G., Izmaylov, Artur F., E-mail: artur.izmaylov@utoronto.ca, and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6. Sun . "Non-stochastic matrix Schrödinger equation for open systems". United States. doi:10.1063/1.4903829.
@article{osti_22413328,
title = {Non-stochastic matrix Schrödinger equation for open systems},
author = {Joubert-Doriol, Loïc and Ryabinkin, Ilya G. and Izmaylov, Artur F., E-mail: artur.izmaylov@utoronto.ca and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6},
abstractNote = {We propose an extension of the Schrödinger equation for a quantum system interacting with environment. This extension describes dynamics of a collection of auxiliary wavefunctions organized as a matrix m, from which the system density matrix can be reconstructed as ρ{sup ^}=mm{sup †}. We formulate a compatibility condition, which ensures that the reconstructed density satisfies a given quantum master equation for the system density. The resulting non-stochastic evolution equation preserves positive-definiteness of the system density and is applicable to both Markovian and non-Markovian system-bath treatments. Our formalism also resolves a long-standing problem of energy loss in the time-dependent variational principle applied to mixed states of closed systems.},
doi = {10.1063/1.4903829},
journal = {Journal of Chemical Physics},
number = 23,
volume = 141,
place = {United States},
year = {Sun Dec 21 00:00:00 EST 2014},
month = {Sun Dec 21 00:00:00 EST 2014}
}
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