Nonstochastic 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 nonstochastic evolution equation preserves positivedefiniteness of the system density and is applicable to both Markovian and nonMarkovian systembath treatments. Our formalism also resolves a longstanding problem of energy loss in the timedependent variational principle applied to mixed states of closed systems.
 Authors:
 Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4 (Canada)
 (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
JoubertDoriol, Loïc, Ryabinkin, Ilya G., Izmaylov, Artur F., Email: artur.izmaylov@utoronto.ca, and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6. Nonstochastic matrix Schrödinger equation for open systems. United States: N. p., 2014.
Web. doi:10.1063/1.4903829.
JoubertDoriol, Loïc, Ryabinkin, Ilya G., Izmaylov, Artur F., Email: artur.izmaylov@utoronto.ca, & Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6. Nonstochastic matrix Schrödinger equation for open systems. United States. doi:10.1063/1.4903829.
JoubertDoriol, Loïc, Ryabinkin, Ilya G., Izmaylov, Artur F., Email: artur.izmaylov@utoronto.ca, and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6. Sun .
"Nonstochastic matrix Schrödinger equation for open systems". United States.
doi:10.1063/1.4903829.
@article{osti_22413328,
title = {Nonstochastic matrix Schrödinger equation for open systems},
author = {JoubertDoriol, Loïc and Ryabinkin, Ilya G. and Izmaylov, Artur F., Email: 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 nonstochastic evolution equation preserves positivedefiniteness of the system density and is applicable to both Markovian and nonMarkovian systembath treatments. Our formalism also resolves a longstanding problem of energy loss in the timedependent 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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