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Title: Non-stochastic matrix Schrödinger equation for open systems

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