Partial-trace-free time-convolutionless equation of motion for the reduced density matrix

Irena Knezevic, David K. Ferry

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

Evolution of a system, coupled to its environment and influenced by external driving fields, is an old problem that remains of interest. In this paper, we derive an equation of motion for the reduced system density matrix, which is time convolutionless and free of the partial trace with respect to the environment states. This new approach uses an extension of the projection-operator technique, which incorporates an isomorphism between the system's Liouville space and the unit eigenspace of the projection operator induced by the uniform environment density matrix. Numerical application of the present approach is particularly useful in large externally driven systems, as the partial-trace-free equation is given in terms of submatrices significantly smaller than the matrices in the conventional time-convolutionless approaches, which alleviates the computational burden. We also show that all time-convolutionless approaches, conventional or partial-trace-free, are based upon a hidden underlying assumption of time reversibility of the system's evolution. This feature puts significant constraints on applicability of time-convolutionless approaches when employing approximations that yield time irreversibility. Also, we investigate the application of the approach in the description of far-from-equilibrium systems.

Original languageEnglish (US)
Article number016131
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume66
Issue number1
DOIs
StatePublished - Jul 2002

Fingerprint

Density Matrix
Equations of Motion
equations of motion
Trace
Partial
Projection Operator
Time Reversibility
projection
Irreversibility
Evolution System
Eigenspace
operators
isomorphism
Coupled System
Isomorphism
Unit
Approximation
matrices
approximation

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Partial-trace-free time-convolutionless equation of motion for the reduced density matrix. / Knezevic, Irena; Ferry, David K.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 66, No. 1, 016131, 07.2002.

Research output: Contribution to journalArticle

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