Thermal symmetry of the Markovian master equation

Journal Article · Mon Oct 15 04:00:00 EDT 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.76.042102· OSTI ID:21020644

Tay, B A; Petrosky, T ^[1]

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1. Department of Physics, Faculty of Science, University Putra Malaysia, 43400 UPM Serdang, Selangor (Malaysia)

The quantum Markovian master equation of the reduced dynamics of a harmonic oscillator coupled to a thermal reservoir is shown to possess thermal symmetry. This symmetry is revealed by a Bogoliubov transformation that can be represented by a hyperbolic rotation acting on the Liouville space of the reduced dynamics. The Liouville space is obtained as an extension of the Hilbert space through the introduction of tilde variables used in the thermofield dynamics formalism. The angle of rotation depends on the temperature of the reservoir, as well as the value of Planck's constant. This symmetry relates the thermal states of the system at any two temperatures. This includes absolute zero, at which purely quantum effects are revealed. The Caldeira-Leggett equation and the classical Fokker-Planck equation also possess thermal symmetry. We compare the thermal symmetry obtained from the Bogoliubov transformation in related fields and discuss the effects of the symmetry on the shape of a Gaussian wave packet.

• OSTI ID: 21020644
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 76; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOGOLYUBOV TRANSFORMATION
COMPARATIVE EVALUATIONS
FIELD THEORIES
FOKKER-PLANCK EQUATION
HARMONIC OSCILLATORS
HILBERT SPACE
MARKOV PROCESS
ROTATION
SYMMETRY
TEMPERATURE ZERO K
THERMODYNAMICS
WAVE PACKETS