2007/05/31 by B. A. Tay, T. Petrosky · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Classical mechanics #Geometry #Harmonic oscillator #Heat transfer #Master equation #Mathematical physics #Mathematics #Mechanical and Optical Resonators #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Symmetry (geometry) #Thermal #Thermal reservoir #Thermodynamics #math-ph #math.MP #msc:03.65.Yz #msc:05.70.Ln
paper · pdf · doi:10.1103/physreva.76.042102
published as Phys. Rev. A 76, 042102 (2007) · Eqs.(64a), (65a)-(68) are corrected
openalex publication_date 2007/10/02 · arxiv created 2012/07/25 · arxiv updated 2012/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.