Exact Markovian kinetic equation for a quantum Brownian oscillator

Abstract

We derive an exact Markovian kinetic equation for an oscillator linearly coupled to a heat bath, describing quantum Brownian motion. Our work is based on the subdynamics formulation developed by Prigogine and collaborators. The space of distribution functions is decomposed into independent subspaces that remain invariant under Liouville dynamics. For integrable systems in Poincaré's sense the invariant subspaces follow the dynamics of uncoupled, renormalized particles. In contrast for non-integrable systems, the invariant subspaces follow a dynamics with broken-time symmetry, involving generalized functions. This result indicates that irreversibility and stochasticity are exact properties of dynamics in generalized function spaces. We comment on the relation between our Markovian kinetic equation and the Hu-Paz-Zhang equation.

arXiv commentA few typos in the published version are corrected

References in corpus (4)

• Exact solution of the Hu-Paz-Zhang master equation
• Strongly Coupled Matter-Field and Non-Analytic Decay Rate of Dipole Molecules in a Waveguide
• Star-unitary transformations. From dynamics to irreversibility and stochastic behavior
• Thermodynamics and small quantum systems

Cited by in corpus (6)

• On the Thermal Symmetry of the Markovian Master Equation
• Symmetry of bilinear master equations for a quantum oscillator
• Liouvillian exceptional points in continuous variable system
• Solutions of generic bilinear master equations for a quantum oscillator -- positive and factorized conditions on stationary states
• Reduced dynamics of two oscillators collectively coupled to a thermal bath
• Nonequilibrium Transport of Quantum Molecular Chain in terms of the Complex Liouvillian Spectrum