Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation

Abstract

The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation.

References in corpus (4)

• Phase space representation of quantum dynamics
• General linear dynamics - quantum, classical or hybrid
• A path integral for classical dynamics, entanglement, and Jaynes-Cummings model at the quantum-classical divide
• Wigner distribution functions for complex dynamical systems: a path integral approach

Cited by in corpus (4)

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• Phase-space approach to polaron response: Kadanoff and FHIP re-examined
• Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility
• Self-energy correction to dynamic polaron response