Wigner Distribution Function Approach to Dissipative Problems in Quantum Mechanics with emphasis on Decoherence and Measurement Theory

Abstract

We first review the usefulness of the Wigner distribution functions (WDF), associated with Lindblad and pre-master equations, for analyzing a host of problems in Quantum Optics where dissipation plays a major role, an arena where weak coupling and long-time approximations are valid. However, we also show their limitations for the discussion of decoherence, which is generally a short-time phenomenon with decay rates typically much smaller than typical dissipative decay rates. We discuss two approaches to the problem both of which use a quantum Langevin equation (QLE) as a starting-point: (a) use of a reduced WDF but in the context of an exact master equation (b) use of a WDF for the complete system corresponding to entanglement at all times.

References in corpus (6)

• Exact solution of the Hu-Paz-Zhang master equation
• Quantum measurement and decoherence
• Decoherence without dissipation
• Wave Packet Spreading: Temperature and Squeezing Effects with Applications to Quantum Measurement and Decoherence
• Decoherence at zero temperature
• Effect of an External Field on Decoherence

Cited by in corpus (11)

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• Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators
• Quantum master equations from classical Lagrangians with two stochastic forces
• Decoherence in Quantum Systems
• Memory Effect in Upper Bound of Heat Flux Induced by Quantum Fluctuations
• Coherent control of levitated nanoparticles via dipole-dipole interaction
• Fluctuations and Noise: A General Model with Applications
• Quantum and semiclassical dynamics as fluid theories where gauge matters
• Understanding Squeezed States of Light Through Wigner's Phase-Space