Classical and quantum measurements of position

Abstract

We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the measured system. Selective and nonselective measurement processes are then introduced according to a selection of or an average over all possible initial configurations of the measurement apparatus. At quantum level, the selective processes are described by a nonlinear stochastic Schrödinger equation whose solutions evolve into properly defined coherent states in the case of linear systems. For arbitrary measured systems, classical behavior is always recovered in the macroscopic limit.

30 pages, REVTeX 3.0, to be published in J. Phys. A

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• A Monte Carlo Method for Modeling Thermal Damping: Beyond the Brownian-Motion Master Equation
• The Markov approximation revisited: Inconsistency of the standard quantum Brownian motion model
• Variational Monte Carlo Approach to Partial Differential Equations with Neural Networks
• Temperature Dependent Motion of a Massive Quantum Particle
• Interacting bosons in two-dimensional lattices with localized dissipation
• Non-Markovian Caldeira--Leggett quantum master equation