1994/04/30 by Peter Goetsch, Robert Graham · 1 citation
Computer Science · Physics and Astronomy · #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Heterodyne (poetry) #Homodyne detection #Linearity #Master equation #Nonlinear system #Open quantum system #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum operation #Quantum superposition #Statistical physics #Superposition principle #Wave equation #Wave function #Wave function collapse #gr-qc
paper · pdf · doi:10.1103/physreva.50.5242
34 pages, Revtex
arxiv created 1994/05/17 · openalex publication_date 1994/12/01 · arxiv updated 2009/11/30 · openalex created_date 2020/05/29 · openalex updated_date 2026/08/06
While the linearity of the Schr"odinger equation and the superposition principle are fundamental to quantum mechanics, so are the backaction of measurements and the resulting nonlinearity. It is remarkable, therefore, that the wave equation of systems in continuous interaction with some reservoir, which may be a measuring device, can be cast into a linear form, even after the degrees of freedom of the reservoir have been eliminated. The superposition principle still holds for the stochastic wave function of the observed system and exact analytical solutions are possible in sufficiently simple cases. We discuss here the coupling to Markovian reservoirs appropriate for homodyne, heterodyne, and photon counting measurements. For these we present a derivation of the linear stochastic wave equation from first principles and analyze its physical content.