1992/06/01 by V. P. Belavkin · 6 citations
Computer Science · Mathematics · Physics and Astronomy · #Gaussian #Hamiltonian (control theory) #Langevin equation #Markov process #Master equation #Mathematical optimization #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum dynamics #Quantum mechanics #Quantum operation #Quantum optics and atomic interactions #Quantum process #Quantum stochastic calculus #Statistical physics #Wave packet #math-ph #math.MP
paper · pdf · doi:10.1007/bf02097018
published as Communications Mathematical Physics 146, pp 611--635 (1992) · 25 pages. See also related papers at http://www.maths.nott.ac.uk/personal/vpb/research/fil_con.html and http://www.maths.nott.ac.uk/personal/vpb/research/evo_equ.html
openalex publication_date 1992/06/01 · arxiv created 2005/12/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A quantum theory for the Markovian dynamics of an open system under the unsharp observation which is continuous in time, is developed within the CCR stochastic approach. A stochastic classical equation for the posterior evolution of quantum continuously observed system is derived and the spontaneous collapse (stochastically continuous reduction of the wave packet) is described. The quantum Langevin evolution equation is solved for the general linear case of a quasi--free Hamiltonian in the initial CCR algebra with a fixed output observable field, and the posterior Kalman dynamics coresponding to an initial Gaussian state is found. It is shown for an example of the posterior dynamics of quantum unstable open system that any mixed state under a complete nondemolition measurement collapses exponentially to a pure Gaussian one.