2000/11/01 by V. P. Belavkin, P. Staszewski
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Hamiltonian (control theory) #Hamiltonian system #Law #Mathematical analysis #Mathematical physics #Mathematics #Open quantum system #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Zeno effect #Quantum mechanics #Quantum system #Semiclassical physics #Statistical physics #Stochastic differential equation #Unitary state #math-ph #math.MP
paper · pdf · doi:10.1063/1.1310357
published as J. Math. Phys. 41 No 11, 2000, 7220--7233 · 17 pages. See also related papers at http://www.maths.nott.ac.uk/personal/vpb/research/evo_equ.html and http://www.maths.nott.ac.uk/personal/vpb/research/mar_dyn.html
openalex publication_date 2000/11/01 · arxiv created 2005/12/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A semiclassical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, η⟼Cη, given by a contraction C. The counting trajectories are assumed to satisfy the Poisson law. A unitary dilation of the concractive stochastic dynamics is found. In particular, in the limit of frequent detection corresponding to the large number limit we obtain the Itô–Schrödinger stochastic unitary evolution for the pure state of unstable quantum system providing a new stochastic version of the quantum Zeno effect.