Continuous Quantum Measurement: Local and Global Approaches

DOI10.1142/S0129055X97000312zbMath0894.47058MaRDI QIDQ4379715

O. G. Smolyanov, Vassili N. Kolokol'tsov, Sergio A. Albeverio

Publication date: 4 March 1998

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Wiener processstochastic equationcontinuously observed quantum systemsFeynman path descriptionMenski's heuristic path integralsnonlinear version of the Schrödinger equation

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Path integrals in quantum mechanics (81S40) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Quantum stochastic calculus (81S25) Quantum measurement theory, state operations, state preparations (81P15) Stochastic mechanics (including stochastic electrodynamics) (81P20)

Related Items (7)

Representations of solutions of Lindblad equations by randomized Feynman formulas ⋮ Representation of solutions of the stochastic Schrödinger equation in the form of a Feynman integral ⋮ STOCHASTIC EVOLUTION AS A QUASICLASSICAL LIMIT OF A BOUNDARY VALUE PROBLEM FOR SCHRÖDINGER EQUATIONS ⋮ ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS ⋮ Mathematical theory of Feynman path integrals ⋮ A REPRESENTATION OF THE BELAVKIN EQUATION VIA PHASE SPACE FEYNMAN PATH INTEGRALS ⋮ Schrödinger equation with signed Hamiltonian

Cites Work

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• On the generators of quantum dynamical semigroups
• Dirichlet forms and Markov semigroups on \(C^*\)-algebras
• On the gap between deterministic and stochastic ordinary differential equations
• Finite dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions
• Continuous quantum jumps and infinite-dimensional stochastic equations
• Scattering theory for the Belavkin equation describing a quantum particle with continuously observed coordinate

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