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109 papers · 1 filter
A Stochastic Hamiltonian Approach for Quantum Jumps, Spontaneous Localizations, and Continuous Trajectories
V. P. Belavkin, O. Melsheimer
We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of qua…
Quantum Stochastic Differential Equation
V. P. Belavkin, P. Staszewski
A semi-classical 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…
Nondemolition Principle of Quantum Measurement Theory
V. P. Belavkin
We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applic…
On Quantum Ito Algebras and their decompositions
V. P. Belavkin
A simple axiomatic characterization of the noncommutative Ito algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. It is proved that ev…
Quantum Continual Measurements and a Posteriori Collapse on CCR
V. P. Belavkin
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 stochast…
Quantum Ito B*-algebras, their Classification and Decomposition
V. P. Belavkin
A simple axiomatic characterization of the general (infinite dimensional, noncommutative) Ito algebra is given and a pseudo-Euclidean fundamental representation for such algebra is…