Quantum continual measurements and a posteriori collapse on CCR
@article{Belavkin1992QuantumCM, title={Quantum continual measurements and a posteriori collapse on CCR}, author={Viacheslav P. Belavkin}, journal={Communications in Mathematical Physics}, year={1992}, volume={146}, pages={611-635} }
A quantum stochastic model for the Markovian dynamics of an open system under the nondemolition unsharp observation which is continuous in time, is given. A stochastic equation for the posterior evolution of a 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 case of a quasi-free Hamiltonian in the initial CCR algebra with a linear output…
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References
SHOWING 1-10 OF 26 REFERENCES
Quantum stochastic calculus, operation valued stochastic processes, and continual measurements in quantum mechanics
- Mathematics
- 1985
The physical idea of a continual observation on a quantum system has been recently formalized by means of the concept of operation valued stochastic process (OVSP). In this article, it is shown how…
Nondemolition observation of a free quantum particle.
- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1992
It is shown that the dispersion of the wave packet does not increase to in½nity like for the free unobserved particle but tends to the
nite limit 1 = (~=2 m) where is the accuracy coe¢ cient of an indirect nondemolition measurement of the particle position, and ~ is Planck constant.
Measurements continuous in time and a posteriori states in quantum mechanics
- PhysicsJournal of Physics A: Mathematical and General
- 1991
Measurements continuous in time have been consistently introduced in quantum mechanics and applications worked out, mainly in quantum optics. In this context a quantum filtering theory has been…
Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles.
- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1990
Stochastic differential equations describing the Markovian evolution of state vectors in the quantum Hilbert space are studied as possible expressions of a universal dynamical principle and the stochastic evolution is proved to induce continuous dynamical reduction of the state vector onto mutually orthogonal subspaces.
Combining stochastic dynamical state-vector reduction with spontaneous localization.
- PhysicsPhysical review. A, General physics
- 1989
A linear equation of motion for the state vector is presented, in which an anti-Hermitian Hamiltonian that fluctuates randomly is added to the usual Hamiltonian of the Schr\"odinger equation. It is…
Unified dynamics for microscopic and macroscopic systems.
- PhysicsPhysical review. D, Particles and fields
- 1986
A modified quantum dynamics for the description of macroscopic objects is constructed and it is shown that it forbids the occurrence of linear superpositions of states localized in far-away spatial regions and induces an evolution agreeing with classical mechanics.
Quantum Ito's formula and stochastic evolutions
- Mathematics
- 1984
Using only the Boson canonical commutation relations and the Riemann-Lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator…