# A stochastic Hamiltonian approach for quantum jumps, spontaneous localizations, and continuous trajectories

@article{Belavkin1996ASH, title={A stochastic Hamiltonian approach for quantum jumps, spontaneous localizations, and continuous trajectories}, author={Viacheslav P. Belavkin and Olaf Melsheimer}, journal={Quantum and Semiclassical Optics: Journal of The European Optical Society Part B}, year={1996}, volume={8}, pages={167-187} }

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 quantum particles that interacts singularly with `bubbles' which admit a continual counting observation. This model allows one to watch a quantum trajectory in a photodetector or in a cloud chamber by spontaneous localizations of the momenta of the scattered photons or bubbles. Thus, the continuous reduction and…

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