arXiv subjects

Andrei Sobolev

Publications and source records attributed to Andrei Sobolev.

3 recordsLinked to original sources

arXiv2005

Stochastic Schrodinger equations as limit of discrete filtering

We consider an open model possessing a Markovian quantum stochastic limit and derive the limit stochastic Schrodinger equations for the wave function conditioned on indirect observations using only the von Neumann projection postulate. We show that the diffusion (Gaussian) situation is universal as a result of the central limit theorem with the quantum jump (Poissonian) situation being an exceptional case. It is shown that, starting from the correponding limiting open systems dynamics, the theory of quantum filtering leads to the same equations, therefore establishing consistency of the quantum stochastic approach for limiting Markovian models.

quant-ph↗

arXiv2004

Continuous measurement of canonical observables and limit Stochastic Schrodinger equations

We derive the stochastic Schrodinger equation for the limit of continuous weak measurement where the observables monitored are canonical position and momentum. To this end we extend an argument due to Smolianov and Truman from the von Neumann model of indirect measurement of position to the Arthurs and Kelly model for simultaneous measurement of position and momentum. We only require unbiasedness of the detector states and an integrability condition sufficient to ensure a central limit effect. Despite taking a weak interaction, as opposed to weak measurement limit, the resulting stochastic wave equation is of the same form as that derived in a recent paper by Scott and Milburn for the specific case of joint Gaussian states.

quant-ph↗

arXiv2003

Quantum Markovian Approximations for Fermionic Reservoirs

We establish a quantum functional central limit for the dynamics of a system coupled to a Fermionic bath with a general interaction linear in the creation, annihilation and scattering of the bath reservoir. Following a quantum Markovian limit, we realize the open dynamical evolution of the system as an adapted quantum stochastic process driven by Fermionic Noise.

quant-ph↗