The Gisin-Percival stochastic Schrödinger equation from standard quantum filtering theory
نویسندگان
چکیده
منابع مشابه
The Schrödinger equation with friction from the quantum trajectory perspective.
Similarity of equations of motion for the classical and quantum trajectories is used to introduce a friction term dependent on the wavefunction phase into the time-dependent Schrödinger equation. The term describes irreversible energy loss by the quantum system. The force of friction is proportional to the velocity of a quantum trajectory. The resulting Schrödinger equation is nonlinear, conser...
متن کاملDecoherence and Localization in Quantum Two-Level Systems
We study and compare the decoherent histories approach, the environmentinduced decoherence and the localization properties of the solutions to the stochastic Schrödinger equation in quantum jump simulation and quantum state diffusion approaches, for a quantum two-level system model. We show, in particular, that there is a close connection between the decoherent histories and the quantum jump si...
متن کاملA semi-discrete scheme for the stochastic nonlinear Schrödinger equation
We study the convergence of a semi-discretized version of a numerical scheme for a stochastic nonlinear Schrödinger equation. The nonlinear term is a power law and the noise is multiplicative with a Stratonovich product. Our scheme is implicit in the deterministic part of the equation as is usual for conservative equations. We also use an implicit discretization of the noise which is better sui...
متن کاملStochastic Acceleration of Solitons for the Nonlinear Schrödinger Equation
The effective dynamics of solitons for the generalized nonlinear Schrödinger equation in a random potential is rigorously studied. It is shown that when the external potential varies slowly in space compared to the size of the soliton, the dynamics of the center of the soliton is almost surely described by Hamilton’s equations for a classical particle in the random potential, plus error terms d...
متن کاملQuantum state diffusion, density matrix diagonalization, and decoherent histories: A model.
We analyse the quantum evolution of a particle moving in a potential in interaction with an environment of harmonic oscillators in a thermal state, using the quantum state diffusion (QSD) picture of Gisin and Percival. The QSD picture exploits a mathematical connection between the usual Markovian master equation for the evolution of the density operator and a class of stochastic non-linear Schr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2018
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.5007917