The Method of Quantum Jumps and Quantum White Noise

Nobuaki Obata

Enmin Feng

The white noise approach for stochastic Schrdinger equation(SSE) driven by pure jump Levy white noise is presented.The potential of the SSE is proportional to the Wick exponential of pure jump Levy white noise,which describes the physical system with jump.The white noise approach is based on (S)-1-characterization theorem.The SSE is firstly reduced to the ordinary non-random Schrdinger equation(OSE) by Hermite transform,which can be solved by Feynmann-Kac formula.Then the solution of the SSE is obtained by(S)-1-characterization theorem,converting the solution of the OSE to a(S)-1-process.Furthermore,the solution is in L1(υ) in sense of weak distribution under some certain conditions.

V. P. Belavkin, Jaeseong Heo, Un Cig Ji

T. HIDA, Ludwig Streit

L. Diósi

S. M. Girvin, Gerald Dennis Mahan

Exact results are presented for the quantum diffusion of a tight-binding spinless many-fermion system in any dimension with site energies having a random white-noise frequency spectrum of arbitrary strength. In the limit of strong coupling to the noise, it is shown that the system reduces to the Chudley-Elliott jump-diffusion model.