Quantum scattering by a Brownian particle with complex potential

Andrei D. Zaikin, Sergey Panyukov

Piotr Garbaczewski

S. E. Cheremshantsev

S. E. Cheremshantsev

L. de la Peña-Auerbach, Ernest Braun, L. S. García Colín

It is shown that the motion of a Brownian particle in the Smoluchowski approximation may be described by a Schrödinger-like equation defining a complex probability amplitude whose norm is the same as the stochastic probability density. Furthermore, the quantum dynamical operators have a physical meaning which arises in a natural way, from the stochastic nature of the process. These operators satisfy the usual commutation relations and thus the uncertainty principle. Here the constant ℏ is replaced by a parameter depending on the characteristics of the system. In particular, the potential-energy operator for a Brownian particle subject to no external forces can be interpreted as a Rayleigh dissipative function.

Gonzalo E. Ordonez

I consider a Brownian particle immersed in a one-dimensional boson gas with delta-function repulsive potentials. I find many-body complex eigenvalues of the Liouville super-operator, up to second order in the coupling constant. The eigenvalues give the diffusion time-scale of the Brownian particle. The eigenvalue problem is solved using a Bethe-ansatz approach.