A formulation of quantum stochastic processes and some of its properties

John T. Lewis

H Okamoto

It is shown that a stochastic process described by a complex Langevin equation leads to real-time quantum mechanics. The author also derives a relation between a transition probability in the theory and a transition probability amplitude in real-time quantum mechanics in the framework of path-integral formulations. Finally, taking a harmonic oscillator case as an example, the Fokker-Planck equation is solved exactly, and a non-dissipation property of the stochastic process is pointed out.

C. V. Heer

Teruaki Nakagomi

A relativistic space-time stochastic process of light-like random motion was constructed in a previous paper by taking proper time as parameter. The same random motion is reformulated by a spatial stochastic process with observer's time as parameter. A crucial point in deriving the latter process from the former is that the two time parameters are stochastically related to each other. Properties of the process are studied, including the Markov property, time evolution equations, transformation properties under the Lorentz group, and an expression for probability over arbitrary space-like hypersurfaces. A formula with close analogy to the Dirac Hamiltonian is also presented. The original model in proper-time formulation is reviewed briefly.

Mateo Londoño, Javier Madroñero, Jesús Pérez‐Ríos

Based on the Langevin equation, a stochastic formulation is implemented to describe the dynamics of a trapped ion in a bath of ultracold atoms, including an excess of micromotion. The ion dynamics is described following a hybrid analytical-numerical approach in which the ion is treated as a classical impurity in a thermal bath. As a result, the ion energy's time evolution and distribution are derived from studying the sympathetic cooling process. Furthermore, the ion dynamics under different stochastic noise terms is also considered to gain information on the bath properties' role in the system's energy transfer processes. Finally, the results obtained from this formulation are contrasted with those obtained with a more traditional Monte Carlo approach.

Mohamed Ben Chrouda, MOHAMED EL OUED, Habib Ouerdiane