Some problems related to quantum-mechanical description of decay and collision processes

Teiji Kunihiro, Berndt Müller, Akira Ohnishi A +1 more

We propose a broadly applicable formalism for the description of coarse grained en-tropy production in quantum mechanical processes. Our formalism is based on the Husimi transform of the quantum state, which encodes the notion that information about any quan-tum state is limited by the experimental resolution. We show in two analytically tractable cases (the decay of an unstable vacuum state and reheating after cosmic inflation) that the growth rate of the Wehrl entropy associated with the Husimi function approaches the classi-cal Kolmogorov-Sinäı entropy. We also discuss various possible applications of our formalism, including the production of entropy in the early stages of a relativistic heavy ion collision. The production of entropy at the quantum level, i. e. the loss of information about the state of the system under consideration, is a long-standing problem in statistical physics. Many of its conceptual aspects are similar to those encountered in classical physics, but quantum mechanics poses the additional, but closely related,

William Band, James L Park

Philip Μ. Morse

Michel De Haan

The compatibility of irreversibility, as expressed by the second law of thermodynamics, with ordinary quantum mechanics is a challenging problem. Our solution requires an extension of the latter. Such an extension of a reversible formalism is made possible by the presence of self‐energy processes (already found in quantum electrodynamics) which enables the widening of the dynamics by the introduction of specific additionnal variables leading to the recognition of such processes. A projection technique modeled on the one introduced long ago by the Brussels group defines a subdynamics which is shown to contain entirely the starting formulation (it corresponds now to a restricted class of initial conditions, namely the reversible one). A new kinetic description is obtained in which e.g. collision processes for privileged components arise from the original interaction. This method is applied successively to various models and we focus in this paper on the possible presence of temporal behaviours excluded in ordinary quantum mechanics. Among those differences, the possibility appears of a purely exponential decay for a particle while ordinary quantum mechanics requires long time tails associated with the finite lower bound in the spectrum of the Hamiltonian.

Mark S. Hillery

Sunipa Som, Ravindra Dhar, Ram Kripal +1 more

Abstract This paper presents Quantum Boltzmann Transport Equation Laboratory (QBTELab), an advanced easy-to-use toolbox to solve many complex problems related to Bose-Einstein Condensate (BEC). The model equation that BTELab solves is the Quantum Boltzmann Transport Equation (QBTE) with all collision terms within trapping potential. Inelastic scattering (Exciton-phonon collision), elastic scattering (exciton-exciton collision), Auger decay and radiative non-radiative decay are included here as the collision terms. The programme code has been written in MATLAB. From the results it can be said that the programme is working properly and it has enough numerical stability. The aim of this paper is to provide programme code to solve the full QBTE. QBTE is a powerful tool for investigating the transport phenomena in various systems like semiconductors, plasmas, nuclear reactors, heat transfer process, fluid dynamics etc and specially different problems related to BEC.