THE APPROACH TO EQUILIBRIUM IN QUANTUM RANDOM-WALKS

Abstract

We use the quantum random walk (QRW) model to build a quantum kinetic theory of diffusion in a one-dimensional, crystalline lattice, with a fixed number of cells. QRW is a reversible model and the quantum interferences are responsible for the process not satisfying an H-theorem. The microscopic entropy which increases statistically not dynamically, shows very large fluctuations. In the long-time limit, the entropy still fluctuates around some mean value, but in the limit of a large number of lattice cells, the relative fluctuations become negligible, allowing for the definition of thermodynamic equilibrium.