Quantum diffusion

TL;DR

This paper investigates quantum diffusion phenomena using dissipative Madelung hydrodynamics, revealing non-universal diffusion coefficients, different diffusion regimes, and effects of potential and particle mass, with implications for tunneling and diffusivity in solids.

Contribution

It introduces a detailed analysis of quantum diffusion regimes and shows the dependence of diffusion coefficients on initial conditions and potential landscapes.

Findings

Initial wave packet spreads ballistically before normal diffusion.

Quantum diffusion coefficient depends on initial wave packet preparation.

Logarithmic spreading occurs in overdamped quantum diffusion in periodic potentials.

Abstract

Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub-diffusive law. It is shown that the apparent quantum diffusion coefficient is not a universal physical parameter since it depends on the initial wave packet preparation. The overdamped quantum diffusion of an electron in the field of a periodic potential is also investigated; in this case the wave packet spreads logarithmically in time. Thermo-quantum diffusion of heavier particles as hydrogen, deuterium and tritium atoms in periodic potentials is studied and a simple estimate of the tunneling effect is obtained in the frames of a quasi-equilibrium semiclassical approach. The effective thermo-quantum temperature is also discussed in relation to the known temperature dependence of muon diffusivity in solids.