Quantum diffusion

Abstract

Basic ideas and results which characterize quantum diffusion of defects in quantum crystals like solid helium as a new phenomenon are presented. Quantum effects in such media lead to a delocalization of point defects (vacancies, impurities etc.) and they turn into quasiparticles of a new type -defectons, which are characterized not by their position in the crystal lattice but by their quasimomentum and dispersion law. Defectondefecton and defecton-phonon scattering are considered and an interpolation formula for the diffusion coefficient valid in all interesting temperature and concentration regions is presented. A comparison with the experimental data is made. Some alternative points of view are discussed in detail and the inconsistency of the Kisvarsanyi-Sullivan theory is shown.

Cooper Pair Formation by Quantizing Brownian Motion

“…As for the quantization of the diffusion coefficient, we assume that it is a constant. For example, supposing the gas kinetic model about defects [22], the diffusion coefficient will be D ∼ Aa 2 / xσ , where A, a, x, and σ are tunneling probability amplitude, lattice constant, fractional concentration, and cross section, respectively. To regard it as a constant, local information should be discarded.…”

“…If we invent the quantum osmotic velocity with a hypothesis formulation, quantization of the stochastic potential becomes clear. Strictly speaking, it must be given by formulating quantum diffusion [22][23][24], but here, we naively quantize them. For the sake of the canonical quantization, fermionic fields are simply represented.…”

Vacancy distribution in a rotating solid 4 He

“…by the diffusion experiments (see e.g. [6] and the references therein). In our investigation we use a nonlinear self-consistent theory based on the elasticity theory equations and a Boltzmann-type transport equation for vacancions.…”