On the defecton statistics in quantum crystals

Abstract

The defecton statistics in quantum crystals is treated, and a new method for determining commutation relations is proposed. Defectons related to defects of a different kind (vacancies, impurities, interstitials) are considered in crystals both of the Bose-type (4He) and Fermi-type (3He). The kinematic interaction is discussed.Es wird die Statistik von Defektonen in Quantenkristallen behandelt und eine neue Methode zur Bestimmung der Vertauschungsrelationen vorgeschlagen. Defektonen, hervorgerufen durch verschiedenartige Defekte (Leerstellen, Verunreinigungen, Zwischengitteratome), werden sowohl fur Kristalle vom Bose-Typ (4He) als auch fur Kristalle vom Fermi-Typ ($He) betrachtet. Die kinematische Wechselwirkung wird diskutiert.

Quantum diffusion

“…The ninth power of temperature is easy to understand (for details see Refs. [1], [19]). The motion of a defect is determined by the number of phonons (N ph ∼ T 3 at low temperatures) and, by the scattering of long wave phonons on defects (Rayleigh scattering) with a cross-section σ ∼ k 4 ∼ T 4 ; finally, the motion of a "heavy and slow" defecton in a gas of "light" phonons depends on the second power of the phonon It could be expected that such a rapid increase of the diffusion with decreasing temperature can easily be observed experimentally.…”

“…in the entire experimentally accessible region. Unfortunately, the experimental precision was not sufficient to distinguish the small difference between the concentration dependencies in (11) and (13), especially considering that both A and J were unknown. In order to solve the paradox, the present author treated the experimental data of the Kharkov group using his theory [18].…”

“…If the temperature is small enough (the exact conditions will be derived below) the number of phonons is negligible, and the defecton free path is controlled by defecton-defecton interaction. Defecton-defecton scattering possesses a series of peculiarities relevant to the energy band width [1,18,19,2]. First of all, the quasiparticle energy cannot vary during the motion more than the energy band width ∆.…”

“…Due to the small value of the defecton band width large regions around the impurities are unscalable for quasiparticles [1,19]. Their linear size R 0 may be estimated from the equation…”

“…by means of nuclear magnetic resonance (NMR) [10]. [2,11]. The degeneracy temperature T 0 is extremely small:…”