The Effective Mass of an Impurity Atom in the Bose Liquid with a Deformed Heisenberg Algebra

Abstract

We consider the movement of a 3 He impurity atom in the Bose liquid. We suggest to describe the many-particle correlations between atoms of the Bose liquid, by using a deformed Heisenberg algebra. As generalized coordinates, we choose the collective variables that are the Fourier components of fluctuations of the density of Bose particles. The wave function of the investigated system in the zeroth approximation is the product of the wave function of the liquid helium-4 within deformed commutation relations between generalized coordinates and momenta and the plane wave of the impurity atom. We calculate the correction to the groundstate energy of the system "Bose liquid plus impurity" and the effective mass of the impurity atom 3 He, by assuming that the boson-impurity interaction is a small perturbation. K e y w o r d s: boson systems, deformed Heisenberg algebra, effective mass.

Behavior of the impurity atom in a weakly-interacting Bose gas

“…The author showed that the interaction potential between the Bose particles and the impurity atom can be expressed as a function of the structure factor of the liquid 4 He. In the work [19], using a deformed Heisenberg algebra, the effective mass and the separation energy of the impurity atom 3 He for different values of the density of 4 He is calculated. …”

Ideal Bose Gas in Some Deformed Types of Thermodynamics. Correspondence between Deformation Parameters

“…In effect, this approach, which consists in the application of nonstandard statistics to effectively model real physical systems, is the main motivation for studying various ways to modify quantum distributions [4][5][6][7][8]. Both the effective consideration of the interaction between particles [9,10] and cosmological models [11,12] can be taken as examples. As a result, it often becomes possible to describe complicated physical phenomena with the help of a simpler mathematical apparatus, which is especially important while studying many-particle systems.…”