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arXiv:1909.01256 · Journal of Physics A Mathematical and Theoretical

Two- and three-body effective potentials between impurities in ideal BEC

G. Panochko, V. Pastukhov

Published Jan 14, 2021• 28 citations
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Abstract

Abstract We exactly calculate the full temperature dependence of Casimir-like forces appearing between two and three static impurities loaded in the ideal Bose gas below the Bose–Einstein condensation transition point. Assuming the short-ranged character of the boson-impurity interaction, the calculation procedure presented here can be easily extended on a Bose system with an arbitrary number of impurities immersed.

DOI
10.1088/1751-8121/abdbc5

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BEC in Nonextensive Statistical Mechanics: Some Additional Results

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In a recent paper [Int. J. Mod. Phys. B 14, 405 (2000)] we discussed the Bose-Einstein condensation (BEC) in the framework of Tsallis’s nonextensive statistical mechanics. In particular, we studied an ideal gas of bosons in a confining harmonic potential. In this memoir we generalize our previous analysis by investigating an ideal Bose gas in a generic power-law external potential. We derive analytical formulas for the energy of the system, the BEC transition temperature and the condensed fraction. PACS numbers: 05.30-d; 03.75.Fi 1 Recently we analyzed the consequences of weak nonextensivity on Bose-Einstein Condensation for an ideal Bose gas 1 by using Tsallis’s nonextensive statistical mechanics (NSM). 2 From the nonextensive Bose-Einstein distribution 3−5 we derived the BEC transition temperature, the condensed fraction and the energy per particle in three different cases: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. In this short contribution we generalize our previous results by considering the ideal Bose gas in a generic power-law potential. All the calculations are performed by assuming a D-dimensional space. The NSM predicts that, for an ideal quantum gas of identical bosons in the grand canonical ensemble, the weak nonextensivity formula of the average number of particles with energy ǫ is given by 〈n(ǫ)〉q = 1

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Abstract We exactly calculate the full temperature dependence of Casimir-like forces appearing between two and three static impurities loaded in the ideal Bose gas below the Bose–Einstein condensation transition point. Assuming the short-ranged character of the boson-impurity interaction, the calculation procedure presented here can be easily extended on a Bose system with an arbitrary number of impurities immersed.
We consider two heavy particles immersed in a Bose-Einstein condensate in three dimensions and compute their mutual interaction induced by excitations of the medium. For an ideal Bose gas, the induced interaction is Newtonian up to a shift in distance, which depends on the coupling strength between impurities and Bosons. For a real BEC, we find that, on short distances, the induced potential is dominated by three-body physics of a single Boson bound to the impurities, leading to an Efimov potential. At large distances of the order of the healing length, a Yukawa potential emerges instead. In particular, we find that both regimes are realized for all impurity-boson couplings and determine the corresponding crossover scales. The transition from the real to the ideal condensate at low gas parameters is investigated.
Abstract We consider two pointlike static impurities without direct interaction immersed in a three-dimensional Bose–Einstein condensate (BEC) at zero temperature. By solving the Gross–Pitaevskii (GP) equation in a perturbative manner, we calculate the ground state energy in the region where the atom–impurity interaction is assumed to be weak. We obtain an analytical expression for the spatial distribution of atom number density and the effective force between these two impurities. The effective force is found to be closely related to the strength of the atom–impurity interaction and the relative distance between these two impurities. Two critical relative distances are found between the two impurities. The first one corresponds to the vanishing of the perturbed energy with impurities, although the effective force between the two impurities still exists. At the second critical value, the energy of the impurities changes linearly with the atom–impurity interaction; otherwise, it changes quadratically with the atom–impurity interaction.
In a recent paper [Int. J. Mod. Phys. B 14, 405 (2000)] we discussed the Bose-Einstein condensation (BEC) in the framework of Tsallis’s nonextensive statistical mechanics. In particular, we studied an ideal gas of bosons in a confining harmonic potential. In this memoir we generalize our previous analysis by investigating an ideal Bose gas in a generic power-law external potential. We derive analytical formulas for the energy of the system, the BEC transition temperature and the condensed fraction. PACS numbers: 05.30-d; 03.75.Fi 1 Recently we analyzed the consequences of weak nonextensivity on Bose-Einstein Condensation for an ideal Bose gas 1 by using Tsallis’s nonextensive statistical mechanics (NSM). 2 From the nonextensive Bose-Einstein distribution 3−5 we derived the BEC transition temperature, the condensed fraction and the energy per particle in three different cases: the homogeneous gas, the gas in a harmonic trap and the relativistic homogenous gas. In this short contribution we generalize our previous results by considering the ideal Bose gas in a generic power-law potential. All the calculations are performed by assuming a D-dimensional space. The NSM predicts that, for an ideal quantum gas of identical bosons in the grand canonical ensemble, the weak nonextensivity formula of the average number of particles with energy ǫ is given by 〈n(ǫ)〉q = 1