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Journal of Northeast Normal University

The interaction between contaminants in ideal Bose-Einstein condensates for periodic boundary condition

Zheng Tai-Yu

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

In this paper the interaction between contaminants of the Ideal Bose-Einstein condensed system for periodic boundary condition is discussed by using Riemann zeta function.The force between the contaminants are obtained,the relationship of the force with distance is also discussed.Our result shows that the larger the distance between contaminants is,the smaller the Casimir force is.

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Annalen der Physik•Jul 1, 2020•7 citations
In this paper the interaction between contaminants of the Ideal Bose-Einstein condensed system for periodic boundary condition is discussed by using Riemann zeta function.The force between the contaminants are obtained,the relationship of the force with distance is also discussed.Our result shows that the larger the distance between contaminants is,the smaller the Casimir force is.
In this paper the interaction between contaminants of the Bose-Einstein condensed system at finite temperature is discussed by using the Thermal Field Dynamics.The system energy and Casimir force between the contaminants are obtained,the relationship of the force with temperature and distance is also discussed.These results will help us further understand the physical effect of contaminants in the Bose-Einstein condensed body and provide certain reference value to Casimir effect and the Bose-Einstein condensation experimental study.
It is hypothesized that, within Bose-Einstein condensates, contaminants will form a potential that effects the energy state of a condensate. While assuming a system governed by the Gross-Pitaevskii equation, contaminants are modelled as boundary conditions for the wave function of the condensate. It is then found that the energy of the system depends directly upon the distance between contaminants. Energy is minimized as two particles either come together or move apart depending on the nature of the condensate. This is due to the presence of induced standing waves in the condensate between two contaminants, similar to the attractive effect caused by standing electromagnetic waves in a vacuum, the Casimir effect. Quantum calculations are also done to determine the expected strength of the "contaminant in condensate" effect.
Abstract We study the Casimir effect for a three dimensional system of ideal free massive Bose gas in a slab geometry with Zaremba and anti-periodic boundary conditions. It is found that for these type of boundary conditions the resulting Casimir force is repulsive in nature, in contrast with usual periodic, Dirichlet or Neumann boundary condition where the Casimir force is attractive (Martin and Zagrebnov 2006 Europhys. Lett. 73 15). Casimir forces in these boundary conditions also maintain a power law decay function below condensation temperature and exponential decay function above the condensation temperature albeit with a positive sign, identifying the repulsive nature of the force.
The Casimir effect of an ideal Bose gas trapped in a generic power-law potential and confined between two slabs with Dirichlet, Neumann, and periodic boundary conditions is investigated systematically, based on the grand potential of the ideal Bose gas, the Casimir potential and force are calculated. The scaling function is obtained and discussed. The special cases of free and harmonic potentials are also discussed. It is found that when T ⩽ T c (where T c is the critical temperature of Bose-Einstein condensation), the Casimir force is a power-law decay function; when T > T c , the Casimir force is an exponential decay function; and when T ≫ T c , the Casimir force vanishes.
Abstract In this study, ideal free and harmonically trapped Bose gases confined by two plates in the x–y‐plane in‐between distance d are considered. The Casimir potential is obtained from the grand canonical potential of these quantum Bose gases for the Zaremba and the anti‐periodic boundary conditions. The Casimir force is then obtained for the Bose–Einstein condensate phase and for the non‐condensate phase . It is shown that Casimir forces are repulsive for these boundary conditions. Additionally, it is shown that Casimir forces exponentially decay in the non‐condensate phase with the decay lengths. These decay lengths were discussed and compared for different boundary conditions. As a result, new results are obtained for harmonically trapped Bose gas and the free gas results are compared with previous results.