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Modern Physics Letters B

BOSE–EINSTEIN CONDENSATION OF A RELATIVISTIC IDEAL BOSE GAS IN RANDOM BOX

Hong Li, Ying Wang, Xiang-Mu Kong, Lin Zhen-Quan

Published Apr 19, 2012• 0 citations
Publisher

Abstract

Using semi-classical approximation method, the Bose–Einstein condensation (BEC) of a relativistic ideal boson gas (RIBG) in random box is studied. The exact BEC transition temperature Tc and Helmholtz free energy at Tc are derived. The phase diagrams in the (Δ, T) plane are obtained, where Δ is the fluctuation of the box length and T is the temperature of the system. We find that Tc is lowered by the presence of the quenched disorder caused by the random boundary conditions. The effects of antibosons on the RIBG are also studied and it is found that the Helmholtz free energy of the system with antibosons at Tc is lower than that of the system without antibosons. This implies that the omission of antibosons always leads to a metastable state.

DOI
10.1142/s0217984912500753

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Using semi-classical approximation method, the Bose–Einstein condensation (BEC) of a relativistic ideal boson gas (RIBG) in random box is studied. The exact BEC transition temperature Tc and Helmholtz free energy at Tc are derived. The phase diagrams in the (Δ, T) plane are obtained, where Δ is the fluctuation of the box length and T is the temperature of the system. We find that Tc is lowered by the presence of the quenched disorder caused by the random boundary conditions. The effects of antibosons on the RIBG are also studied and it is found that the Helmholtz free energy of the system with antibosons at Tc is lower than that of the system without antibosons. This implies that the omission of antibosons always leads to a metastable state.
Using semiclassical approximation method, Bose-Einstein condensation (BEC) of a relativistic ideal boson gas (RIBG) with and without antibosons in three-dimensional (3-D) harmonic traps is investigated. The BEC transition temperature T_{c} and the Helmholtz free energy at T_{c} are calculated. The effect of the rest mass of the boson on the properties of the system is also studied. We find that T_{c} of RIBG is higher than that of the nonrelativistic approximation. The RIBG with antibosons is also investigated and it is found that the Helmholtz free energy of the system with antibosons at T_{c} is lower than that of the system without antibosons. It implies that the system with antibosons is more stable.
The q-deformed Bose–Einstein distribution is used to study the Bose–Einstein condensation (BEC) of a q-deformed Bose gas in random box. It is shown that the BEC transition temperature is lowered due to random boundary conditions. The effects of q-deformation on the properties of the system are also discussed. We find some properties of a q-deformed Bose gas, which are different from those of an ordinary Bose gas. Similar results are also shown for q-bosons confined in a harmonic oscillator potential well.
The Bose–Einstein condensation in the presence of quenched disorder due to random boundary conditions is considered. We have shown that for bosons confined in a box with volume Ld and for random L the Bose condensation temperature is lowered by the presence of disorder and the onset of condensation may even be completely prohibited. Similar results hold for bosons confined in a harmonic oscillator potential well, the geometry used in recent experiments on Bose–Einstein condensation in atomic traps. Comments on possible consequences of quenched disorder in boundary conditions for many fermion systems are also given.
The Bose-Einstein condensation of the Bose gas is studied in a d-dimensional random box.When the length of the box L satisfies the uniform and the Gauss distributions,the critical temperature of the Bose-Einstein condensation TC is obtained respectively.Compared with that of the rigid box TRC,we find that TC is not more than TRC,and their specific relations are depended on the given distribution functions.In the same way,the condensate problem is discussed for the Bose gas confined in a potential well of harmonic-oscillator,and harmonic trap frequency is a random variable.The similar results are obtained.
We investigate the thermodynamics of a self-interacting relativistic charged scalar field in the presence of weak disorder. We consider quenched disorder which couples linearly to the mass of the scalar field. After performing noise averages over the free energy of the system, we find that disorder increases the mean-field critical temperature for Bose–Einstein condensation at finite density in the ultrarelativistic limit. In turn, preliminary non-relativistic calculations indicate that the presence of randomness affects the Bose gas in the opposite way in such a limit, i.e. disorder reduces the mean-field condensation temperature. The effect of disorder on the temperature dependence of the chemical potential for a fixed charge density is investigated. Significant differences from the mean-field temperature dependence of the chemical potential are observed as the strength of the noise intensity increases. Finally, the temperature dependence of the chemical potential with fixed total charge and entropy is investigated. It is found that there is no Bose–Einstein condensation for a fixed charge to entropy ratio in the presence of weak disorder. The possible relevance of the findings in the present paper in different areas is discussed.