We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential.By taking into account the conservation of the total number N of particles an...We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential.By taking into account the conservation of the total number N of particles and using a saddle-point approximation,we derive analytically the simple explicit expression of mean occupation number in any state of the finite system.The temperature dependence of the chemical potential,specific heat,and condensate fraction for the trapped finite-size Bose system is obtained numerically.We compare our results with the usual treatment which is based on the grand canonical ensemble.It is shown that there exists a considerable difference between them at sufficiently low temperatures,especially for the relative small numbers of Bose atoms.The finite-size scaling at the transition temperature for the harmonically trapped systems is also discussed.We find that the scaled condensate fractions for various system sizes and temperatures collapse onto a single scaled form.展开更多
We investigate the thermodynamic properties of an ideal charged Bose gas confined in an anisotropic harmonic potential and a constant magnetic field. Using an accurate density of states, we calculate analytically the ...We investigate the thermodynamic properties of an ideal charged Bose gas confined in an anisotropic harmonic potential and a constant magnetic field. Using an accurate density of states, we calculate analytically the thermodynamic potential and consequently various intriguing thermodynamic properties, including the Bose–Einstein transition temperature, the specific heat, magnetization, and the corrections to these quantities due to the finite number of particles are also given explicitly. In contrast to the infinite number of particles scenarios, we show that those thermodynamic properties,particularly the Bose–Einstein transition temperature depends upon the strength of the magnetic field due to the finiteness of the particle numbers, and the collective effects of a finite number of particles become larger when the particle number decreases. Moreover, the magnetization varies with the temperature due to the finiteness of the particle number while it keeps invariant in the thermodynamic limit N →∞.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775032 and 10574028)
文摘We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential.By taking into account the conservation of the total number N of particles and using a saddle-point approximation,we derive analytically the simple explicit expression of mean occupation number in any state of the finite system.The temperature dependence of the chemical potential,specific heat,and condensate fraction for the trapped finite-size Bose system is obtained numerically.We compare our results with the usual treatment which is based on the grand canonical ensemble.It is shown that there exists a considerable difference between them at sufficiently low temperatures,especially for the relative small numbers of Bose atoms.The finite-size scaling at the transition temperature for the harmonically trapped systems is also discussed.We find that the scaled condensate fractions for various system sizes and temperatures collapse onto a single scaled form.
基金supported by the National Natural Science Foundation of China(Grant No.11375090)the K.C.Wong Magna Foundation of Ningbo University,China
文摘We investigate the thermodynamic properties of an ideal charged Bose gas confined in an anisotropic harmonic potential and a constant magnetic field. Using an accurate density of states, we calculate analytically the thermodynamic potential and consequently various intriguing thermodynamic properties, including the Bose–Einstein transition temperature, the specific heat, magnetization, and the corrections to these quantities due to the finite number of particles are also given explicitly. In contrast to the infinite number of particles scenarios, we show that those thermodynamic properties,particularly the Bose–Einstein transition temperature depends upon the strength of the magnetic field due to the finiteness of the particle numbers, and the collective effects of a finite number of particles become larger when the particle number decreases. Moreover, the magnetization varies with the temperature due to the finiteness of the particle number while it keeps invariant in the thermodynamic limit N →∞.
