A Study On The Distinguishability Of Bosons In Harmonic Trap At High Temperature

The theoretical and experimental physics research of Bose--Einstein condensation is a hot research area. It relates to many sub-fields of physics,from fundamental to applied,covering the atomic and molecular physics, quantum optics, statistical physics and condensed matter physics, and so on. Along with the progress of the experiments on the Bose--Einstein condensation,the sutble nature of the physics world will be gradually understood.In 1999, a study on entropy of a harmonic oscillator system indicated that, the extensiveness of the entropy within classical statistical mechanics may be destroyed. We analyse this puzzle, and propose that if the harmonic oscillator can be distinguishable at high temperature. If so, the difficulty does not present anymore. This is the first innovative point of the article.Bose-Einstein condensation of Bose gas in harmonic trap is widely studied, but very few people pay attention to the situation at high temperature. In this paper, through the research of one-dimensional bose gas in the harmonic trap show that, in high temperature, the difficulty of non-extensive entropy will appear. No one before has studied this problem. In the statistical theory of free particles, the entropy of the classical theory is non-extensive. It becomes extensive once quantum statistics mechiacs is utilized. In contrast, harmonic oscillators at low temperatures can be indistinguishable, but in high temperatures it can be distinguishable, otherwise extensive entropy will be destroyed. We believe that the Bose gas in harmonic trap at high temperatures can be distinguishable; the fundamental reason is the difference of their amplitudes. This is the main result of the paper, and is also the second innovation of this study.Reference to a Bose gas entropy change measurement experiment reported in 2009 in harmonic trap, we sketch an experimental method to verify the correctness of our results. This is the third innovation points of the study.Entropy is a fundamental physical quantity. The nature of the entropy of bose gas in harmonic trap shows some very important and specific natures. Studying this issue will undoubtedly deepen our understanding of thermodynamics, statistical physics and so on. In this paper, through the study of extensiveness of entropy for one-dimensional bose gas in harmonic trap under high temperature, we firstly point out an intriguing nature that is different from the that of ideal gas entropy, and the micro-particles at high temperatures can not always be indistinguishable, we gives an experimental method to test our result.