Do bosons obey Bose-Einstein distribution: two iterated limits of Gentile distribution - Condensed Matter > Statistical MechanicsReport as inadecuate




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Abstract: It is a common impression that by only setting the maximum occupation numberto infinity, which is the demand of the indistinguishability of bosons, one canachieve the statistical distribution that bosons obey - the Bose-Einsteindistribution. In this letter, however, we show that only with an infinitemaximum occupation number one cannot uniquely achieve the Bose-Einsteindistribution, since in the derivation of the Bose-Einstein distribution, theproblem of iterated limit is encountered. For achieving the Bose-Einsteindistribution, one needs to take both the maximum occupation number and thetotal number of particles to infinities, and, then, the problem of the order oftaking limits arises. Different orders of the limit operations will lead todifferent statistical distributions. For achieving the Bose-Einsteindistribution, besides setting the maximum occupation number, we also need tostate the order of the limit operations.



Author: Wu-Sheng Dai, Mi Xie

Source: https://arxiv.org/







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