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arXiv · 1511.08720

New mathematics for the non additive Tsallis' scenario

G. L. Ferri·F. Pennini·A. Plastino·M. C. Rocca
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Abstract

In this manuscript we investigate quantum uncertainties in a Tsallis' non additive scenario. To such an end we appeal to q-exponentials, that are the cornerstone of Tsallis' theory. In this respect, it is found that some new mathematics is needed and we are led to construct a set of novel special states that are the q-exponential equivalents of the ordinary coherent states of the harmonic oscillator. We then characterize these new Tsallis' special states by obtaining the associated i) probability distributions for a state of momentum $k$, ii) mean values for some functions of space an momenta, and iii) concomitant quantum uncertainties. The latter are then compared to the usual ones.

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G. L. Ferri, F. Pennini, A. Plastino, M. C. Rocca. 2015-11-27. New mathematics for the non additive Tsallis' scenario. https://arxiv.org/abs/1511.08720

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