Optimality entropy and complexity in quantum scattering
200222 pages
Published in:
- Chaos Solitons Fractals 13 (2002) 547-568
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Abstract: (Elsevier)
In this paper, by introducing [ S J ( p ), S θ ( q )] Tsallis-like entropies , the optimality and complexities as well as the nonextensive statistical behavior of the [ J and θ ]- quantum states in hadronic scatterings are investigated in an unified manner. A connection between optimal states obtained from the principle of minimum distance in the space of quantum states (PMD-SQS) and the most stringent (MaxEnt) entropic bounds on Tsallis-like entropies for quantum scattering is established. A measure of the complexity of quantum scattering in terms of Tsallis-like entropies is proposed. The generalized entropic uncertainty relations as well as a possible correlation between the nonextensivities p and q of the [ J and θ ]-statistics are proved. The results on the experimental tests of the PMD-SQS-optimality , as well as on the optimal entropic bands and optimal complexity , obtained by using the experimental pion–nucleon pion–nucleus phase shifts, are presented. The nonextensivity indices p and q are determined from the experimental entropies by a fit with the optimal entropies [ S J o1 ( p ), S θ o1 ( q )] obtained from the principle of minimum distance in the space of states . In this way strong experimental evidences for the p -nonextensivities in the range 0.5⩽ p ⩽0.6 with q = p /(2 p −1)>3 are obtained [with high accuracy (CL>99%)] from the experimental data of pion–nucleon and pion–nucleus scatterings.References(0)
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