Entropic Lower Bound for the Quantum Scattering of Spinless Particles

Abstract

In this paper the angle-angular momentum entropic lower bound is proved by using Tsallis-like entropies and Riesz theorem for the quantum scattering of the spinless particles. Numerical estimations of the scattering entropies, as well as an experimental test of the state-independent entropic lower bound, are obtained by using the amplitude reconstruction from the available phase shift analyses for the pionnucleus scatterings. A standard interpretation of these results in terms of the optimal state dominance is presented. Then, it is shown that experimental pion-nucleus entropies are well described by optimal entropies and that the experimental data are consistent with the principle of minimum distance in the space of scattering states. [S0031-9007 (98)08033-8] PACS numbers: 03.65.Ca, 25.80.DjOver the past two decades there has been increasing interest [1] in the investigation of the entropic uncertainty relations introduced in Ref. [2]. In this paper the entropic lower bound for the quantum scattering [3] is investigated in a more general form by introducing Tsallis-like entropies (see Refs. [4,5]). Hence, by using Riesz theorem [6], the state-independent angle-angular momentum entropic lower bound is proved for the scattering of spinless particles. The results on the first experimental test of this state independent entropic bound in pion-nucleus scattering are obtained by calculations of the scattering entropies from the experimental available phase shifts [7][8][9][10][11]. Moreover, comparisons of these results with the optimal state [12] prediction are presented.Angular entropy S u .-The informational angular entropy

Optimal Bounds for Tsallis-like Entropies in Quantum Scattering

“…[1]) in the investigation of quantum entropy not only by proving new entropic uncertainty relations (see, e.g., Refs. [1][2][3][4]) for the standard additive system but also by a generalization of such results to nonextensive statistics [5][6][7][8]. In Ref.…”

“…Using Tsallislike entropies and the Riesz theorem [9] in Ref. [4], the state independent angle-angular momentum entropic lower bounds were proved for the quantum scattering of the spinless particles. Then, it was shown that the experimental pion-nucleus scattering entropies are well described by the optimal entropies corresponding to the optimal states which were introduced in Ref.…”

“…Also, in Refs. [3,4], it was suggested that extremal properties of entropy, such as maximum entropy, can be important for the characterization of the optimal states derived from the principle of minimum distance in the space of states (Ref.[10]).In this Letter, we report the results on the investigation of some fundamental physical questions concerning entropic bounds, once the basic experimental information is fixed and used as constraints in the variational procedure. The optimal entropic upper bounds are proved by using the Lagrange multipliers method and Tsallis-like entropies [5] for quantum scattering of spinless particles.…”

I. Nonextensive Statistical Mechanics and Thermodynamics: Historical Background and Present Status

“…We refer to (i) Linear response theory [94]; (ii) Perturbation expansion [113]; (iii) Variational method (based on the Bogoliubov inequality) [113]; (iv) Many-body Green functions [114]; (v) Path integral and Bloch equation [115], as well as related properties [116]; (vi) Dynamical themostatting for the canonical ensemble [117]; (vii) Simulated annealing and related optimization, Monte Carlo and Molecular dynamics techniques [118][119][120][121][122][123][124][125][126][127][128][129]; (viii) Information theory and related issues (see [43,74,130,131] and references therein); (ix) Entropic lower and upper bounds [132][133][134] (related to Heinberg uncertainty principle); (x) Quantum statistics [135] and those associated with the Gentile and the Haldane exclusion statistics [136,137]. In particular, Fermi-Dirac and Bose-Einstein (escort) distributions could be generalizable as follows…”

Nonextensive statistical effects on the relativistic nuclear equation of state

“…In particular, recently, many authors outline the possible connection to the nonextensive statistical framework with nuclear and high energy physical applications [2,3,4,5,6,7]. The aim of this work is to generalize the basic concepts of the nonextensive statistical mechanics to the relativistic regime and to investigate, through the obtained relativistic thermodynamic relations, the relevance of nonextensive statistical effects on the hadronic and on the quark-gluon plasma (QGP) equation of state (EOS).…”