Description of quantum scattering via principle of minimum distance in the space of states

Ion, D.B.

doi:10.1016/0370-2693(96)00285-7

Cited by 10 publications

(16 citation statements)

References 27 publications

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“…2, we see that the experimental values of ͑S u , S L ͒ entropies for the pion-nucleus scatterings are systematically described by the optimal entropies ͑S o1 u , S o1 u ͒ at all available pion kinetic energies. In this sense the results obtained here can also be considered as new experimental signatures for the validity of the principle of minimum distance in space of scattering states even in the crude form [12].…”

Section: Institute Of Atomic Physics Bucharest-magurele Romaniamentioning

confidence: 58%

“…This result allows us to conclude that the opti- mal state (26) from Ref. [12] is the state of equilibrium of the angular momenta channels considered as a quantum statistical ensemble. Hence, the optimal angular distribution P o1 ͑x͒ ͓K͑x, 1͔͒ 2 ͞K͑1, 1͒ can be considered as a signature of this equilibrium distribution of the L channels.…”

Section: Institute Of Atomic Physics Bucharest-magurele Romaniamentioning

confidence: 60%

“…Therefore, the index q fi 1 controls the degree of entropy nonextensivity reflected in the pseudoadditivity entropy rule (12). Entropic inequalities.-It is interesting to present here the following generalized entropic inequalities for the Tsallis-like entropies.…”

Section: Institute Of Atomic Physics Bucharest-magurele Romaniamentioning

confidence: 99%

“…(22) and (23) of Ref. [12]. The values of optimal ͑S o1 u , S o1 L ͒, entropies for the scattering of spinless particles, are obtained by numerical integration and direct, respectively, and are presented in Table I only for 0 # L 0 # 12.…”

Section: Institute Of Atomic Physics Bucharest-magurele Romaniamentioning

confidence: 99%

“…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 …”

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Entropic Lower Bound for the Quantum Scattering of Spinless Particles

Ion

1998

Phys. Rev. Lett.

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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

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Section: Institute Of Atomic Physics Bucharest-magurele Romaniamentioning

confidence: 58%

Section: Institute Of Atomic Physics Bucharest-magurele Romaniamentioning

confidence: 60%

Section: Institute Of Atomic Physics Bucharest-magurele Romaniamentioning

confidence: 99%

Section: Institute Of Atomic Physics Bucharest-magurele Romaniamentioning

confidence: 99%

mentioning

confidence: 99%

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Entropic Lower Bound for the Quantum Scattering of Spinless Particles

Ion

1998

Phys. Rev. Lett.

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Nonextensive quantum statistics and saturation of the PMD-SQS optimality limit in hadron–hadron scattering

Ion

2004

Physica A: Statistical Mechanics and its Applications

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In this paper, new results on the analysis in hadron-hadron scattering (πN , KN , KN , etc) are obtained by using the nonextensive quantum entropy and principle of minimum distance in the space of quantum states (PMD-SQS). So, using [SJ (p), S θ (q), S J θ (p), S J θ (p, q)]-Tsallis-like scattering entropies, the optimality as well as the nonextensive statistical behavior of the [J and θ]-quantum systems of states produced 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) [17] and the most stringent (Max-Ent) entropic bounds on Tsallis-like entropies for quantum scattering, is established. The generalized entropic uncertainty relations as well as the correlation between the nonextensivities p and q of the [J and θ]-statistics are proved. New results on the experimental tests of the saturation of the PMD-SQS-optimality limit, as well as on the test of optimal entropic bands obtained by using the experimental pion-nucleon, kaon-nucleon, antikaon-nucleon phase shifts, are presented. The nonextensivity indices p and q are determined from the experimental entropies by a fit with the optimal entropies [S o1 J (p), S o1 θ (q), S o1 J θ (p, q)]] obtained from the principle of minimum distance in the space of states. In this way strong experimental evidences for the p−nonextensivities index in the range p = 0.6 with q = p/(2p − 1) = 3, is obtained from the experimental data of the (πN, KN, KN )-scattering. The experimental evidence obtained here for the nonextensive statistical behavior of the (J, θ)−quantum scatterings states in the above hadron-hadron scattering can be interpreted as an indirect manifestation of the presence of the quarks and gluons as fundamental constituents of the scattering system having the strong-coupling long-range regime required by the Quantum Chromodynamics.

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Limited entropic uncertainty as new principle of quantum physics

Ion

2000

Physics Letters B

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Description of quantum scattering via principle of minimum distance in the space of states

Cited by 10 publications

References 27 publications

Entropic Lower Bound for the Quantum Scattering of Spinless Particles

Entropic Lower Bound for the Quantum Scattering of Spinless Particles

Nonextensive quantum statistics and saturation of the PMD-SQS optimality limit in hadron–hadron scattering

Limited entropic uncertainty as new principle of quantum physics

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