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Nonlinear nonextensive kinetics and quantum mechanics

A. Lavagno, G. Gervino

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

On the basis of generalized classical kinetic equations, reproducing the sta- tionary distribution of the Tsallis nonextensive thermostatistics, we postulate a nonlinear generalized Schroedinger equation. Such a dynamical equation satisfies the basic assumptions of the quantum mechanics under an appropriate generalization of the operator properties. In this framework, we apply the above introduced classical nonlinear equation to a phenomenological study of observable measured in the relativistic heavy-ion collisions experiments.

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On the basis of generalized classical kinetic equations, reproducing the sta- tionary distribution of the Tsallis nonextensive thermostatistics, we postulate a nonlinear generalized Schroedinger equation. Such a dynamical equation satisfies the basic assumptions of the quantum mechanics under an appropriate generalization of the operator properties. In this framework, we apply the above introduced classical nonlinear equation to a phenomenological study of observable measured in the relativistic heavy-ion collisions experiments.
On the basis of generalized classical kinetic equations, reproducing the stationary distribution of the Tsallis nonextensive thermostatistics, we formulate two generalized Schr¨odinger equations which satisfy the basic assumptions of the quantum mechanics under an appropriate generalization of the operator properties. Moreover, we study the generalization of the previously introduced dynamic equations in a relativistic regime and we apply our results to the study of the rapidity distribution in the relativistic heavy-ion collisions.
The traditional basis of description of the many-particle systems in terms of the Green functions is here generalized when the system is nonextensive by incorporating the Tsallis form of the density matrix, indexed by a nonextensive parameter, qqq. This extension enables us to predict possible experimental tests for the validity of this framework by expressing some observable quantities in terms of the qqq averages.
All measurable predictions of classical mechanics can be reproduced from a quantum‐like interpretation of a nonlinear Schrödinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical‐like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics.
In this thesis, we discussed the derivation of quantum kinetic equations appropriate for applications in nuclear physics, both in a non-relativistic and in a relativistic context. In each case we obtained a kinetic equation together with an equation for the effective interaction. The latter serves as the dynamical input of the former. In the kinetic equation both mean-field and collision effects are described in a self-consistent way because both are expressed in terms of the effective interaction. This self-consistency enforces us to solve a statistical problem (kinetic equation) and a dynamical problem (effective interaction) simultaneously. The interaction, that we obtained as a result of our considerations, is a generalized version of the usual Brueckner G-matrix in the sense that single-particle energies are corrected for collision effects by the so called rearrangement-term. 0nly in this way kinetic theory and interaction are consistent with one another and therefore constitute a conserving approximation.... Zie epilogue
Using the general framework of nonequilibrium statistical mechanics for relativistic quantum field systems we derive the basic equations of quantum field kinetics. The main aim of the approach is calculation of observables associated with quark-gluon plasma which is out of thermal and chemical equilibrium. We show that in the regime of high rate of the phase and statistical mixing the perturbation theory for many-body quantum field system should have the form which much differs from the standard expansion in powers of coupling constant. ( Figures can be obtained from the author )