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arXiv:0709.0033 · Journal of Nanoelectronics and Optoelectronics

Generalized Quantum Hydrodynamics and Principles of Non-Local Physics

Boris V. Alexeev

Published Jul 1, 2008• 24 citations
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Abstract

This paper addresses the fundamental principles of generalized Boltzmann physical kinetics, as a part of non-local physics. It is shown that the theory of transport processes (including quantum mechanics) can be considered in the frame of unified theory based on the non-local physical description. The paper can be considered also as comments and prolongation of the materials published in the known author's monograph (Boris V. Alexeev, Generalized Boltzmann Physical Kinetics. Elsevier. 2004).

DOI
10.1166/jno.2008.207

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This paper addresses the fundamental principles of generalized Boltzmann physical kinetics, as a part of non-local physics. It is shown that the theory of transport processes (including quantum mechanics) can be considered in the frame of unified theory based on the non-local physical description. The paper can be considered also as comments and prolongation of the materials published in the known author's monograph (Boris V. Alexeev, Generalized Boltzmann Physical Kinetics. Elsevier. 2004).
We present basic equations of nonequilibrium thermo field dynamics of dense quantum systems. A formulation of nonequilibrium thermo field dynamics has been performed using the nonequilibrium statistical operator method by D.N.Zubarev. Generalized transfer and hydrodynamic equations of a consistent description of kinetics and hydrodynamics have been obtained in thermo field representation. To demonstrate how obtained results do work at the description of kinetics and hydrodynamics of a dense nuclear matter we consider quantum system with strongly coupled states.
Quantum solitons are discovered with the help of generalized quantum hydrodynamics (GQH). The solitons have the character of the stable quantum objects in the self consistent electric field. These effects can be considered as explanation of the existence of lightning balls. The delivered theory demonstrates the great possibilities of the generalized quantum hydrodynamics in investigation of the quantum solitons. The paper can be considered also as comments and prolongation of the materials published in the known author`s monograph (Boris V. Alexeev, Generalized Boltzmann Physical Kinetics. Elsevier. 2004). The theory leads to solitons as typical formations in the generalized quantum hydrodynamics. Key words: Foundations of the theory of transport processes; The theory of solitons; Generalized hydrodynamic equations; Foundations of quantum mechanics; The theory of lightning balls. PACS: 67.55.Fa, 67.55.Hc
A consistent approach to the description of kinetics and hydrodynamics of many-Boson systems is proposed.The generalized transport equations for strongly and weakly nonequilibrium Bose systems are obtained.Here we use the method of nonequilibrium statistical operator by D.N. Zubarev.New equations for the time distribution function of the quantum Bose system with a separate contribution from both the kinetic and potential energies of particle interactions are obtained.The generalized transport coefficients are determined accounting for the consistent description of kinetic and hydrodynamic processes.
Many-body theory stands at the foundation of modern quantum statistical mechanics. It is introduced here to graduate students in physics, chemistry, engineering and biology. The book provides a contemporary understanding of irreversibility, particularly in quantum systems. It explains entropy production in quantum kinetic theory and in the master equation formulation of non-equilibrium statistical mechanics. The first half of the book focuses on the foundations of non-equilibrium statistical mechanics with emphasis on quantum mechanics. The second half of the book contains alternative views of quantum statistical mechanics, and topics of current interest for advanced graduate level study and research. Unique to textbooks on this subject, this book contains a discussion of the fundamental Gleason theorem. Quantum entanglements are treated in application to quantum computation and the difficulties arising from decoherence. The relativistic generalization of the Boltzmann equation is derived, and modern transport applications to reservoir ballistic transport are developed.
The Boltzmann equation (BE) is a commonly used tool for the study of non-equilibrium many particle systems. It has been introduced in 1872 by Ludwig Boltzmann and has been widely generalized throughout the years. Today it is commonly used in physical applications, from the study of ordinary fluids to problems in particle Cosmology where Quantum Field Theoretical techniques are essential. Despite its numerous experimental successes, the conceptual basis of the BE is not entirely clear. For instance, it is well known that it is not a fundamental equation of physics like, say, the Heisenberg equation (HE). A natural question then arises whether it is possible to derive the BE from physical first principles, i.e. the Heisenberg equation in Quantum Field Theory. In this work we attempted to answer this question and succeeded in deriving the BE from the HE, thus further clarifying its conceptual status. In particular, the results we have obtained are as follows. Firstly, we establish the non-perturbative validity of what we call the "pre-Boltzmann equation". The crucial point here is that this latter equation is equivalent to the Heisenberg equation. Secondly, we proceed to consider various limits of the pre-Boltzmann equation, namly the "low density" and the "weak coupling" limits, to obtain two equations that can be considered as generalizations of the BE. These limits are always taken together with the "long time" limit, which allows us to interpret the BE as an appropriate long time limit of the HE. The generalization we obtain consists in additional "correction" terms to the usual Boltzmann collision factor, and can be associated to multiple particle scattering. Unlike the pre-Boltzmann equation, these latter results are only valid pertubatively. Finally, we briefly consider the possibility to extend these results beyond said limits and outline some important aspects in this case.