Irreversible quantum hydrodynamics from kinetic theory

Antonio Boulhosa Nassar

Massimo Tessarotto, Marco Ellero, Piero Nicolini

A remarkable feature of standard quantum mechanics is its analogy with classical fluid dynamics. This has motivated in the past efforts to formulate phase-space techniques based on various statistical models of quantum hydrodynamic equations. In this work an inverse kinetic theory for the Schr\"odinger equation has been constructed in order to formally describe the standard quantum dynamics by means of a classical dynamical system (to be denoted as phase-space Schr\"odinger dynamical system). It is shown that the inverse kinetic theory can be (non)uniquely determined under suitable mathematical prescriptions. In particular, when the quantum linear momentum is identified with a suitable linear kinetic momentum, it follows that the fluctuations of the position vector and the kinetic linear momentum satisfy identically the Heisenberg theorem.

Moise Bonilla–Licea, Dieter Schuch

Boris V. Alexeev

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

Makoto Tsubota, Michikazu Kobayashi, Hiromitsu Takeuchi

Christophe Josserand, Yves Pomeau A

The study of imperfect Bose gases provides an opportunity to understand how irreversibility arises in superflows, as it is a unique dynamical model where hydrodynamics can be related in a rational way to microscopic quantum dynamics. Over the years various specific problems have been investigated in this field, all with interesting implications in nonlinear science. Within the framework of kinetic theory we first review the way the condensate appears - an interesting example of finite-time blow-up of solutions of a nonlinear equation, with exponents derived from a nonlinear eigenvalue problem. Then we examine how the presence of the condensate changes the kinetic theory - something that is not yet fully understood. Finally, we look at the phenomenon of vortex nucleation and release in a model of superflow. This interesting example of a transonic transition can be analysed by solving locally the equation of compressible (super)fluid mechanics near the elliptic/hyperbolic transition.