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Journal of Nanoelectronics and Optoelectronics

Application of Generalized Quantum Hydrodynamics in the Theory of Quantum Soliton's Evolution

Boris V. Alexeev

Published Dec 1, 2008• 23 citations
Publisher

Abstract

Quantum solitons are discovered with the help of generalized quantum hydrodynamics. The solitons have the character of the stable quantum objects in the self consistent electric field. Particularly 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 theory leads to solitons as typical formations in the generalized quantum hydrodynamics.

DOI
10.1166/jno.2008.311

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Quantum solitons are discovered with the help of generalized quantum hydrodynamics. The solitons have the character of the stable quantum objects in the self consistent electric field. Particularly 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 theory leads to solitons as typical formations in the generalized quantum hydrodynamics.
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
We show that the equations of generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, emerge in full generality in a family of classical gases, which generalize the gas of hard rods. In this family, the particles, upon colliding, jump forward or backward by a distance that depends on their velocities, reminiscent of classical soliton scattering. This provides a "molecular dynamics" for GHD: a numerical solver which is efficient, flexible, and which applies to the presence of external force fields. GHD also describes the hydrodynamics of classical soliton gases. We identify the GHD of any quantum model with that of the gas of its solitonlike wave packets, thus providing a remarkable quantum-classical equivalence. The theory is directly applicable, for instance, to integrable quantum chains and to the Lieb-Liniger model realized in cold-atom experiments.
Abstract We establish the explicit correspondence between the theory of soliton gases in classical integrable dispersive hydrodynamics, and generalized hydrodynamics (GHD), the hydrodynamic theory for many-body quantum and classical integrable systems. This is done by constructing the GHD description of the soliton gas for the Korteweg–de Vries equation. We further predict the exact form of the free energy density and flux, and of the static correlation matrices of conserved charges and currents, for the soliton gas. For this purpose, we identify the solitons’ statistics with that of classical particles, and confirm the resulting GHD static correlation matrices by numerical simulations of the soliton gas. Finally, we express conjectured dynamical correlation functions for the soliton gas by simply borrowing the GHD results. In principle, other conjectures are also immediately available, such as diffusion and large-deviation functions for fluctuations of soliton transport.
Quantum hydrodynamic equations are used to describe motion of single electron. The initial and boundary conditions are formulated from the analytic formula for the electron packet in a free space. The numerical integration of equations for the free packet is performed. Then, we investigated the wave packet propagation through the back-ground positive charge, when the electric field is self-consistent. Moreover, we studied the influence of the external harmonic electric fields on the properties of the motion. The purpose of the present work consists in study of the spatial-temporal processes including packets when the quantum wave effects are essential.
During the past decade, a number of attempts to formulate a continuum description of complex states of matter have been proposed to circumvent more cumbersome many-body and simulation methods.Typically, these have been quantum systems (e.g., electrons) and the resulting phenomenologies collectively often called "quantum hydrodynamics."However, there is extensive work from the past based in nonequilibrium statistical mechanics on the microscopic origins of macroscopic continuum dynamics that has not been exploited in this context.Although formally exact, its original target was the derivation of Navier-Stokes hydrodynamics for slowly varying states in space and time.The objective here is to revisit that work for the present interest in complex quantum states-possible strong degeneracy, strong coupling, and all space-time scales.The result is an exact representation of generalized hydrodynamics suitable for introducing controlled approximations for diverse specific cases and for critiquing existing work.
Abstract We give a pedagogical introduction to the generalized hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of the theory. Finally, we present some open questions and suggest perspectives on possible future directions.