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Radiation effects and defects in solids

Wave propagation and landau-type damping in quantum liquids

Vincenzo G. Molinari, D. Mostacci

Published Feb 1, 2018• 0 citations
Publisher

Abstract

Starting from Bohm’s point of view on Quantum Mechanics, adopting the Bohm potential description, a Quantum Kinetic Equation can be derived. When molecular interactions are described as a self-consistent field, a Quantum Vlasov Equation (QVE) can be written. With this QVE, the evolution of a small perturbation can be described, yielding a wave propagation with or without a damping coefficient, depending on conditions. With this approach applied to a liquid of either fermions or bosons, the propagation of waves in quantum liquids is described.

DOI
10.1080/10420150.2018.1442457

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Starting from Bohm’s point of view on Quantum Mechanics, adopting the Bohm potential description, a Quantum Kinetic Equation can be derived. When molecular interactions are described as a self-consistent field, a Quantum Vlasov Equation (QVE) can be written. With this QVE, the evolution of a small perturbation can be described, yielding a wave propagation with or without a damping coefficient, depending on conditions. With this approach applied to a liquid of either fermions or bosons, the propagation of waves in quantum liquids is described.
Abstract Bohm’s interpretation of Quantum Mechanics leads to the derivation of a Quantum Kinetic Equation (QKE): in the present work, propagation of waves in charged quantum gases is investigated starting from this QKE. Dispersion relations are derived for fully and weakly degenerate fermions and bosons (for the latter above critical temperature) and the differences discussed. Use of a kinetic equation permits investigation of “Landau-type” damping: it is found that the presence of damping in fermion gases is dependent upon the degree of degeneracy, whereas it is always present in boson gases. In fully degenerate fermions a phenomenon appears that is akin to the “zero sound” propagation.
In Bohm's interpretation of Quantum Mechanics, quantum effects are governed by a “quantum potential” (known as Bohm potential), and particles follow definite trajectories. In the present work, Liouville's theorem is invoked, an appropriate Liouville equation is derived, and following the BBGKY method a quantum kinetic equation (QKE) is derived. To demonstrate the working of the QKE, two examples of application are presented: the thermal equilibrium of a quantum gas and the propagation of disturbances in a force free gas of non-interacting bosons. In contrast to the classical collisionless Boltzmann equation, waves are found to be possible in the absence of interaction or external forces, due only to Bohm potential (zero sound propagation).
From the quantum kinetic equation of Bogoliubov, Gurov, Born, and Green, the equations of motion for macroscopic variables are examined in many different ways. First, in the configuration space a hierarchy of generalized fluid-dynamical equations can be obtained by taking the appropriate limits of the quantum kinetic equation. The resultant equations of continuity, of momentum, and of energy are similar in form to those one encounters in classical fluid dynamics with the exception of additional terms proportional to ${\ensuremath{\hbar}}^{2}$ Secondly, the quantum kinetic equation is examined in phase space. The same set of equations of continuity, of momentum, and of energy can be derived by taking the first three moments of the quantum kinetic equation. The exact results we obtained are utilized to form the starting point for many simplifying approximations for the investigation of the dynamics of quantum many-body systems such as the elastic response limit, the hydrodynamical limit, Landau's Fermi-liquid theory, and finally the time-dependent Hartree-Fock and the multideterminant time-dependent Hartree-Fock approximations. The fact that all these different dynamical descriptions can be traced to a common origin provides a unifying viewpoint to the present approach with the quantum kinetic equation.NUCLEAR STRUCTURE Dynamics of nuclear fluid, quantum kinetic equation, and generalized fluid-dynamical equation. Elastic response, hydrodynamical limit, Landau's Fermi-liquid theory, time-dependent Hartree-Fock approximation, and multideterminant time-dependent Hartree-Fock approximation.