Wave propagation and “Landau-type” damping from Bohm potential

Abstract

From Bohm's interpretation of quantum mechanics, a quantum kinetic equation (QKE) can be derived. It is found that waves propagate in force-free gases of non interacting particles, only due to Bohm potential. In the present article the existence of Landau damping in such propagations is investigated. It is found that the Bohm potential alone gives indeed rise to a damping entirely analogous to the classical Landau damping, both for bosons and for weakly degenerate fermions.

Effect of Bohm potential on a charged gas

“…Inverse Laplace transformation of Eq. (16) is rather involved, however, it is not indispensable if interest is focused on the asymptotic solution for large t [7,[10][11][12][13]. Then the evolution is dominated by the rightmost zero of the denominator in Eq.…”

“…In a plasma, the above expression is the plasma frequency. Laplace antitransformation of ( 16) is rather involved, however it is not indispensable if interest is focused on the asymptotic solution for large t [10,11,12,13,7], for then the evolution is dominated by the rightmost zero of the denominator in (23), and if its imaginary part is negative this will give rise to a "Landautype" damping. The problem is hence reduced to finding the solutions of the following equation ( )…”

“…, therefore the ratio on the rhs of (26) can be expanded in series of exponentials, and then integration performed leading to the following dispersion relation, paralleling [7]:…”

“…The present work does not analyse a specific problem, but rather its aim is to investigate quantum effects on certain fundamental phenomena, like wave propagation and Landau damping in fermion and in boson systems: to this end, a kinetic equation approach is needed. Kinetic equations incorporating quantum effects can be derived from a Bohm potential point of view [7,8]. The Bohm potential is given by the following expression for a system of N identical particles of mass m: …”

“…* Corresponding author -fax: +39-051-6441747; tel. : +39-051-6441711; e-mail: domiziano.mostacci@unibo.it Kinetic equations incorporating quantum effects can be derived from a Bohm potential point of view [7,8]. Bohm potential is given by the following expression for a system of N identical particles of mass m:…”