In this search, we have calculated thetransverse component of energy distortion in
elasticity wave modes of quantum liquid, by using Landau's theory in Fermi liquid taken
in consideration the effect of transverse component of an external disturbanc
e on the
liquid. We calculated the current density related to this component, and the stress tensor
component according with this state.In our search we have been considered the
temperature is low enough since the relation is true, where is the Fermi
temperature.
We have compared the response of the liquid, for transverse componentof the
external disturbance, with its response for longitudinal one in same conditions, by studding
the transverse and longitudinal shear modulus (which equivalent these responses) as
functions of the frequency and wave vector of the external disturbance. We have
found in general that these responses are different, but they become equal in particular
case , where the velocity on Fermi surface, and in this case the
viscoelastic model hypotheses become true.
In this study, an Interaction Function between quasi particles has been introduced
into an energy formula in Kinetic Equation of Quantum Plasmas. Such new type can be
used to study quasi Particles of Quantum Fermi Plasmas, since it contains quantum
term
that is correlated with Bohm Potential, when the mean inter-particle distance is of the same
order as the de-Broglie thermal wavelength. An interaction function between quasi
particles has been expressed using spherical Functions in three-dimensional space with
Landau’s spread coefficients for ℓ = 0 , 1 , 2 . Using such representation led to obtaining
the dispersion relation of the structural waves and its energy Spectrum in balanced local
condition. The use of Landau parameters in this study isconsidered new comparing to other
studies in this field. It allows us to get more generic and more precise dispersion relations
with new previously unknown spectrum energy in Quantum Fermi Plasmas.
