Abstract
The properties of highly viscous fluids at high frequencies become similar to the properties of amorphous solids. In particular, it becomes possible to propagate not only longitudinal sound waves (plasmons for the case of an electron fluid), but also transverse sound waves associated with shear deformations. In this work, transverse sound waves at high frequencies in a twodimensional electron liquid in a magnetic field are studied. The consideration was carried out in the framework of the Landau Fermi-liquid model. It is shown that for a sufficiently large interaction between quasiparticles, the dynamics of excitations of a Fermi liquid is described by the equations of hydrodynamics. The Navier-Stokes equation and expressions for high-frequency shear viscosity coefficients are derived. Based on the equations obtained, the dispersion laws are calculated for transverse and longitudinal magnetosonic waves. It is shown that the cyclotron frequency, which enters in the viscosity coefficients and the dispersion law of transverse magnetosonic waves, is renormalized and typically becomes less than the usual cyclotron frequency, which determines the cyclotron resonance. The latter fact was apparently observed in the photoresistance of highly mobile GaAs quantum wells, in which two-dimensional electrons form a viscous fluid.
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