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Register a new userNo-slip boundary conditions for electron hydrodynamics and the thermal Casimir pressure
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We derive modified reflection coefficients for electromagnetic waves in the THz and far infrared range. The idea is based on hydrodynamic boundary conditions for metallic conduction electrons. The temperature-dependent part of the Casimir pressure between metal plates is evaluated. The results should shed light on the thermal anomaly where measurements deviate from the standard fluctuation electrodynamics for conducting metals.
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We present the results of an experiment on measuring the gradient of the Casimir force between an Au-coated hollow glass microsphere and graphene-coated fused silica plate by means of a modified atomic force microscope cantilever based technique operated in the dynamic regime. These measurements were performed in high vacuum at room temperature. The energy gap and the concentration of impurities in the graphene sample used have been measured utilizing scanning tunnelling spectroscopy and Raman spectroscopy, respectively. The measurement results for the gradients of the Casimir force are found to be in a very good agreement with theory using the polarization tensor of graphene at nonzero temperature depending on the energy gap and chemical potential with no fitting parameters. The theoretical predictions of the same theory at zero temperature are experimentally excluded over the measurement region from 250 to 517 nm. We have also investigated a dependence of the thermal correction to the Casimir force gradient on the values of the energy gap, chemical potential, and on the presence of a substrate supporting the graphene sheet. It is shown that the observed thermal effect is consistent in size with that arising for pristine graphene sheets if the impact of real conditions such as nonzero values of the energy gap, chemical potential, and the presence of a substrate is included. Implications of the obtained results to the resolution of the long-standing problems in Casimir physics are discussed. In addition to the paper published previously [M. Liu {it et al}., Phys. Rev. Lett. {bf 126}, 206802 (2021)], we present measurement results for the energy gap of the graphene sample, double the experimental data for the Casimir force, and perform a more complete theoretical analysis.
We obtain new expressions for the Casimir energy between plates that are mimicked by the most general possible boundary conditions allowed by the principles of quantum field theory. This result enables to provide the quantum vacuum energy for scalar fields propagating under the influence of a one-dimensional crystal represented by a periodic potential formed by an infinite array of identical potentials with compact support.
We derive general conditions of slip of a fluid on the boundary. Under these conditions the velocity of the fluid on the immovable boundary is a function of the normal and tangential components of the force acting on the surface of the fluid. A problem on stationary flow of an electrorheological fluid in which the terms of slip are specified on one part of the boundary and surface forces are given on the other is formulated and studied. Existence of a solution of this problem is proved by using the methods of penalty functions, monotonicity and compactness. It is shown that the method of penalty functions and the Galerkin approximations can be used for the approximate solution of the problem under consideration.
We develop the theory of hydrodynamics of an isotropic Fermi liquid of electrons coupled to isotropic acoustic phonons, assuming that umklapp processes may be neglected. At low temperatures, the fluid is approximately Galilean invariant; at high temperatures, the fluid is nearly relativistic; at intermediate temperatures, there are seven additional temperature regimes with unconventional thermodynamic properties and hydrodynamic transport coefficients in a three-dimensional system. We predict qualitative signatures of electron-phonon fluids in incoherent transport coefficients, shear and Hall viscosity, and plasmon dispersion relations. Our theory may be relevant for numerous quantum materials where strong electron-phonon scattering has been proposed to underlie a hydrodynamic regime, including $mathrm{WTe}_2$, $mathrm{WP}_2$, and $mathrm{PtSn}_4$.
In net-neutral systems correlations between charge fluctuations generate strong attractive thermal Casimir forces and engineering these forces to optimize nanodevice performance is an important challenge. We show how the normal and lateral thermal Casimir forces between two plates containing Brownian charges can be modulated by decorrelating the system through the application of an electric field, which generates a nonequilibrium steady state with a constant current in one or both plates, reducing the ensuing fluctuation-generated normal force while at the same time generating a lateral drag force. This hypothesis is confirmed by detailed numerical simulations as well as an analytical approach based on stochastic density functional theory.
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