A generalized Kramers-Kronig transform for Casimir effect computations

Recent advances in experimental techniques now permit to measure the Casimir force with unprecedented precision. In order to achieve a comparable precision in the theoretical prediction of the force, it is necessary to accurately determine the electric permittivity of the materials constituting the plates along the imaginary frequency axis. The latter quantity is not directly accessible to experiments, but it can be determined via dispersion relations from experimental optical data. In the experimentally important case of conductors, however, a serious drawback of the standard dispersion relations commonly used for this purpose, is their strong dependence on the chosen low-frequency extrapolation of the experimental optical data, which introduces a significant and not easily controllable uncertainty in the result. In this paper we show that a simple modification of the standard dispersion relations, involving suitable analytic window functions, resolves this difficulty, making it possible to reliably determine the electric permittivity at imaginary frequencies solely using experimental optical data in the frequency interval where they are available, without any need of uncontrolled data extrapolations.Comment: 10 pages, 6 encapsulated figures. A few typos corrected, some references added. The new version matches the one accepted for publication on Phys. Rev.

Vanishing bulk viscosities and conformal invariance of unitary Fermi gas

By requiring general-coordinate and conformal invariance of the hydrodynamic equations, we show that the unitary Fermi gas has zero bulk viscosity, zeta=0, in the normal phase. In the superfluid phase, two of the bulks viscosities have to vanish, zeta_1=zeta_2=0, while the third one zeta_3 is allowed to be nonzero.Comment: 4 page

Effects of electrostatic fields and Casimir force on cantilever vibrations

The effect of an external bias voltage and fluctuating electromagnetic fields on both the fundamental frequency and damping of cantilever vibrations is considered. An external voltage induces surface charges causing cantilever-sample electrostatic attraction. A similar effect arises from charged defects in dielectrics that cause spatial fluctuations of electrostatic fields. The cantilever motion results in charge displacements giving rise to Joule losses and damping. It is shown that the dissipation increases with decreasing conductivity and thickness of the substrate, a result that is potentially useful for sample diagnostics. Fluctuating electromagnetic fields between the two surfaces also induce attractive (Casimir) forces. It is shown that the shift in the cantilever fundamental frequency due to the Casimir force is close to the shift observed in recent experiments of Stipe et al. Both the electrostatic and Casimir forces have a strong effect on the cantilever eigenfrequencies, and both effects depend on the geometry of the cantilever tip. We consider cylindrical, spherical, and ellipsoidal tips moving parallel to a flat sample surface. The dependence of the cantilever effective mass and vibrational frequencies on the geometry of the tip is studied both numerically and analytically

Bernoulli Potential, Hall Constant and Cooper Pairs Effective Masses in Disordered BCS Superconductors

It is analyzed what fundamental new information for the properties of the superconductors can be obtained by systematic investigation of the Bernoulli effect. It is shown that it is a tool to determine the effective mass of Cooper pairs, the volume density of charge carriers, the temperature dependence of the penetration depth and condensation energy. The theoretical results for disordered and anisotropic gap superconductors are systematized for this aim. For clean-anisotropic-gap superconductors is presented a simple derivation for the temperature dependence of the penetration depthComment: 13 pages, 3 figures, LaTeX 2e, New figure and reference

Effect of the Heterogeneity of Metamaterials on Casimir-Lifshitz Interaction

The Casimir-Lifshitz interaction between metamaterials is studied using a model that takes into account the structural heterogeneity of the dielectric and magnetic properties of the bodies. A recently developed perturbation theory for the Casimir-Lifshitz interaction between arbitrary material bodies is generalized to include non-uniform magnetic permeability profiles, and used to study the interaction between the magneto-dielectric heterostructures within the leading order. The metamaterials are modeled as two dimensional arrays of domains with varying permittivity and permeability. In the case of two semi-infinite bodies with flat boundaries, the patterned structure of the material properties is found to cause the normal Casimir-Lifshitz force to develop an oscillatory behavior when the distance between the two bodies is comparable to the wavelength of the patterned features in the metamaterials. The non-uniformity also leads to the emergence of lateral Casimir-Lifshitz forces, which tend to strengthen as the gap size becomes smaller. Our results suggest that the recent studies on Casimir-Lifshitz forces between metamaterials, which have been performed with the aim of examining the possibility of observing the repulsive force, should be revisited to include the effect of the patterned structure at the wavelength of several hundred nanometers that coincides with the relevant gap size in the experiments.Comment: 9 pages, 13 figures. Rewriting equations (10) and (12) and increasing the size of the lettering/numeral in figure

Making precise predictions of the Casimir force between metallic plates via a weighted Kramers-Kronig transform

The possibility of making precise predictions for the Casimir force is essential for the theoretical interpretation of current precision experiments on the thermal Casimir effect with metallic plates, especially for sub-micron separations. For this purpose it is necessary to estimate very accurately the dielectric function of a conductor along the imaginary frequency axis. This task is complicated in the case of ohmic conductors, because optical data do not usually extend to sufficiently low frequencies to permit an accurate evaluation of the standard Kramers-Kronig integral used to compute $\epsilon(i \xi)$. By making important improvements in the results of a previous paper by the author, it is shown that this difficulty can be resolved by considering suitable weighted dispersions relations, which strongly suppress the contribution of low frequencies. The weighted dispersion formulae presented in this paper permit to estimate accurately the dielectric function of ohmic conductors for imaginary frequencies, on the basis of optical data extending from the IR to the UV, with no need of uncontrolled data extrapolations towards zero frequency that are instead necessary with standard Kramers-Kronig relations. Applications to several sets of data for gold films are presented to demonstrate viability of the new dispersion formulae.Comment: 18 pages, 15 encapsulated figures. In the revised version important improvements have been made, which affect the main conclusions of the pape

A theory of electromagnetic fluctuations for metallic surfaces and van der Waals interactions between metallic bodies

A new general expression is derived for the fluctuating electromagnetic field outside a metal surface, in terms of its surface impedance. It provides a generalization to real metals of Lifshitz theory of molecular interactions between dielectric solids. The theory is used to compute the radiative heat transfer between two parallel metal surfaces at different temperatures. It is shown that a measurement of this quantity may provide an experimental resolution of a long-standing controversy about the effect of thermal corrections on the Casimir force between real metal plates.Comment: 4 pages, 2 figures; typos corrected, minor changes to match the published version in Physical Review Letter

Zero Lattice Sound

We study the N_f-flavor Gross-Neveu model in 2+1 dimensions with a baryon chemical potential mu, using both analytical and numerical methods. In particular, we study the self-consistent Boltzmann equation in the Fermi liquid framework using the quasiparticle interaction calculated to O(1/N_f), and find solutions for zero sound propagation for almost all mu > mu_c, the critical chemical potential for chiral symmetry restoration. Next we present results of a numerical lattice simulation, examining temporal correlation functions of mesons defined using a point-split interpolating operator, and finding evidence for phonon-like behaviour characterised by a linear dispersion relation in the long wavelength limit. We argue that our results provide the first evidence for a collective excitation in a lattice simulation.Comment: 18 pages, 6 figure