arXiv subjects

Ignat Fialkovsky

Publications and source records attributed to Ignat Fialkovsky.

5 recordsLinked to original sources

arXiv2020

Casimir-Polder force and torque for anisotropic molecules close to conducting planes and their effects on CO$_2$

We derive the Casimir-Polder force and Casimir torque expressions for an anisotropic molecule close to a conducting plane with a tensorial conductivity. We apply our general expressions to the case of a carbon dioxide CO$_2$ molecule close to a plane with pure Hall conductivity and to graphene. We show that the equilibrium position of this linear molecule is with its main axis perpendicular to the surface. We hence conjecture a possible way to exploit the Casimir torque to mechanically improve the performance of CO$_2$ separation membranes useful for an efficient atmospheric CO$_2$ reduction.

cond-mat.mes-hall↗

arXiv2019

Signatures of Complex Optical Response in Casimir Interactions of Type I and II Weyl Semimetals

The Casimir interaction is induced by electromagnetic fluctuations between objects and it is strongly dependent upon the electronic and optical properties of the materials making up the objects. Here we investigate this ubiquitous interaction between Weyl semimetals, a class of 3D systems with low energy linear dispersion and nontrivial topology due to symmetry conditions and stemming from separated energy cones. A comprehensive examination of all components of the bulk conductivity tensor as well as the surface conductivity due to the Fermi arc states in real and imaginary frequency domains is presented using the Kubo formalism for Weyl semimetals with different degree of tilting of their linear energy cones. The Casimir energy is calculated using a generalized Lifhsitz approach, for which electromagnetic boundary conditions for anisotropic materials were derived and used. We find that the Casimir interaction between Weyl semimetals is metallic-like and its magnitude and characteristic distance dependence can be modified by the degree of tilting and chemical potential. The nontrivial topology plays a secondary role in the Casimir interaction of these 3D materials and thermal fluctuations are expected to have similar effects as in metallic systems.

cond-mat.mtrl-sci↗

arXiv2018

The quest for Casimir repulsion between Chern-Simons surfaces

In this paper we critically reconsider the Casimir repulsion between surfaces that carry the Chern-Simons interaction (corresponding to the Hall type conductivity). We present a derivation of the Lifshitz formula valid for arbitrary planar geometries and discuss its properties. This analysis allows us to resolve some contradictions in the previous literature. We compute the Casimir energy for two surfaces that have constant longitudinal and Hall conductivities. The repulsion is possible only if both surfaces have Hall conductivities of the same sign. However, there is a critical value of the longitudinal conductivity above which the repulsion disappears. We also consider a model where both parity odd and parity even terms in the conductivity are produced by the polarization tensor of surface modes. In contrast to the previous publications L. Chen and S.-L. Wan, Phys. Rev. B84, 075149 (2011); B85, 115102 (2012), we include the parity anomaly term. This term ensures that the conductivities vanish for infinitely massive surface modes. We find that at least for a single mode regardless of the sign and value of its mass, there is no Casimir repulsion.

cond-mat.mes-hall↗

arXiv2016

A unifying asymptotic approach for nonadiabatic transitions near pairs of real or complex turning points

An asymptotic approach for a Schroedinger type equation with non selfadjoint Hamiltonian of a special type in the case of two close degeneracy (turning) points is developed. Both real and complex degeneracy points are treated by a method of matched asymptotic expansions in the context of a unifying approach. An asymptotic expansion near degeneracy point containing the parabolic cylinder functions is constructed and the transition matrix connecting the coefficients of adiabatic modes in front of and behind the degeneracy point is derived. A simple non-technical recipe is also provided, which enables one to apply results to different physical problems without performing intermediate calculations.

math-ph↗

arXiv2009

Comment on "Casimir energies with finite-width mirrors"

We comment on a recent publication [1] by Fosco, Lombardo and Mazzitelli on Casimir energies for material slabs (`finite width mirrors') and report a discrepancy between results obtained there for a single mirror and some previous calculations. We provide a simple consistency check which proves that the method used in [1] is not reliable when applied to approximations of piecewise constant profile of the mirror. We also present an alternative method for calculation of the Casimir energy in such systems based on our recent work. Our results coincide both with perturbation theory and with some older \cite{Bordag'95} and more recent \cite{Vassilevitch'08} calculations, but differ from those of [1].

hep-th↗