Related papers: On polarization interface conditions for time-harm…
In this paper we prove a stable determination of the coefficients of the time-harmonic Maxwell equations from local boundary data. The argument --due to Isakov-- requires some restrictions on the domain.
We show that Maxwell theory with a codimension-$1$ Chern-Simons interface supports chiral electromagnetic surface waves on the interface, even when the bulk theory on both sides is conventional vacuum electrodynamics in infinite space.…
This paper provides a view of Maxwell's equations from the perspective of complex variables. The study is made through complex differential forms and the Hodge star operator in $\mathbb{C}^2$ with respect to the Euclidean and the Minkowski…
In most electronic devices, electric current of both types (electrons and holes) flows through a junction. Usually the boundary conditions have been formulated exclusively for open circuit. The boundary conditions proposed here bypass this…
We propose a closed form formulation for the impedance of the Metal-Insulator-Metal (MIM) plasmonic transmission lines by solving the Maxwell's equations. We provide approximations for thin and thick insulator layers sandwiched between…
We consider the thermal Casimir effect in systems of parallel plates coupled to a mass-less free field theory via quadratic interaction terms which suppress (i) the field on the plates (ii) the gradient of the field in the plane of the…
We consider a magnetic Schroedinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary conditions. Assuming that the homogenized boundary condition is the Dirichlet or the Robin…
Modeling a normal/superconducting interface, we consider a semi-infinite wire whose edge is adjacent to a normal magnetic metal, assuming asymptotic convergence, away from the boundary, to the purely superconducting state. We obtain that…
We prove the existence of infinitely many nontrivial solutions for time-harmonic nonlinear Maxwell's equations on bounded domains and on $\mathbb{R}^3$ using dual variational methods. In the dual setting we apply a new version of the…
We consider the anharmonic oscillator with an arbitrary-degree anharmonicity, a damping term and a forcing term, all coefficients being time-dependent: u" + g_1(x) u' + g_2(x) u + g_3(x) u^n + g_4(x) = 0, n real. Its physical applications…
We derive the essential space-time spectrum of the Maxwell equations in linear isotropic inhomogeneous media together with the corresponding essential modes. These modes represent the collapse of the electromagnetic field into a single…
A statistical mechanics expression is derived for the space-dependent dielectric permittivity of a polar solvent near an interface. The asymptotic behaviour of this local permittivity is calculated in the low density limit, near a planar…
This paper considers a family of second-order parabolic equations in divergence form with rapidly oscillating and time-dependent periodic coefficients and an interface between two periodic structures. Following a framework initiated by…
A microscopic theory of the magnetic-field modulation of critical currents is developed for plane Josephson junctions with anharmonic current-phase relations. The results obtained allow examining temperature-dependent deviations of the…
This article establishes sufficient conditions for a linear-in-time bound on the non-asymptotic variance of particle approximations of time-homogeneous Feynman-Kac formulae. These formulae appear in a wide variety of applications including…
By starting with the Maxwell theory of electromagnetism, we study the change of polarization state of light transmitting through optically anisotropic media. The basic idea is to reduce the Maxwell equation to the Schroedinger like equation…
In this work we present for the first time an exact solution of Maxwell equations in vacuum, having non trivial topology, in which there is an exchange of helicity between the electric and magnetic part of such field. We calculate the…
We consider the time-harmonic Maxwell equations at a nonzero wavenumber $k\in\mathbb{C}$ on a bounded and simply connected Lipschitz domain $\Omega$ with an analytic boundary $\Gamma$, on which we impose impedance boundary conditions. We…
We consider the polarization of thermal emission in the near-field of various materials including dielectrics and metallic systems with resonant surface modes. We find that at thermal equilibrium, the degree of polarization exhibits spatial…
The multi-dimensional six-wave interaction system is derived in the context of nonlinear optics. Starting from Maxwell's equations, a reduced system of equations governing the dynamics of the electric and polarization fields are obtained.…