Related papers: Quantization of edge currents for continuous magne…
An extended Landau-Lifshitz-Gilbert (LLG) equation is introduced to describe the dynamics of inhomogeneous magnetization in a current-carrying wire. The coefficients of all the terms in this equation are calculated quantum-mechanically for…
This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…
Spontaneous edge currents are known to occur in systems of two space dimensions in a strong magnetic field. The latter creates chirality and determines the direction of the currents. Here we show that an analogous effect occurs in a…
Circuit quantization links a physical circuit to its corresponding quantum Hamiltonian. The standard quantization procedure generally assumes any external magnetic flux to be static. Time dependence naturally arises, however, when flux is…
In order to analyse classical electromagnetism in a medium at finite temperature we introduce `an optical density operator', and reformulate Maxwell's equations with the operator, starting from the Dirac-equation-like formulation of…
We give a unified statement and proof of a class of wellknown mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on…
We consider a class of constant-coefficient partial differential operators on a finite-dimensional real vector space which exhibit a natural dilation invariance. Typically, these operators are anisotropic, allowing for different degrees in…
Canonical quantization of electromagnetic field inside the time--spatially dispersive inhomogeneous dielectrics is presented. Interacting electromagnetic and matter excitation fields create the closed system, Hamiltonian of which may be…
The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential…
Conventional wisdom dictates that the conducting edge states of two-dimensional topological insulators of the Bi$_2$Se$_3$ family are protected by time-reversal symmetry. However, theoretical bulk calculations and a recent experiment show…
We consider the heat operator acting on differential forms on spaces with complete and incomplete edge metrics. In the latter case we study the heat operator of the Hodge Laplacian with algebraic boundary conditions at the edge singularity.…
The Landau-Lifshitz equation is a coupled set of nonlinear partial differential equations that describes the dynamics of magnetization in a ferromagnet. This equation has an infinite number of stable equilibria. Steering the system from one…
The quantization of the energy in a magnetic field (Landau quantization) at a three-quarter Dirac point is studied theoretically. The three-quarter Dirac point is realized in the system of massless Dirac fermions with the critically tilted…
We show that the dynamic magnetization at the edges of a thin magnetic element with finite lateral size can be described by new effective boundary conditions that take into account inhomogeneous demagnetizing fields near the element edges.…
A review is presented of some recent progress in spectral geometry on manifolds with boundary: local boundary-value problems where the boundary operator includes the effect of tangential derivatives; application of conformal variations and…
A quantum mechanical model is used to derive a generalized Landau-Lifshitz equation for a magnetic moment, including fluctuations and dissipation. The model reproduces the Gilbert-Brown form of the equation in the classical limit. The…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
This paper concerns the asymmetric transport observed along interfaces separating two-dimensional bulk topological insulators modeled by (continuous) differential Hamiltonians and how such asymmetry persists after numerical discretization.…
We study the persistent edge current in the fractional quantum Hall effect. We give the grand partition functions for edge excitations of hierarchical states coupled to an Aharanov-Bohm flux and derive the exact formula of the persistent…
We study quantum transport properties of two-dimensional electron gases under high perpendicular magnetic fields. For this purpose, we reformulate the high-field expansion, usually done in the operatorial language of the guiding-center…