Related papers: Trace formula for the magnetic Laplacian at zero e…
In this article we study point configurations minimizing the discrete energy on a compact Riemannian manifold, where the energy kernel is taken to be the Green's function for the Laplacian. We show that every point in a minimizing…
We prove that the lowest eigenvalue of the Laplace operator with a magnetic field having a self-intersecting zero set is a monotone function of the parameter defining the strength of the magnetic field, in a neighborhood of infinity. We…
For Toeplitz operators on bounded symmetric domains of arbitrary rank, we define a Hilbert quotient module corresponding to partitions of length $1$ and prove that it belongs to the Macaev class ${\mathcal{L}}^{n,\infty}$. We next obtain an…
The magnetic properties of a circular graphene nanoribbon (carbon belt) in a magnetic field parallel to its central axis is studied using a tight-binding model. Orbital magnetic susceptibility is calculated using an analytical expression of…
We elucidate the dependence of the Casimir energy on the trace anomaly coefficients for a six-dimensional CFT on $R\times S^5$. This extends the universal dependence on the central charge in 2D and the relation by Cappelli and Coste in 4D,…
Let $F$ be a number field, $\pi$ either a unitary cuspidal automorphic representation of $\mathrm{GL}(2)/F$ or a unitary Eisenstein series, and $\chi$ a unitary Hecke character of analytic conductor $C(\chi).$ We develop a regularized…
In this paper we study the existence of periodic orbits with prescribed energy levels of convex Lagrangian systems on complete Riemannian manifolds. We extend the existence results of Contreras by developing a modified minimax principal to…
We introduce the notion of discrete cusp for a weighted graph. In this context, we provethat the form-domain of the magnetic Laplacian and that of thenon-magnetic Laplacian can be different. We establish the emptiness of the essential…
We investigate the existence of magnetohydrostatic equilibria for topologically complex magnetic fields. The approach employed is to perform ideal numerical relaxation experiments. We use a newly-developed Lagrangian relaxation scheme that…
This paper focuses on the following class of fractional magnetic Schr\"{o}dinger equations \begin{equation*} (-\Delta)_{A}^{s}u+V(x)u=g(\vert u\vert^{2})u+\lambda\vert u\vert^{q-2}u, \quad \mbox{in } \mathbb{R}^{N}, \end{equation*} where…
We study the role of zero-point quantum fluctuations in a range of magnetic states which on the classical level are close to spin-aligned ferromagnets. These include Skyrmion textures characterized by non-zero topological charge, and…
We prove an entanglement principle for fractional Laplace operators on $\mathbb R^n$ for $n\geq 2$ as follows; if different fractional powers of the Laplace operator acting on several distinct functions on $\mathbb R^n$, which vanish on…
We show that the additional contribution to the Michael lattice energy sum rule for the static quark-antiquark potential, pointed out recently, can be identified with the contribution to the field energy arising from the trace anomaly of…
We obtain general trace formulae in the case of perturbation of self-adjoint operators by self-adjoint operators of class $\bS_m$, where $m$ is a positive integer. In \cite{PSS} a trace formula for operator Taylor polynomials was obtained.…
We investigate the Casimir pressure between two parallel plates made of magnetic materials at nonzero temperature. It is shown that for real magnetodielectric materials only the magnetic properties of ferromagnets can influence the Casimir…
Under certain hypothesis on the underlying classical Hamiltonian flow, we produce local scaling asymptotics in the semiclassical regime for a Berezin-T\"oplitz version of the Gutzwiller trace formula on a quantizable compact K\"ahler…
We investigate the electronic structure of the helium atom in a magnetic field b etween B=0 and B=100a.u. The atom is treated as a nonrelativistic system with two interactin g electrons and a fixed nucleus. Scaling laws are provided…
We extend an axiomatic approach to classical electrodynamics, which we developed recently, to the case of non-vanishing magnetic charge. Then two axioms, namely those of the existence of the Lorentz force (Axiom 2) and of magnetic flux…
We study the Laplacian on family preserving metric graphs. These are graphs that have a certain symmetry that, as we show, allows for a decomposition into a direct sum of one-dimensional operators whose properties are explicitly related to…
We establish an infinitesimal variant of Guo-Jacquet trace formula for the case of a central simple algebra over a number field $F$ containing a quadratic field extension $E/F$. It is an equality between a sum of geometric distributions on…