Related papers: Two-parameter Asymptotics in Magnetic Weyl Calculu…
We demonstrate that a disordered magnetic Weyl semimetal may be mapped onto a two-dimensional array of coupled replicated Hubbard chains, where the Hubbard $U$ is directly related to the variance of the disorder potential. This is a…
We consider non-interacting particles subject to a fixed external potential $V$ and a self-generated magnetic field $B$. The total energy includes the field energy $\beta \int B^2$ and we minimize over all particle states and magnetic…
We analyze a general class of difference operators $H_\varepsilon = T_\varepsilon + V_\varepsilon$ on $\ell^2(\varepsilon \mathbb{Z}^d)$, where $V_\varepsilon$ is a one-well potential and $\varepsilon$ is a small parameter. We construct…
The asymptotic iteration method is applied, to calculate the angular spheroidal eigenvalues $\lambda^{m}_{\ell}(c)$ with arbitrary complex size parameter $c$. It is shown that, the obtained numerical results of $\lambda^{m}_{\ell}(c)$ are…
Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is…
The first purpose of this article is to provide conditions for a bounded operator in $L^2(\R^n)$ to be the Weyl (resp. anti-Wick) quantization of a bounded continuous symbol on $\R^{2n}$. Then, explicit formulas for the Weyl (resp.…
We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we modify and use the variational method suggested by…
We theoretically address the effects of strong magnetic fields in three-dimensional Weyl semimetals (WSMs) built out of Weyl nodes with a monopole charge $n$. For $n=1$, $2$, and $3$ we realize single, double, and triple WSM, respectively,…
Asymptotic expansion of the wavelet transform for small values of the dilation parameter a is obtained using asymptotic expansion of the Mellin convolution technique ofWong. Asymptotic expansions of Morlet wavelet transform, Mexican hat…
Weyl degeneracies in spectra of magnetoplasma waves enable nonreciprocal energy flow and topologically protected modes, yet conventional materials require impractical magnetic fields to operate. Developing an effective Hamiltonian framework…
We continue the program first initiated in [Geom. Funct. Anal. 26, 288-305 (2016)] and develop a modification of the technique introduced in that paper to study the spectral asymptotics, namely the Riesz means and eigenvalue counting…
The concern of this article is a semiclassical Weyl calculus on an infinite dimensional Hilbert space $H$. If $(i, H, B)$ is a Wiener triplet associated to $H$, the quantum state space will be the space of $L^2$ functions on $B$ with…
Let $\mathcal{M}$ be a smooth manifold of positive dimension $n$ equipped with a smooth density $d\mu_{\mathcal{M}}$. Let $A$ be a polyhomogeneous elliptic pseudo-differential operator of positive order $m$ on $\mathcal{M}$ which is…
We obtain large N asymptotics for the Hermitian random matrix partition function \[Z_N(V)=\int_{\mathbb R^N}\prod_{i<j}(x_i-x_j)^2 \prod_{j=1}^N e^{-N V(x_j)}dx_j,\] in the case where the external potential $V$ is a polynomials such that…
Let $\mathbb{P}$ denote the set of primes and $\mathcal{N}\subset \mathbb{N}$ be a set with arbitrary weights attached to its elements. Set $\mathfrak{p}_{\mathcal{N}}(n)$ to be the restricted partition function which counts partitions of…
Weyl semi-metals are three dimensional generalizations of graphene with point-like Fermi surfaces. Their linear electronic dispersion leads to a window in the particle-hole excitation spectrum which allows for undamped propagation of…
We present general prescriptions for the asymptotic expansion of massive multi-loop Feynman integrals near threshold. As in the case of previously known prescriptions for various limits of momenta and masses, the terms of the threshold…
The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation. A scalar theory is considered, both as a simple example and for its own sake. This theory…
We study the effects a strong Coulomb disorder on the transverse magnetoresistance in Weyl semimetals at low temperatures. Using the diagrammatic technique and the Keldysh model to sum up the leading terms in the diagrammatic expansion, we…
We consider differential operators defined as Friedrichs extensions of quadratic forms with non-smooth coefficients. We prove a two term optimal asymptotic for the Riesz means of these operators and thereby also reprove an optimal Weyl law…