Related papers: Algebraic localization implies exponential localiz…
The article is devoted to the following question. Consider a periodic self-adjoint difference (differential) operator on a graph (quantum graph) G with a co-compact free action of the integer lattice Z^n. It is known that a local…
Conduction electrons interacting with a dynamic impurity can give rise to a local Fermi liquid. The latter has the same low energy spectrum as an ideal Fermi gas containing a static impurity. The Fermi liquids's elementary excitations are…
In insulators, the method of Marzari and Vanderbilt [Phys. Rev. B {\bf 56}, 12847 (1997)] can be used to generate maximally localized Wannier functions whose centers are related to the electronic polarization. In the case of layered…
We prove a localization theorem for affine $W$-algebras in the spirit of Beilinson--Bernstein and Kashiwara--Tanisaki. More precisely, for any non-critical regular weight $\lambda$, we identify $\lambda$-monodromic Whittaker $D$-modules on…
We consider the $(1+1)$-dimensional quasilinear wave equation $g(x)w_{tt}-w_{xx}+h(x) (w_t^3)_t=0$ on $\mathbb{R}\times\mathbb{R}$ which arises in the study of localized electromagnetic waves modeled by Kerr-nonlinear Maxwell equations. We…
We extended the notion of Newton-Wigner localization, already constructed in the bi-dimensional de Sitter space, to the tri-dimensional case for both principal and complementary series. We identify the one-particle subspace, generated by…
Maximally localized Wannier functions (MLWFs) are conventionally constructed by iteratively minimizing a spread functional over a high-dimensional gauge landscape. In this work, we present a non-variational constructive algorithm that…
A technically convenient signature of localization, exhibited by discrete operators with random potentials, is exponential decay of the fractional moments of the Green function within the appropriate energy ranges. Known implications…
Fourier multiplier analysis is developed for nonlocal peridynamic-type Laplace operators, which are defined for scalar fields in $\mathbb{R}^n$. The Fourier multipliers are given through an integral representation. We show that the integral…
The dichotomy of localization versus delocalization is a historic topic central to quantum and condensed matter physics. We discover a new delocalization mechanism attributed to a residue imaginary (part of) velocity $\operatorname{Im}(v)$,…
We find two-sided estimates for Kolmogorov, Bernstein, linear and projection widths of the classes of convolutions of $2\pi$-periodic functions $\varphi$, such that $\|\varphi\|_2\le1$, with fixed generated kernels $\Psi_{\bar{\beta}}$,…
Bloch theorem for a periodic operator is being revisited here, and we notice extra orthogonality relationships. It is shown that solutions are bi-periodic, in the sense that eigenfunctions are periodic with respect to one argument, and…
We consider spin-1/2 Fermi gases in arbitrary, integer or non-integer spatial dimensions, interacting via a Dirac delta potential. We first generalize the method of Tan's distributions and implement short-range boundary conditions to…
Maximally-localized Wannier functions (MLWFs) are widely employed as an essential tool for calculating the physical properties of materials due to their localized nature and computational efficiency. Projectability-disentangled Wannier…
We show Strichartz estimates for quasi-periodic functions with decaying Fourier coefficients via $\ell^2$-decoupling. When we additionally average in time, further improvements can be obtained. Next, we apply multilinear refinements to show…
Disordered systems exhibiting exponential localization are mapped to anisotropic spin chains with localization length being related to the anisotropy of the spin model. This relates localization phenomenon in fermions to the rotational…
Maximally-localized Wannier functions are quantum wavefunctions resembling atomic orbitals that are used to describe electrons in condensed matter. Since their introduction in 1997, these functions have become ubiquitous in ab initio…
A general method to construct basis functions for fermionic systems which account for the $SU(2)$ symmetry and for the translational invariance of the Hamiltonian is presented. The method does not depend on the dimensionality of the system…
The three dimensional cubic defocusing nonlinear wave equation is known to be ill-posed for general low regularity initial data. However, well-posedness can be recovered globally in time on a probabilistic level when considering random…
It is proved that a Poincare invariant Wightman function which fulfils the spectral property and can be defined at sharp times is local if and only if the integration over both the energy variables of a commutator in momentum space is a…