相关论文: Some Estimates Regarding Integrated density of Sta…

One-dimensional Schr\"odinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized…

The asymptotic behavior of the integrated density of states (IDS), \(N(E)\), is investigated for random Schr\"{o}dinger operators with a single-site potential \(V\) satisfying \(\mathrm{essinf}\, V = -\infty\). Under the assumption that the…

We prove concentration bounds for the following classes of quantum states: (i) output states of shallow quantum circuits, answering an open question from [DPMRF22]; (ii) injective matrix product states; (iii) output states of dense…

The present paper extends the landscape theory pioneered in [FM, ADFJM2, DFM] to the tight-binding Schr\"odinger operator on $\Z^d$. In particular, we establish upper and lower bounds for the integrated density of states in terms of the…

We prove that the local eigenvalue statistics for $d=1$ random band matrices with fixed bandwidth and, for example, Gaussian entries, is given by a Poisson point process and we identify the intensity of the process. The proof relies on an…

This paper sets out to study the spectral minimum for operator belonging to the family of random Schr\"{o}dinger operators of the form $H\_{\lambda,\omega}=-\Delta+W\_{\text{per}}+\lambda V\_{\omega}$, where we suppose that $V\_{\omega}$ is…

We consider eigenvalue sums of Schr\"odinger operators $-\Delta+V$ on $L^2(\R^d)$ with complex radial potentials $V\in L^q(\R^d)$, $q<d$. We prove quantitative bounds on the distribution of the eigenvlaues in terms of the $L^q$ norm of $V$.…

Given a finitely generated amenable group we consider ergodic random Schr\"odinger operators on a Cayley graph with random potentials and random boundary conditions. We show that the normalised eigenvalue counting functions of finite volume…

The local density of states \rho(x,E) is calculated for a Bloch electron in an electric field. Depending on the system size, we can see one or more sequences of Wannier-Stark ladders in \rho(x,E), with Lorentz type level widths and apparent…

We study the spectral properties of a Schr\"{o}dinger operator $H_0$ modified by $\delta$ interactions and show explicitly how the poles of the new Green's function are rearranged relative to the poles of original Green's function of $H_0$.…

We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given $k$ and a target density $\rho$, there exist potentials having $k^{\text{th}}$ bound mixed states which densities…

We show persistence of both Anderson and dynamical localization in Schr\"odinger operators with non-positive (attractive) random decaying potential. We consider an Anderson-type Schr\"odinger operator with a non-positive ergodic random…

We consider a random family of Schr\"odinger operators on a cover $X$ of a compact Riemannian manifold $M = X/\Gamma$. We present several results on their spectral theory, in particular almost sure constancy of the spectral components and…

The subject of this work are random Schroedinger operators on regular rooted tree graphs $\T$ with stochastically homogeneous disorder. The operators are of the form $H_\lambda(\omega) = T + U + \lambda V(\omega)$ acting in $\ell^2(\T)$,…

We study the number $N_{<0}(H_s)$ of negative eigenvalues, counting multiplicities, of the fractional Schr\"odinger operator $H_s=(-\Delta)^s-V(x)$ on $L^2(\mathbb{R}^d)$, for any $d\ge1$ and $s\ge d/2$. We prove a bound on $N_{<0}(H_s)$…

The integrated density of states (IDS) is a fundamental spectral quantity for quantum Hamiltonians modeling condensed matter systems, describing how densely energy levels are distributed. It can be interpreted as a volume-averaged spectral…

We studied global density-of-states correlation function $R(\omega)$ for L\'evy-Rosenzweig-Porter random matrix ensemble in the non-ergodic extended phase. Using an extension of Efetov's supersymmetry approach we calculated $R(\omega)$…

We consider continuum random Schr\"odinger operators of the type $H_{\omega} = -\Delta + V_0 + V_{\omega}$ with a deterministic background potential $V_0$. We establish criteria for the absence of continuous and absolutely continuous…

We consider random Schr\"{o}dinger operators on $\ell^2(\mathbb{Z}^d)$ when the distribution of single site potentials is $\alpha$-H\"{o}lder continuous ($0<\alpha\leq 1$). In localized regime we study the distribution of eigenfunctions…

We consider the 1d Schr\"odinger operator with decaying random potential, and study the joint scaling limit of the eigenvalues and the measures associated with the corresponding eigenfunctions which is based on the formulation by…