Related papers: Central spectral gaps of the almost Mathieu operat…

Let $0<\gamma_1\leq \gamma_2 \leq \cdots $ denote the ordinates of nontrivial zeros of the Riemann zeta function with positive imaginary parts. For $c>0$ fixed (but possibly small), $T$ large, and $\gamma_n\leq T$, we call a gap…

Consider the Hill operator $Ty=-y''+q'(t)y$ in $L^2(\R)$, where $q\in L^2(0,1)$ is a 1-periodic real potential. The spectrum of $T$ is is absolutely continuous and consists of bands separated by gaps $\g_n,n\ge 1$ with length $|\g_n|\ge 0$.…

The Harper (or ``almost Mathieu'') equation plays an important role in studies of localization. Through a simple transformation, this equation can be converted into an iterative two dimensional skew--product mapping of the cylinder to…

We consider problems associated with the computation of spectra of self-adjoint operators in terms of the eigenvalue distributions of their n x n sections. Under rather general circumstances, we show how these eigenvalues accumulate near…

We consider Schr\"odinger operator in dimension $d\ge 2$ with a singular interaction supported by an infinite family of concentric spheres, analogous to a system studied by Hempel and coauthors for regular potentials. The essential spectrum…

In the paper we study the behaviour of the lengths of spectral gaps $\{\gamma_{q}(n)\}_{n\in \mathbb{N}}$ in a continuous spectrum of the Hill-Schr\"{o}dinger operators $$S(q)u=-u"+q(x)u,\quad x\in\mathbb{R},$$ with 1-periodic real-valued…

Curious spectral properties of an ensemble of random unitary matrices appearing in the quantization of a map p -> p+alpha, q -> q+f(p+alpha) in [Giraud et al. nlin.CD/0403033] are investigated. When alpha=m/n with integer co-prime m,n and…

We have experimentally investigated a chaotic reverberation chamber in the regime of strong modal overlap ($1{<}d{<}150$) varying the opening as well as the coupling strength $\kappa$ of the two attached antennas. We find a good agreement…

We consider a $2\times2$ block operator matrix ${\mathcal A}_\mu$ $($$\mu>0$ is a coupling constant$)$ acting in the direct sum of one- and two-particle subspaces of a bosonic Fock space. The location of the essential spectrum of ${\mathcal…

Under an appropriate symmetric extensive bipartition in a one-dimensional symmetry protected topological (SPT) phase, a bulk critical entanglement spectrum can be obtained, resembling the excitation spectrum of the critical point separating…

We present a model for spectral theory of families of selfadjoint operators, and their corresponding unitary one-parameter groups (acting in Hilbert space.) The models allow for a scale of complexity, indexed by the natural numbers…

In this paper we perform a numerical study of the spectra, eigenstates, and Lyapunov exponents of the skew-shift counterpart to Harper's equation. This study is motivated by various conjectures on the spectral theory of these…

Let M_n be the collection of n x n complex matrices equipped with operator norm. Suppose U, V \in M_n are two unitary matrices, each possessing a gap larger than \Delta in their spectrum, which satisfy ||UV-VU|| \le \epsilon. Then it is…

The gaps in the sequence $\{\sqrt{n}\}$ were shown by Elkies-McMullen (2004) to have a limiting distribution which is not the exponential distribution. However it is conjectured that the distribution of gaps in the sequence…

This paper provides decay bounds for Green matrices and generalized eigenvectors of block Jacobi operators when the real part of the spectral parameter lies in a bounded gap of the operator's essential spectrum. The case of the spectral…

We consider the Schr\"odinger operator $H$ on the half-line with a periodic potential $p$ plus a compactly supported potential $q$. For generic $p$, its essential spectrum has an infinite sequence of open gaps. We determine the asymptotics…

The goal of this paper is to provide sharp spectral gap estimates for problems involving higher-order operators (including both the clamped and buckling plate problems) on Cartan-Hadamard manifolds. The proofs are symmetrization-free --…

In this paper, we provide the spectral decomposition in Hilbert space of the $\mathcal{C}_0$-semigroup $P$ and its adjoint $\hatP$ having as generator, respectively, the Caputo and the right-sided Riemann-Liouville fractional derivatives of…

Let $H_0$ and $H$ be self-adjoint operators in a Hilbert space. In the scattering theory framework, we describe the essential spectrum of the difference $\varphi(H)-\varphi(H_0)$ for piecewise continuous functions $\varphi$. This…

Being a determination at low energies, the analysis of hadronic tau decay data provides a rather precise determination of the strong coupling alpha_s after evolving the result to M_Z. At such a level of precision, even small…