Related papers: Eigenvalue problem meets Sierpinski triangle: comp…

We study the isospectrality problem for a relativistic free quantum particle, described by the Dirac Hamiltonian, confined in a one-dimensional ring with a junction. We analyze all the self-adjoint extensions of the Hamiltonian in terms of…

We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realisations of Laplacians acting on functions defined on pairs of edges in such a way that…

We introduce a new technique to prove bounds for the spectral radius of a random matrix, based on using Jensen's formula to establish the zerofreeness of the associated characteristic polynomial in a region of the complex plane. Our…

We investigate the relation between the spectrum of a non-normal matrix and the norm of its resolvent. We provide spectral estimates for the resolvent of matrices whose largest singular value is bounded by $1$ (so-called Hilbert space…

An eigenvalue problem relevant for non-linear sigma model with singular metric is considered. We prove the existence of a non-degenerate pure point spectrum for all finite values of the size R of the system. In the infrared (IR) regime…

We consider the Hamiltonian of a system of three quantum mechanical particles on the three-dimensional lattice $\Z^3$ interacting via short-range pair potentials. We prove for the two-particle energy operator $h(k),$ $k\in \T^3$ the…

We prove quantitative bounds on the eigenvalues of non-selfadjoint unbounded operators obtained from selfadjoint operators by a perturbation that is relatively-Schatten. These bounds are applied to obtain new results on the distribution of…

For a general class of large non-Hermitian random block matrices $\mathbf{X}$ we prove that there are no eigenvalues away from a deterministic set with very high probability. This set is obtained from the Dyson equation of the Hermitization…

We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the…

We analyze eigenvalues emerging from thresholds of the essential spectrum of one-dimensional Dirac operators perturbed by complex and non-symmetric potentials. In the general non-self-adjoint setting we establish the existence and…

Using an isomorphism between Hilbert spaces $L^2$ and $\ell^{2}$ we consider Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in a discrete basis and an eigenvalue problem is reduced to solving a three term…

In this paper, we investigate the spectrum of the self adjoint differential operator with operator coefficitent in a separable Hilbert space. We also derive asymptotic formulas for the sum of eigenvalues of this operator.

In this paper we introduce and study generally non-self-adjoint realizations of the Dirac operator on an arbitrary finite metric graph. Employing the robust boundary triple framework, we derive, in particular, a variant of the Birman…

A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…

Non-self-adjoint Schrodinger operators A which correspond to non-symmetric zero-range potentials are investigated. For a given A, the description of non-real eigenvalues, spectral singularities and exceptional points are obtained; the…

A common challenge to proving asymptotic stability of solitary waves is understanding the spectrum of the operator associated with the linearized flow. The existence of eigenvalues can inhibit the dispersive estimates key to proving…

A unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of hermitian matrices of finite or infinite dimensions. It can be considered as a matrix version of exactly solvable Schr\"odinger…

The paper considers the general form of self-adjoint boundary value problems for momentum operators with nonlocal potentials. We give an analysis of the eigenvalue distribution as zeros of the characteristic functions, for which their…

The relative distance between eigenvalues of the compression of a not necessarily semibounded self-adjoint operator to a closed subspace and some of the eigenvalues of the original operator in a gap of the essential spectrum is considered.…

Non-Hermitian many-body systems can be spectrally unstable, so small perturbations may induce large eigenvalue shifts. The pseudospectrum quantifies this instability and provides a perturbation-robust diagnostic. For inverse-polynomially…