Related papers: On the optimization of the principal eigenvalue fo…
We consider the boundary value problem for the deflection of a finite beam on an elastic foundation subject to vertical loading. We construct a one-to-one correspondence $\Gamma$ from the set of equivalent well-posed two-point boundary…
We analyze scattering in a system of two (distinguishable) particles moving on the half-line $\overline{\rz}_+$ under the influence of singular two-particle interactions. Most importantly, due to the spatial localization of the interactions…
We study the eigenvalues of the Laplacian with a strong attractive Robin boundary condition in curvilinear polygons. It was known from previous works that the asymptotics of several first eigenvalues is essentially determined by the corner…
In the first part of this manuscript a relationship between the spectrum of self-adjoint operator matrices and the spectra of their diagonal entries is found. This leads to enclosures for spectral points and in particular, enclosures for…
This paper addresses the geometric optimization problem of the first Robin eigenvalue in exterior domains, specifically the lowest point of the spectrum of the Laplace operator under Robin boundary conditions in the complement of a bounded…
We explain how the spectrum of a closed embedded surface $\Sigma \subset \mathbb{R}^3$ relates to the Dirichlet spectrum of the bounded domain $\Omega \subset \mathbb{R}^3$ with $\partial \Omega = \Sigma$. We prove that there exists a…
Using the Bethe ansatz analysis as was reformulated by Edwards, we calculate the spectral properties of a particle interacting with a bath of fermions in one dimension for the case of equal particle-fermion masses. These are directly…
The paper deals with homogenisation problems for high-contrast symmetric convolution-type operators with integrable kernels in media with a periodic microstructure. We adapt the two-scale convergence method to nonlocal convolution-type…
The static path approximation to the path integral representation of partition function provides a natural microscopic basis to deal with thermal fluctuations around mean field configurations. Using this approach for one-dimensional…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
We consider the problem of a quantum particle interacting with $N$ attractive point $\delta$-interactions in two and three dimensional Riemannian manifolds and discuss its some spectral properties. The main aim of this paper is to give a…
In the paper the one-dimensional one-center scattering problem with the initial potential $\alpha |x|^{-1}$ on the whole axis is treated and reduced to the search for allowable self-adjoint extensions. Using the laws of conservation as…
We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one…
We present a framework to characterize Mott insulating phases within the interacting one-body picture, focusing on the Hubbard diamond chain featuring both Hubbard interactions and spin-orbit coupling simulated within cellular dynamical…
We consider singular self-adjoint extensions for the Schr\"{o}dinger operator of spin-$1/2$ particle in one dimension. The corresponding boundary conditions at a singular point are obtained. There are boundary conditions with the spin-flip…
We study the exterior derivative as a symmetric unbounded operator on square integrable 1-forms on a 3D bounded domain $D$. We aim to identify boundary conditions that render this operator self-adjoint. By the symplectic version of the…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
We consider the one-parametric family of self-adjoint realizations of the two-dimensional massive Dirac operator with a Lorentz scalar $\delta$-shell interaction of strength $\tau\in\mathbb{R}\setminus\{-2,0,2\}$ supported on a broken line…
We consider the hamiltonian operator associated with planar sec- tions of infinitely long cylindrical solenoids and with a homogeneous magnetic field in their interior. First, in the Sobolev space $\mathcal H^2$, we characterize all…
The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…