Related papers: Point contacts and boundary triples
In this paper we develop certain aspects of perturbation theory for self-adjoint operators subject to small variations of their domains. We use the abstract theory of boundary triplets to quantify such perturbations and give the second…
We study the behavior of a quantum particle confined to a hard--wall strip of a constant width in which there is a finite number $ N $ of point perturbations. Constructing the resolvent of the corresponding Hamiltonian by means of Krein's…
We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on…
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…
We investigate the eigengenvalues problem for self-adjoint operators with the singular perturbations. The general results presented here includes weakly as well as strongly singular cases. We illustrate these results on two models which…
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 give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for…
We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians…
We investigate almost-degenerate perturbation theory of eigenvalue problems, using spectral projectors, also named density matrices. When several eigenvalues are close to each other, the coefficients of the perturbative series become…
The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension depending on real parameters. The cases of weak and strong coupling are distinguished and their geometric interpretation in two and…
Model two-dimensional singular perturbed eigenvalue problem for Laplacian with frequently alternating type of boundary condition is considered. Complete two-parametrical asymptotics for the eigenelements are constructed.
We consider the problem of finding the spectrum of an operator taking the form of a low-rank (rank one or two) non-normal perturbation of a well-understood operator, motivated by a number of problems of applied interest which take this…
We consider a general weak perturbation of a non-interacting quantum lattice system with a non-degenerate gapped ground state. We prove that the presence of isolated eigenvalues in the spectrum of the decoupled model leads to the existence…
We present a scheme for tuning two quantum point contacts as a quantum-limited charge detector. Based on the scattering matrix approach, we analyze a general condition of quantum-limited detection with a single-channel quantum detector…
The effect of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The analysis is most easily performed in a space of constant curvature the…
The character of quantum corrections to the gravitational action of a conformally invariant field theory for a self-interacting scalar field on a manifold with boundary is considered at third loop-order in the perturbative expansion of the…
We construct models of many-particle quantum graphs with singular two-particle contact interactions, which can be either hardcore- or delta-interactions. Self-adjoint realisations of the two-particle Laplacian including such interactions…
We consider single-channel transmission through a double quantum dot system consisting of two single dots that are connected by a wire and coupled each to one lead. The system is described in the framework of the S-matrix theory by using…
An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be written as a Laplacian growth model regularized by a `kinetic undercooling' boundary condition. We study the linear stability of uniformly…
We prove quadratic eigenvalue perturbation bounds for generalized Hermitian eigenvalue problems. The bounds are proportional to the square of the norm of the perturbation matrices divided by the gap between the spectrums. Using the results…