Related papers: Spectral analysis of a quantum system with a doubl…
The spheroidal harmonics $S_{lm}(\theta;c)$ have attracted the attention of both physicists and mathematicians over the years. These special functions play a central role in the mathematical description of diverse physical phenomena,…
The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are…
Entanglement is central to our understanding of many-body quantum matter. In particular, the entanglement spectrum, as eigenvalues of the reduced density matrix of a subsystem, provides a unique footprint of properties of strongly…
An interference experiment with entangled particles is theoretically analyzed, where one of the entangled pair (particle 1) goes through a multi-slit before being detected at a fixed detector. In addition, one introduces a mechanism for…
We study the isospectrality problem for a free quantum particle confined in a ring with a junction, analyzing all the self-adjoint realizations of the corresponding Hamiltonian in terms of a boundary condition at the junction. In…
We study a family of closed quantum graphs described by one singular vertex of order n=4. By suitable choice of the parameters specifying the singular vertex, we can construct a closed sequence of paths in the parameter space that…
The large N spectrum of the quantum mechanical hamiltonian of two hermitean matrices in a harmonic potential is studied in a framework where one of the matrices is treated exactly and the other is treated as a creation operator impurity in…
Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of…
This paper is concerned with regular approximations of spectra of singular discrete linear Hamiltonian systems with one singular endpoint. For any given self-adjoint subspace extension (SSE) of the corresponding minimal subspace, its…
We discuss an eigenvalue problem which arises in the studies of asymptotic stability of a self-similar attractor in the sigma model. This problem is rather unusual from the viewpoint of the spectral theory of linear operators and requires…
In this study we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$. We impose the Neumann boundary condition on a disc window of radius $a$ and Dirichlet…
We consider a quadratic operator pencil with a small periodic perturbation multiplied by the spectral parameter. It is motivated, in particular, by a one-dimensional Klein-Gordon equation with a time-parity-symmetric perturbation. We study…
Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization. Also, for the study of open quantum systems, non-Hermitian systems have attracted much attention. As mathematical models for such systems,…
Consider two quantum graphs with the standard Laplace operator and non-Robin type boundary conditions at all vertices. We show that if their eigenvalue-spectra agree everywhere aside from a sufficiently sparse set, then the…
A review of discrete quantum walk with two particle is given. The use of different states encountered in identical particle, and the idea of entanglement and superposition is explored to explored the interesting dynamics of two particle…
We introduce n-particle quantum graphs with singular two-particle interactions in such a way that eigenfunctions can be given in the form of a Bethe ansatz. We show that this leads to a secular equation characterising eigenvalues of the…
Nonlinear eigenvalue problems for pairs of homogeneous convex functions are particular nonlinear constrained optimization problems that arise in a variety of settings, including graph mining, machine learning, and network science. By…
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 compute the electron spin resonance (ESR) intensity for one-dimensional quantum wires in semiconductor heterostructures, taking into account electron-electron interactions and spin-orbit coupling. The ESR spectrum is shown to be very…
Motivated by the theory of quantum waveguides, we investigate the spectrum of the Laplacian, subject to Dirichlet boundary conditions, in a curved strip of constant width that is defined as a tubular neighbourhood of an infinite curve in a…