Related papers: Three types of spectra in one-dimensional systems …
A major application of the mathematical concept of graph in quantum mechanics is to model networks of electrical wires or electromagnetic wave-guides. In this paper, we address the dynamics of a particle trapped on such a network in…
We study positive bound states for the semiclassical stationary nonlinear Schr\"odinger equation. We are especially interested in solutions which concentrate on a lower dimensional sphere. We adopt a purely variational approach which allows…
A reliable and efficient computation of the entire single-particle spectrum of correlated molecules is an outstanding challenge in the field of quantum chemistry, with standard density functional theory approaches often giving an inadequate…
A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…
For the Lagrange spectrum and other applications, we determine the smallest accumulation point of binary sequences that are maximal in their shift orbits. This problem is trivial for the lexicographic order, and its solution is the fixed…
We propose a hybrid (continuous-discrete variable) quantum repeater protocol for distribution of entanglement over long distances. Starting from entangled states created by means of single-photon detection, we show how entangled coherent…
A simple expression is derived for the band structure of a one-dimensional periodic potential in terms of two solutions of the Schroedinger equation within the unit cell, one with a zero-derivative boundary condition on the left-hand end of…
The direct and inverse scattering problems on the full line are analyzed for a first-order system of ordinary linear differential equations associated with the derivative nonlinear Schr\"odinger equation and related equations. The system…
Spectral method related to Lame equation with finite-gap potential is used to study the optical cascading equations. These equations are known not to be integrable by inverse scattering method. Due to "partial integrability" two-gap…
The spectrum of a one-dimensional Hamiltonian with potential $V(x)=ix^2$ for negative $x$ and $V(x)=-ix^2$ for positive $x$ is analyzed. The Schr\"odinger equation is algebraically solvable and the eigenvalues are obtained as the zeros of…
In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea…
The relativistic quark model is presented. The quark-antiquark potential for the Schroedinger-like equation is constructed with the account of retardation effects and one-loop radiative corrections. It consists of the one-gluon exchange…
We describe a broad class of bounded non-periodic potentials in one-dimensional stationary quantum mechanics having the same spectral properties as periodic potentials. The spectrum of the corresponding Schroedinger operator consists of a…
A new method to calculate the spectrum using cascaded open systems and master equations is presented. The method uses two state analyzer atoms which are coupled to the system of interest, whose spectrum of radiation is read from the…
Using the Wilson formulation of lattice gauge theories, a gauge invariant grid discretization of a one-particle Hamiltonian in the presence of an external electromagnetic field is proposed. This Hamiltonian is compared both with that…
We study statistics of resonances in a one-dimensional disordered chain coupled to an outer world simulated by a perfect lead. We consider a limiting case for weak disorder and derive some results which are new in these studies. The main…
The existence and construction of periodic approximations with convergent spectra is crucial in solid state physics for the spectral study of corresponding Schr\"odinger operators. In a forthcoming work [9] (arXiv:1709.00975) this task was…
From the mathematical side, nonlinear Schr\"odinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome this problem by focusing on spherically symmetric…
We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support…
We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many…