Related papers: An optimization problem for finite point interacti…
In realistic distributed optimization scenarios, individual nodes possess only partial information and communicate over bandwidth constrained channels. For this reason, the development of efficient distributed algorithms is essential. In…
The amount of correlation attainable between the components of a quantum system is constrained if the system is closed. We provide some examples, largely from the field of quantum thermodynamics, where knowing the maximal possible variation…
This paper is concerned with eigenvalue problems for non-symmetric elliptic operators with large drifts in bounded domains under Dirichlet boundary conditions. We consider the minimal principal eigenvalue and the related principal…
The problem of calculating of the mass spectrum of the two-body Bethe-Salpeter equation is studied with no reduction to the three-dimensional ("quasipotential") equation. The method to find the ground state and excited states for a channel…
For one-dimensional systems with delta-contact interactions, the convergence of the exact-diagonalization method is tested with a basis of harmonic oscillator eigenfunctions with frequency $\Omega$ optimized through the minimization of the…
We discuss a pair of isoperimetric problems which at a glance seem to be unrelated. The first one is classical: one places $N$ identical point charges at a closed curve $\Gamma$ at the same arc-length distances and asks about the energy…
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…
In this paper, we study the optimal control problem with terminal and inequality state constraints for state equations described by Volterra integral equations having singular and nonsingular kernels. The singular kernel introduces abnormal…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
The exact ground state of the many-body Schr\"odinger equation for $N$ bosons on a one-dimensional ring interacting via pairwise $\delta$-function interaction is presented for up to fifty particles. The solutions are obtained by solving…
We consider a one-dimensional trapped gas of strongly interacting few spin-1 atoms which can be described by an effective spin chain Hamiltonian. Away from the SU(3) integrable point, where the energy spectrum is highly degenerate, the…
Reliable communication over the discrete-input/continuous-output noncoherent multiple-input multiple-output (MIMO) Rayleigh block fading channel is considered when the signal-to-noise ratio (SNR) per degree of freedom is low. Two key…
We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points). Call a configuration sharp if there are m…
This paper develops a sequential-linearization feedback optimization framework for driving nonlinear dynamical systems to an optimal steady state. A fundamental challenge in feedback optimization is the requirement of accurate first-order…
We develop lower bounds for the energy of configurations in $\mathbb{R}^d$ periodic with respect to a lattice. In certain cases, the construction of sharp bounds can be formulated as a finite dimensional, multivariate polynomial…
We develop an algebraic approach to studying the spectral properties of the stationary Schr\"odinger equation in one dimension based on its high order conditional symmetries. This approach makes it possible to obtain in explicit form…
We discuss spectral properties of the Laplacian with multiple ($N$) point interactions in two-dimensional bounded regions. A mathematically sound formulation for the problem is given within the framework of the self-adjoint extension of a…
We analyze a family of singular Schr\"odinger operators with local singular interactions supported by a hypersurface $\Sigma \subset \mathbb{R}^n, n \ge 2$, being the boundary of a Lipschitz domain, bounded or unbounded, not necessarily…
We explore the spectral properties and behaviour of confining superexponential potentials. Several prototypes of these highly nonlinear potentials are analyzed in terms of the eigenvalues and eigenstates of the underlying stationary…
We investigate optimal control problems with $L^0$ constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation…