Related papers: A general algorithm for computing bound states in …

Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and practical quantum…

With a generic lattice model for electrons occupying a semi-infinite crystal with a hard surface, we study the eigenstates of the system with a bulk band gap (or the gap with nodal points). The exact solution to the wave functions of…

Floquet states have been used to describe the impact of periodic driving on lattice systems, either using a tight-binding model, or by using a continuum model where a Kronig-Penney-like description has been used to model spatially periodic…

We describe methods for proving bounds on infinite-time averages in differential dynamical systems. The methods rely on the construction of nonnegative polynomials with certain properties, similarly to the way nonlinear stability can be…

We consider one dimensional scattering and show how the presence of a mild positive barrier separating the interaction region from infinity implies that the bound and antibound states are symmetric modulo exponentially small errors in 1/h.…

We investigate how quantum bound states bounce from a hard surface. Our analysis has applications to ab initio calculations of nuclear structure and elastic deformation, energy levels of excitons in semiconductor quantum dots and wells, and…

We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We…

We provide here a new and exact formalism to describe the formation of end, edge or surface states through the evolution of impurity-induced states. We propose a general algorithm that consists of finding the impurity states via the…

We have developed an efficient tensor network algorithm for spin ladders, which generates ground-state wave functions for infinite-size quantum spin ladders. The algorithm is able to efficiently compute the ground-state fidelity per lattice…

The past years have witnessed impressive advances in electronic structure calculation, especially in the complexity and size of the systems studied, as well as in computation time. Linear scaling methods based on empirical tight-binding…

We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…

We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is that these linear systems, which are symmetric and positive semidefinite, are well approximated by…

An effective optimization strategy has been developed to construct highly accurate bound state wave functions in various three-body systems. Our procedure appears to be very effective for computations of weakly bound states and various…

We consider the stability and the input-output analysis problems of a class of large-scale hybrid systems composed of continuous dynamics coupled with discrete dynamics defined over finite alphabets, e.g., deterministic finite state…

A new algorithm for determining the eigenstates of n-dimensional billiards is presented. It is based on the application of the Cauchy theorem for the determination of the null space of the boundary overlap matrix. The method is free from…

Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way.…

This paper presents a rigorous mathematical analysis for symmetry-based Bound States in the Continuum (BICs) in optical waveguide arrays. Different from existing research, we consider a finite system of horizontally and equidistantly…

If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present…

We present an implementation of an efficient algorithm for the calculation of the spectrum of one-dimensional quantum systems with periodic boundary conditions. This algorithm is based on a matrix product representation for quantum states…

The discovery of topologically non-trivial electronic systems has opened a new age in condensed matter research. From topological insulators to topological superconductors and Weyl semimetals, it is now understood that some of the most…