Related papers: Eigenvalues and Eigenfunctions of Two Coupled Norm…
We analyze the origin and features of localized excitations in a discrete two-dimensional Hamiltonian lattice. The lattice obeys discrete translational symmetry, and the localized excitations exist because of the presence of nonlinearities.…
A simple tight-binding model is used to illustrate how the time dependence of a state vector can be obtained from all the eigenvalues and eigenvectors of the Hamiltonian. The behavior of the eigenvalues and eigenvectors is studied for…
We study generalized eigenvalue problems for meet and join matrices with respect to incidence functions on semilattices. We provide new bounds for generalized eigenvalues of meet matrices with respect to join matrices under very general…
Relativistic thick ring models are constructed using previously found analytical Newtonian potential-density pairs for flat rings and toroidal structures obtained from Kuzmin-Toomre family of discs. In particular, we present systems with…
The correlated Kondo-lattice model is used to describe the interaction of electrons in a single conduction band with localized magnetic moments as well as their mutual repulsion. It is our intension to provide an analytical exact result for…
We explore the use of first and second order same-time atomic spatial correlation functions as a diagnostic for probing the small scale spatial structure of atomic samples trapped in optical lattices. Assuming an ensemble of equivalent…
In one-dimensional quantum lattice models with open boundaries, we find and study localization at the lattice edge. We show that edge-localized eigenstates can be found in both bosonic and fermionic systems, specifically, in the…
We present a theoretical analysis of methods to synthesize entangled states of two superconducting resonators. These methods use experimentally demonstrated interactions of resonators with artificial atoms, and offer efficient routes to…
We introduce two partially overlapping classes of pathwise dualities between interacting particle systems that are based on commutative monoids (semigroups with a neutral element) and semirings, respectively. For interacting particle…
We study the generalized eigenvalue problem on the whole space for a class of integro-differential elliptic operators. The nonlocal operator is over a finite measure, but this has no particular structure. Some of our results even hold for…
Topological properties of solid states have sparked considerable recent interest due to their importance in the physics of lattices with a non-trivial basis and their potential in the design of novel materials. Here we describe an…
The number state method is used to study soliton bands for three anharmonic quantum lattices: i) The discrete nonlinear Schr\"{o}dinger equation, ii) The Ablowitz-Ladik system, and iii) A fermionic polaron model. Each of these systems is…
Using the Density Matrix Renormalization Group and two-leg ladders, we investigate an electronic two-orbital Hubbard model including plaquette diagonal hopping amplitudes. Our goal is to search for regimes where charges added to the undoped…
The existence of flat bands is generally thought to be physically possible only for dimensions larger than one. However, by exciting a system with different orthogonal states this condition can be reformulated. In this work, we demonstrate…
Various exact solutions of two-particle eigenvalue problems for nonrelativistic contact four-fermion current-current interaction are obtained. Specifics of Goldstone mode is investigated. The connection between a renormalization procedure…
Two-dimensional (2D) lateral heterojunctions of transition metal dichalcogenides (TMDCs) have become a reality in recent years. Semiconducting TMDC layers in their common H -structure have a nonzero in-plane electric polarization, which is…
Artificial magnetic honeycomb lattice provides a two-dimensional archetypal system to explore novel phenomena of geometrically frustrated magnets. According to theoretical reports, an artificial magnetic honeycomb lattice is expected to…
We investigate the entanglement properties of resonating-valence-bond states on two and higher dimensional lattices, which play a significant role in our understanding of various many-body systems. We show that these states are genuinely…
Recent literature on delocalization in non-Hermitian systems has stressed criteria based on sensitivity of eigenvalues to boundary conditions and the existence of a non-zero current. We emphasize here that delocalization also shows up…
When two or more metallic nanoparticles are in close proximity, their plasmonic modes may interact through the near field, leading to additional resonances of the coupled system or to shifts of their resonant frequencies. This process is…