Related papers: Extended Bloch theorem for topological lattice mod…
We study the scaling limit of a statistical system, which is a special case of the integrable inhomogeneous six-vertex model. It possesses $U_q\big(\mathfrak{sl}(2)\big)$ invariance due to the choice of open boundary conditions imposed. An…
A class of quasi-variational-hemivariational inequalities in reflexive Banach spaces is studied. The inequalities contain a convex potential, a locally Lipschitz superpotential, and an implicit obstacle set of constraints. Results on the…
We numerically study the problem of two fermions in a three dimensional optical lattice interacting via a zero-range Feshbach resonance, and display the dispersions of the bound states as a two-particle band structure with unique features…
In this work, we establish a generalized transfer matrix method that provides exact analytical and numerical solutions for lattice versions of topological models with surface termination in one direction. We construct a generalized…
New boundary conditions for integrable nonlinear lattices of the XXX type, such as the Heisenberg chain and the Toda lattice are presented. These integrable extensions are formulated in terms of a generic XXX Heisenberg magnet interacting…
The quest for new realizations of higher-order topological system has garnered much recent attention. In this work, we propose a paradigmatic brick lattice model where corner modes requires protection by nonsymmorphic symmetry in addition…
We examine theoretically and experimentally the localized %and extended electrical modes existing in a bi-inductive electrical lattice containing a bulk or a surface capacitive impurity. By means of the formalism of lattice Green's…
We study the landscape of solutions of the coherent quantum states in a ring shaped lattice potential in the context of ultracold atoms with an effective positive nonlinearity induced by interatomic interactions. The exact analytical…
We study boundary integral formulations for an interior/exterior initial boundary value problem arising from the thermo-elasto-dynamic equations in a homogeneous and isotropic domain. The time dependence is handled, based on Lubich's…
Wave functions on periodic lattices are commonly described by Bloch band theory. Besides Abelian Bloch states labeled by a momentum vector, hyperbolic lattices support non-Abelian Bloch states that have so far eluded analytical treatments.…
Existence of nontrivial topological phases in a tight binding Haldane-like model on the depleted Lieb lattice is reported. This two-band model is formulated by considering the nearest-neighbor, next-nearest-neighbor and…
We study multidimensional quadrilateral lattices satisfying simultaneously two integrable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is…
Interest in finite-size systems has risen in the last decades, due to the focus on nanotechnological applications and because they are convenient for numerical treatment that can subsequently be extrapolated to infinite lattices.…
The formation of nonlinear Bloch states in open driven-dissipative system of exciton-polaritons loaded into a weak-contrast 1D periodic lattice is studied numerically and analytically. The condensate is described within the framework of…
Mechanical lattices support topological wave phenomena governed by geometric phases. We develop a compact Hilbert space description for one-dimensional elastic chains, expressing intra-cell motion as a normalized superposition of orthogonal…
We introduce new $U_q\mathfrak{sl}_2$-invariant boundary conditions for the open XXZ spin chain. For generic values of $q$ we couple the bulk Hamiltonian to an infinite-dimensional Verma module on one or both boundaries of the spin chain,…
An exact analytical expression is derived for Bloch states in three dimensions, based on the only assumption that the electronic wavefunction can be expanded in terms of Gaussian type orbitals. The resulting expression features…
The dynamics of Bose-Einstein condensates trapped in a deep optical lattice is governed by a discrete nonlinear equation (DNL). Its degree of nonlinearity and the intersite hopping rates are retrieved from a nonlinear tight-binding…
The notions of Bloch wave, crystal momentum, and energy bands are commonly regarded as unique features of crystalline materials with commutative translation symmetries. Motivated by the recent realization of hyperbolic lattices in circuit…
We study the exact solution for two atomic particles in an optical lattice interacting via a Feshbach resonance. The analysis includes the influence of all higher bands, as well as the proper renormalization of molecular energy in the…