Boundary-induced energy localization in a nonlinear quantum lattice

Abstract

The dynamics of v bosons initially created on the same site of a finite-size lattice is analyzed according to a Bose version of the Hubbard model. For a boson number greater than 2, it is shown that the interplay between symmetry breaking and nonlinearity favors the occurrence of localized bound states. In a localized state, the v bosons are trapped close to each other and they behave as a single particle whose wave function is exponentially localized near a lattice side. Consequently, the creation of v bosons on a side site mainly excites a localized state so that the main part of the energy stays localized on the excited site over an infinite time scale.

Edge-localized states in quantum one-dimensional lattices

“…For the Bose-Hubbard model, some dynamical results have appeared in Ref. [13], In Figure 12, we present temporal dynamics results for the spinless-fermion model.…”

“…The answer turns out to be subtle -this phenomenon is not present for the case of two particles, but appears when the particle number is three or more, as follows from numerical studies in Ref. [13].…”

Two-exciton bound state quantum self-trapping in an extended star graph

“…As discussed in detail in previous works 50,55,61 , the calculation of the Hamiltonian matrix elements ( s, s |H| 1 s 1 , 1 s 1 ) reveals that the Schrodinger equation for the two-exciton wave function Ψ s s is isomorphic to a tight-binding model for a single fictitious particle. This particle moves quantum mechanically on a more complex network whose nodes are labeled by the indexes ( s, s ).…”

“…The quantum equivalent of the DNLS equation is the Bose-Hubbard model [43][44][45] in which the nonlinearity favors a coupling between bosonic excitations, called excitons in the following of the text. It leads to the occurrence of specific states, namely two-exciton bound states (TEBS) [45][46][47][48][49][50][51][52][53][54][55] , which have been observed in various molecular structures [56][57][58][59][60] . A TEBS corresponds to the trapping of two quanta over a few neighboring sites.…”

Dynamical Tunneling and Control

“…Numerical studies by Pouthier were done to answer the edge-localization question in a lattice with a few bosons [42], where the mean-field approximation (DNLS equation) cannot a priori be expected to provide the correct intuition. The answer turns out to be subtle -this phenomenon is not present for the case of two particles, but appears when the particle number is three or more [42]. Further studies focused on the energy spectrum and eigenstates (Fig.…”