Related papers: Chaotic and regular dynamics in the three-site Bos…
We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schr\"odinger (or Gross-Pitaevski) equation. Our formula applies…
We study the mixed-type classical dynamics of the three-particle Fermi-Pasta-Ulam-Tsingou (FPUT) model in relationship with its quantum counterpart, and present new results on aspects of quantum chaos in this system. First we derive for the…
We present a numerical study of the spectral properties of the 1D Bose-Hubbard model. Unlike the 1D Hubbard model for fermions, this system is found to be non-integrable, and exhibits Wigner-Dyson spectral statistics under suitable…
Energy spectra of a particle with mass $m$ and charge $e$ in the cubic Aharonov-Bohm billiard containing around $10^4$ consecutive levels starting from the ground state have been analysed. The cubic Aharonov-Bohm billiard is a plane…
We present a two-band Bose-Hubbard model which is shown to be minimal in the necessary coupling terms at resonant tunneling conditions. The dynamics of the many-body problem is studied by sweeping the system across an avoided level…
We study the dynamics of a three-mode bosonic system with mode-changing interactions. For large mode occupations the short-time dynamics is well described by classical mean-field equations allowing us to study chaotic dynamics in the…
We study the quantum mechanics of a billiard (Robnik 1983) in the regime of mixed-type classical phase space (the shape parameter \lambda=0.15) at very high-lying eigenstates, starting at about 1.000.000th eigenstate and including the…
We discuss applications of the theory of Quantum Chaos to one of the paradigm models of many-body quantum physics -- the Bose-Hubbard model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After…
In this work the two site Bose-Hubbard model is studied analytically in the limit of weak coupling u and large number of particles N . The semiclassical approximation where \frac{1}{N} plays the role of Planck's constant was used and…
Numerical calculation and analysis of extremely high-lying energy spectra, containing thousands of levels with sequential quantum number up to 62,000 per symmetry class, of a generic chaotic 3D quantum billiard is reported. The shape of the…
e formulate a method for studying the quantum field dynamics of ultracold Bose gases confined within optical lattice potentials, within the lowest Bloch-band Bose-Hubbard model. Our formalism extends the two-sites results of Phys. Rev.…
We comment on the recent paper by Abul-Magd (J.Phys.A: Math.Gen. 29 (1996) 1) concerning the energy level statistics in the mixed regime, i.e. such having the mixed classical dynamics where regular and chaotic regions coexist in the phase…
We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing…
We study Krylov complexity of a one-dimensional Bosonic system, the celebrated Bose-Hubbard Model. The Bose-Hubbard Hamiltonian consists of interacting bosons on a lattice, describing ultra-cold atoms. Apart from showing superfluid-Mott…
The attractive two-site Bose-Hubbard model is studied within the framework of the analytical solution obtained by the application of Quantum Inverse Scattering Method. The structure of the ground and excited states is analyzed in terms of…
The spectrum of phonon-like collective excitations in the system of Bose-atoms in optical lattice (more generally, in the system of quantum particles described by the Bose-Hubbard model) is investigated. Such excitations appear due to…
We present a multi-site formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with inter-cluster hopping being…
Chaotic systems that decompose into two cells connected only by a narrow channel exhibit characteristic deviations of their quantum spectral statistics from the canonical random-matrix ensembles. The equilibration between the cells…
We study the ground state of the disordered Bose-Hubbard model for spin-1 particles by means of the stochastic mean-field theory. This approach enables the determination of the probability distributions of various physical quantities, such…
Quantum chaos in isolated quantum systems is intimately linked to thermalization and the rapid relaxation of observables. Although the spectral properties of the chaotic phase in the tilted Bose-Hubbard model have been well characterized,…