50 research outputs found
Non-Gibbs states on a Bose-Hubbard lattice
We study the equilibrium properties of the repulsive quantum Bose-Hubbard
model at high temperatures in arbitrary dimensions, with and without disorder.
In its microcanonical setting the model conserves energy and particle number.
The microcanonical dynamics is characterized by a pair of two densities: energy
density and particle number density . The macrocanonical Gibbs
distribution also depends on two parameters: the inverse nonnegative
temperature and the chemical potential . We prove the existence of
non-Gibbs states, that is, pairs which cannot be mapped onto
. The separation line in the density control parameter space
between Gibbs and non-Gibbs states corresponds to
infinite temperature . The non-Gibbs phase cannot be cured into a
Gibbs one within the standard Gibbs formalism using negative temperatures.Comment: 8 pages, 1 figure, misprints correcte
Chimera patterns in conservative systems and ultracold atoms with mediated nonlocal hopping
Chimera patterns, characterized by coexisting regions of phase coherence and
incoherence, have so far been studied in non-conservative systems with
dissipation. Here, we show that the formation of chimera patterns can also be
observed in conservative Hamiltonian systems with nonlocal hopping in which
both energy and particle number are conserved. Effective nonlocality can be
realized in a physical system with only local coupling if different time scales
exist, which can be illustrated by a minimal conservative model with an
additional mediating channel. Finally, we show that the patterns should be
observable in ultracold atomic systems. Nonlocal spatial hopping over up to
tens of lattice sites with independently tunable hopping strength and on-site
nonlinearity can be implemented in a two-component Bose-Einstein condensate
with a spin-dependent optical lattice, where the untrapped component serves as
the matter-wave mediating field. The present work highlights the connections
between chimera patterns, nonlinear dynamics, condensed matter, and ultracold
atoms.Comment: 4 figures with supplementar
Non-Equilibrium Properties of Open Quantum Systems
We study two classes of open systems: discrete-time quantum walks (a type of
Floquet-engineered discrete quantum map) and the Lindblad master equation (a
general framework of dissipative quantum systems), focusing on the
non-equilibrium properties of these systems. We study localization and
delocalization phenomena, soliton-like excitations, and quasi-stationary
properties of open quantum systems
Wannier solitons in spin-orbit-coupled Bose-Einstein condensates in optical lattices with a flat-band
We investigate families of soliton solutions in a spin-orbit coupled
Bose-Einstein condensate embedded in an optical lattice, which bifurcate from
the nearly flat lowest band. Unlike the conventional gap solitons the obtained
solutions have the shape well approximated by a Wannier function (or a few
Wannier functions) of the underlying linear Hamiltonian with amplitudes varying
along the family and with nearly constant widths. The Wannier solitons (WSs)
sharing all symmetries of the system Hamiltonian are found to be stable. Such
solutions allow for the construction of Wannier breathers, that can be viewed
as nonlinearly coupled one-hump solitons. The breathers are well described by a
few-mode model and manifest stable behavior either in an oscillatory regime
with balanced average populations or in a self-trapping regime characterized by
unbalanced atomic populations of the local potential minima (similarly to the
conventional boson Josephson junction), with the frequencies controlled by the
inter-atomic interactions.Comment: Accepted for publication in Physical Review
Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States
The system of a cold atomic gas in an optical lattice is governed by two
factors: nonlinearity originating from the interparticle interaction, and the
periodicity of the system set by the lattice. The high level of controllability
associated with such an arrangement allows for the study of the competition and
interplay between these two, and gives rise to a whole range of interesting and
rich nonlinear effects. This review covers the basic idea and overview of such
nonlinear phenomena, especially those corresponding to extended states. This
includes "swallowtail" loop structures of the energy band, Bloch states with
multiple periodicity, and those in "nonlinear lattices", i.e., systems with the
nonlinear interaction term itself being a periodic function in space.Comment: 39 pages, 21 figures; review article to be published in a Special
Issue of Entropy on "Non-Linear Lattice