Related papers: Quantum breathers in an attractive fermionic Hubba…
Nonlinearity and disorder are key players in vibrational lattice dynamics, responsible for localization and delocalization phenomena. $q$-Breathers -- periodic orbits in nonlinear lattices, exponentially localized in the reciprocal linear…
We consider the Bose-Hubbard model describing attractive bosonic particles hopping across the sites of a translation-invariant lattice, and compare the relevant ground-state properties with those of the corresponding symmetry-breaking…
We investigate the two dimensional generalized attractive Hubbard model in a bipartite lattice, and and a "quantum phase liquid" phase, in which the fermions are paired but don't have phase coherence at zero temperature, in analogy to…
Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
We consider a macroscopic quantum system such as a qubit, interacting with a bath of fermions as in the Fr\"ohlich polaron model. The interaction Hamiltonian is thus linear in the macroscopic system variable, and bilinear in the fermions.…
Interactions between particles normally induce the decay of the particles Bloch oscillations (BOs) in a periodic lattice. In the limit of strong on-site interactions, spin-$1/2$ fermions may form doublon bound states and undergo BOs in the…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
We describe a lattice of asymmetrical qubit pairs in one or two dimensions, with couplings arranged so that the motion of single-qubit excited states mimics the behavior of charged lattice bosons hopping in a magnetic field. We show in…
A quantum anti-ferromagnetic spin-1 model is characterised on a 2D lattice with the following requirements: i) The Hamiltonian is made out of nearest neighbour interactions. ii) It is homogeneous, translational and rotational invariant.…
We study discrete surface breathers in two-dimensional lattices of inductively-coupled split-ring resonators with capacitive nonlinearity. We consider both Hamiltonian and dissipative systems and analyze the properties of the modes…
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…
Strongly interacting bosons in 2D in a rotating square lattice are investigated via a modified Bose-Hubbard Hamiltonian. Such a system corresponds to a rotating lattice potential imprinted on a trapped Bose-Einstein condensate. Second-order…
We study anharmonic localization in a periodic five atom chain with quadratic-quartic spring potential. We use discrete symmetries to eliminate the degeneracies of the harmonic chain and easily find periodic orbits. We apply linear…
Breathers may be mobile close to an instability threshold where the frequency of a pinning mode vanishes. The translation mode is a marginal mode that is a solution of the linearized (Hill) equation of the breather which grows linearly in…
We review research on the role of nonlinear coherent phenomena (e.g breathers and kinks) in the formation linear decorations in mica crystal. The work is based on a new model for the motion of the mica hexagonal K layer, which allows…
We study the particle-hole symmetry in the Hubbard model using ultracold fermionic atoms in an optical lattice. We demonstrate the mapping between charge and spin degrees of freedom and, in particular, show the occurrence of a state with…
Collision process between breather and moving kink-soliton is investigated both analytically and numerically in Fermi-Pasta-Ulam (FPU) chains. As it is shown by both analytical and numerical consideration low amplitude breathers and soft…
We investigate the transport properties of neutral, fermionic atoms passing through a one-dimensional quantum wire containing a mesoscopic lattice. The lattice is realized by projecting individually controlled, thin optical barriers on top…
We study the dynamics of discrete breathers -- spatially localized and time-periodic solutions -- inside the bandgap of a nonlinear honeycomb lattice where the dispersion landscape approaches a so-called semi-Dirac point in which the bands…