Originally, the Hubbard model was derived for describing the behavior of strongly correlated
electrons in solids. However, for over a decade now, variations of it have also routinely been …

During the last decade, many exciting phenomena have been experimentally observed and
theoretically predicted for ultracold atoms in optical lattices. This paper reviews these rapid …

We derive a novel lattice Hamiltonian, the molecular Hubbard Hamiltonian, which describes
the essential many-body physics of closed-shell ultracold heteronuclear molecules in their …

Dark solitons of ultracold bosons in the vicinity of the Mott-insulator–superfluid phase
transition are studied. Making use of the Gutzwiller ansatz we have found antisymmetric …

The search for new computational machines beyond the traditional von Neumann
architecture has given rise to a modern area of nonlinear science—development of …

We study the real-time evolution of solitary excitations in one-dimensional quantum spin
chains using exact diagonalization and the density-matrix renormalization group. The …

Typical treatments of superconducting or superfluid Josephson junctions rely on mean-field
or two-mode models; we explore many-body dynamics of an isolated, ultracold, Bose-gas …

We study quantum dynamics of a dark soliton in a one-dimensional Bose gas in an optical
lattice within the truncated Wigner approximation. Previous work has revealed that in the …

Topological physics in optical lattices have attracted much attention in recent years. The
nonlinear effects on such optical systems remain well-explored and a large amount of …

We present different techniques to numerically solve the equations of motion for the widely
studied Discrete Nonlinear Schroedinger equation (DNLS). Being a Hamiltonian system, the …