Related papers: Sensitivity to the initial state of interacting ul…
Dynamics of attractive ultra-cold bosonic clouds in one dimension are studied by solving the many-particle time-dependent Schr\"odinger equation. The initially coherent wave-packet can dynamically dissociate into two parts when its energy…
We model the expansion of an interacting atomic Bose-Einstein condensate in a disordered lattice with a nonlinear diffusion equation normally used for a variety of classical systems. We find approximate solutions of the diffusion equation…
We study the spreading of initially localized states in a nonlinear disordered lattice described by the nonlinear Schr\"odinger equation with random on-site potentials - a nonlinear generalization of the Anderson model of localization. We…
The Anderson model in one dimension is a quantum particle on a discrete chain of sites with nearest-neighbor hopping and random on-site potentials. It is a progenitor of many further models of disordered systems, and it has spurred numerous…
We study the equilibrium and non-equilibrium properties of strongly interacting bosons on a lattice in presence of a random bounded disorder potential. Using a Gutzwiller projected variational technique, we study the equilibrium phase…
We develop an alternative scaling approach to determine the criteria for Anderson localization in one-dimensional tight-binding models with random site energies having a bandwidth that decays as a power law in space, $H_{ij} \propto |i -…
We study the dynamics of a ultra-cold boson gas in a lattice submitted to a constant force. We track the route of the system towards chaos created by the many-body-induced nonlinearity and show that relevant information can be extracted…
We study the transport dynamics of matter-waves in the presence of disorder and nonlinearity. An atomic Bose-Einstein condensate that is localized in a quasiperiodic lattice in the absence of atom-atom interaction shows instead a slow…
We derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schr\"odinger equation at the leading order in the number of particles. The…
Random interaction models have been successful in describing the amorphous properties of solids such as spin-glasses and structural glasses. This modelling approach is applied to a system of zero-spin cold bosons moving in an amorphous…
The variational determination of the two-boson reduced density matrix is described for a one-dimensional system of $N$ (where $N$ ranges from $2$ to $10^4$) harmonically trapped bosons interacting via contact interaction. The ground-state…
We study a partially disordered one-dimensional system with interacting particles. Concretely, we impose a disorder potential to only every other site, followed by a clean site. Our numerical analysis of eigenstate properties is based on…
We study the dynamics of one and two dimensional disordered lattice bosons/fermions initialized to a Fock state with a pattern of $1$ and $0$ particles on $A$ and ${\bar A}$ sites. For non-interacting systems we establish a universal…
Systems consisting of cold interacting bosons show interesting collective phenomena such as Bose-Einstein condensation or superfluidity and are currently studied in condensed matter and atomic physics. Of particular interest are nonideal…
An ultracold gas is considered, loaded into a lattice, each site of which is formed by a double-well potential. Initial conditions, after the loading, correspond to a nonequilibrium state. The nonlinear dynamics of the system, starting with…
We have been investigating the problem of the Anderson localization in a disordered one dimensional tight-binding model. The disorder is created by the interaction of mobile particles with other species, immobilized at random positions. We…
In disordered systems, our present understanding of the Anderson transition is hampered by the possible presence of interactions between particles. We demonstrate that in boson gases, even weak interactions deeply alter the very nature of…
We investigate the behavior of solutions of the complex Gross-Pitaevskii equation, a model that describes the dynamics of pumped decaying Bose-Einstein condensates. The stationary radially symmetric solutions of the equation are studied and…
We study the dynamics of a system of $N$ interacting bosons in a disc-shaped trap, which is realised by an external potential that confines the bosons in one spatial dimension to a region of order $\varepsilon$. The interaction is…
Single-particle transport in disordered potentials is investigated on scales below the localization length. The dynamics on those scales is concretely analyzed for the 3-dimensional Anderson model with Gaussian on-site disorder. This…