Related papers: Numerical results for two interacting particles in…
Real materials always contain, to some extent, randomness in the form of defects or irregularities. It is known since the seminal work of Anderson that randomness can drive a metallic phase to an insulating one, and the mechanism…
The Cooper problem is studied numerically for the Anderson model with disorder in two-dimensions. It is shown that the attractive Hubbard interaction creates a phase of bi-particle localized states in the regime where non-interacting states…
We investigate Anderson localization of two particles moving in a two-dimensional (2D) disordered lattice and coupled by contact interactions. Based on transmission-amplitude calculations for relatively large strip-shaped grids, we find…
We investigate a two-dimensional system of with two values of the internal (spin) degree of freedom. It is confined by a deformed harmonic trap and subject to a Zeeman field, Rashba or Dresselhaus one-body spin-orbit couplings and two-body…
We numerically investigate the transport properties of interacting spinless electrons in disordered systems. We use an efficient method which is based on the diagonalization of the Hamiltonian in the subspace of the many-particle Hilbert…
The localization length $L_2$ of two interacting particles in a one-dimensional disordered system is studied for very large system sizes by two efficient and accurate variants of the Green function method. The numerical results (at the band…
We study the effect of electron-electron interaction on a two dimensional (2D) disordered lattice. For the case of two electrons the analytical estimates are presented showing a transition from localized to delocalized states in a way…
The genuine physical reasons explaining the delocalization effect of the Hubbard repulsion U are analyzed. First it is shown that always when this effect is observed, U acts on the background of a macroscopic degeneracy present in a…
The phase separation that occurs in two-temperature mixtures, which are driven out of equilibrium at the local scale, has been thoroughly characterized, but much less is known about the depletion interactions that drive it. Using numerical…
At long times residual couplings to the environment become relevant even in the most isolated experiments, creating a crucial difficulty for the study of fundamental aspects of many-body dynamics. A particular example is many-body…
We consider two models for a pair of interacting particles in a random potential: (i) two particles with a Hubbard interaction in arbitrary dimensions and (ii) a strongly bound pair in one dimension. Establishing suitable correpondences we…
We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of…
We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…
Two electrons move in a quasi one--dimensional wire under the influence of a short--range interaction. We restrict Hilbert space to those states where the two electrons are close to each other. Using supersymmetry, we present a complete…
Dynamics of two particles with short range repulsive or attractive interaction is studied numerically in the Harper model. It is shown that interaction leads to appearance of localized states and pure-point spectrum component in the case…
The interplay between the quantum interferences responsible for one particle localization over a length L_1, and the partial dephasing induced by a local interaction of strength U with another particle leading to partial delocalization over…
Anderson localization1 in a random system is sensitive to a distance dependence of the excitation transfer amplitude V(r). If V(r) decreases with the distance r slower than 1/r^d in a d-dimensional system then all excitations are…
Statistics of many particle energy levels of a finite two-dimensional system of interacting electrons is numerically studied. It is shown that the statistics of these levels undergoes a Poisson to Wigner crossover as the strength of the…
We study the spectral statistics of interacting spinless fermions in a two-dimensional disordered lattice. Within a full quantum treatment for small few-particle-systems, we compute the low-energy many-body states numerically. While at weak…
We analyze the effect of the non-vanishing range of electron-electron repulsion on the mechanism of unconventional superconductivity. We present asymptotically exact weak-coupling results for dilute electrons in the continuum and for the 2D…