Related papers: Anderson localisation for an interacting two-parti…
We consider N interacting quantum particles on a one-dimensional lattice, and subjected to an external linear potential. For N = 1, the corresponding Hamiltonian is explicitly diagonalizable, with superexponentially localized eigenstates.…
In this paper, we study the multidimensional lattice Schr\"odinger operators with $C^2$-cosine like quasi-periodic (QP) potential. We establish quantitative Green's function estimates, the arithmetic version of Anderson (and dynamical)…
This paper deals with the asymptotic behaviour of a widely used correlation characteristic in large quantum systems. The correlations are known as quantum entanglement, the characteristic is called entanglement entropy, and the system is an…
General local spin $S$ ground states, described by a Valence Bond Solid (VBS) on a two dimensional lattice are studied. The norm of these ground states is mapped to a classical O(3) model on the same lattice. Using this quantum-to-classical…
We evaluate the particle current flowing in steady state through a Bose-Einstein condensate subject to a constant force in a quasi-onedimensional lattice and to attractive interactions from fermionic atoms that are localized in various…
Spectrum of boson fields and two-point correlators are analyzed in a quantum bar system (a superlattice formed by two crossed interacting arrays of quantum wires), with short range interwire interaction. The standard bosonization procedure…
We consider a system of fermions with local interactions on a lattice (Hubbard model) and apply a novel extension of the Laplace's method (saddle-point approximation) for evaluating the corresponding partition function. There, we introduce…
We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…
Starting from the hamiltonian for the Heisenberg ferromagnet which comprise randomly distributed nonmagnetic ions as impurities in a Bravais lattice, we express the spin operators by means of the Dyson-Maleev transformation in terms of the…
In this paper we present a class of Anderson type operators with independent, non-stationary (non-decaying) random potentials supported on a subset of positive density in the odd-dimensional lattice and prove the existence of pure…
In this paper, we consider particle systems with interaction and Brownian motion. We prove that when the initial data is from the sampling of Chorin's method, i.e., the initial vertices are on lattice points $hi\in \mathbb{R}^d$ with mass…
We address the old and widely debated question of the statistical properties of integrable quantum systems, through the analysis of the paradigmatic Lieb-Liniger model. This quantum many-body model of 1-d interacting bosons allows for the…
We study discrete magnetic random Schr\"odinger operators on the square and honeycomb lattice. For the non-random magnetic operator on the hexagonal lattice with any rational magnetic flux, we show that the middle two dispersion surfaces…
We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to a strong electric field. In the non-interacting case, due to Wannier-Stark localization, the single-particle wave…
We consider a class of ensembles of lattice Schr\"odinger operators with deterministic random potentials, including quasi-periodic potentials with Diophantine frequencies, depending upon an infinite number of parameters in an auxiliary…
Strong repulsive interactions in a one-dimensional electron system suppress the exchange coupling J of electron spins to a value much smaller than the Fermi energy E_F. The conventional theoretical description of such systems based on the…
We study the localization properties of a disordered tight-binding Hamiltonian on a generic bipartite lattice close to the band center. By means of a fermionic replica trick method, we derive the effective non-linear $\sigma$-model…
A lattice model of radiative decay (so-called spin-boson model) of a two level atom and at most two photons is considered. The location of the essential spectrum is described. For any coupling constant the finiteness of the number of…
We study the Anderson localization of atomic gases exposed to simple-cubic optical lattices with a superimposed disordered speckle pattern. The two mobility edges in the first band and the corresponding critical filling factors are…
The spectral properties of the spinless fermion model with nearest-neighbor repulsive interactions on a one-dimensional lattice are investigated using the Bethe ansatz. Although its bulk quantities are exactly the same as those of the…