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We suggest a time-dependent mean-field hydrodynamic model for a binary dipolar boson-fermion mixture to study the stability and collapse of fermions in the $^{164}$Dy-$^{161}$Dy mixture. The condition of stability of the dipolar mixture is…
We study the correlation properties of the ground states of few ultracold bosons, trapped in double wells of varying barrier height in one dimension. Extending previous results on the signature of the transition from a Bose-condensed state…
Composite structure of particles somewhat modifies their statistics, compared to the pure Bose- or Fermi-ones. The spin-statistics theorem, so, is not valid anymore. Say, $\pi$-mesons, excitons, Cooper pairs are not ideal bosons, and,…
We investigate magnetic properties and statistical effects in 1D strongly repulsive two-component fermions and in a 1D mixture of strongly repulsive polarized fermions and bosons. Universality in the characteristics of phase transitions,…
We study a mixture of fermionic and bosonic cold atoms on a two-dimensional optical lattice, where the fermions are prepared in two hyperfine (isospin) states and the bosons have Bose-Einstein condensed (BEC). The coupling between the…
We explore the groundstates of a few dipolar bosons in optical lattices with incommensurate filling. The competition of kinetic, potential, and interaction energies leads to the emergence of a variety of crystal state orders with…
We study ground-state properties of interacting two-component boson gases in a one-dimensional harmonic trap by using the exact numerical diagonalization method. Based on numerical solutions of many-body Hamiltonians, we calculate the…
The fermionization regime and entanglement correlations of two distinguishable harmonically confined fermions interacting via a zero-range potential is addressed. We present two alternative representations of the ground state that we…
The theory of the preroughening transition of an unreconstructed surface, and the ensuing disordered flat (DOF) phase, is formulated in terms of interacting steps. Finite terraces play a crucial role in the formulation. We start by mapping…
Using Density Matrix renormalization group (DMRG), we study the ground state properties of spin one-half fermions and scalar bosons in the soft-core limit, with weak s-wave inter and intra species interactions. We considered the system…
We address the problem of the bosonization of finite fermionic systems with two different approaches. First we work in the path integral formalism, showing how a truly bosonic effective action can be derived from a generic fermionic one…
We study a mixture of $N_{b}$ bosons with point hard-core boson-boson interactions and $N_{f}$ noninteracting spinless fermions with point hard-core boson-fermion interactions in 1D optical lattice with external harmonic confine potential.…
We derive a dynamical mean-field theory for mixtures of interacting bosons and fermions on a lattice (BF-DMFT). The BF-DMFT is a comprehensive, thermodynamically consistent framework for the theoretical investigation of Bose-Fermi mixtures…
We have studied the appearance of chaos in the many-body spectrum of interacting Fermions. The coupling of a single state to the Fermi sea is considered. This state is coupled to a hierarchy of states corresponding to one or several…
We explore a few-fermion mixture consisting of two components which are repulsively interacting and confined in a one-dimensional harmonic trap. Different scenarios of population imbalance ranging from the completely imbalanced case where…
An imaginary-time nonuniform mesh method is presented and used to find the first 50 eigenstates and energies of up to five strongly interacting spinless quantum Lennard-Jones particles trapped in a one-dimensional harmonic potential. We…
We study the ground state phase diagram of a mixture of bosonic and fermionic cold atoms confined on two- and three-dimensional optical lattices. The coupling between bosonic fluctuations and fermionic atoms can be attractive or repulsive…
After release from the trap the momentum distribution of an impenetrable gas asymptotically approaches that of a spinless noninteracting Fermi gas in the initial trap. This phenomenon is called dynamical fermionization and, very recently,…
We numerically study the expansion dynamics of initially localized dipolar bosons in a homogeneous 1D optical lattice for different initial states. Comparison is made to interacting bosons with contact interaction. For shallow lattices the…
Repulsive Bose-Einstein condensate, where the short-range interaction is included up to the third order by the interaction radius, demonstrates existence of a bright soliton in a narrow interval of parameters. This soliton is studied here…