Classical Solutions and 'Hidden' Symmetry of Bose-fermi System

Egor S. Babaev, Faddeev, Antti J. Niemi

FRANCESCO IACHELLO, P. Van Isacker

Y. B. Band, Isaac N. Towers, Boris A. Malomed

We present semiclassical descriptions of Bose-Einstein condensates for configurations with spatial symmetry, e.g., cylindrical symmetry, and without any symmetry. The description of the cylindrical case is quasi-one-dimensional (Q1D), in the sense that one only needs to solve an effective 1D nonlinear Schr\"odinger equation, but the solution incorporates 3D aspects of the problem, as a result of which the 1D equation is supplemented by a noncanonical (quartic) normalization condition. The solution in classically allowed regions is matched onto that in classically forbidden regions by a connection formula that properly accounts for the nonlinear mean-field interaction. Special cases for vortex solutions are treated too. Comparisons of the Q1D solution with the full 3D and Thomas-Fermi ones are presented, and conditions for the applicability of the effective low-dimensional equations are obtained.

Bess Fang, Patrizia Vignolo, M. Gattobigio +2 more

We present the exact solution for the many-body wavefunction of a one-dimensional mixture of bosons and spin-polarized fermions with equal masses and infinitely strong repulsive interactions under external confinement. Such a model displays a large degeneracy of the ground state. Using a generalized Bose-Fermi mapping, we find the solution for the whole set of ground-state wave functions of the degenerate manifold and we characterize them according to group-symmetry considerations. We find that the density profile and the momentum distribution depends on the symmetry of the solution. By combining the wave functions of the degenerate manifold with suitable symmetry and guided by the strong-coupling form of the Bethe-Ansatz solution for the homogeneous system, we propose an analytic expression for the many-body wave function of the inhomogeneous system which well describes the ground state at finite, large, and equal interaction strengths, as validated by numerical simulations.

R. Casalbuoni

Ofir E. Alon, Alexej I. Streltsov, Lorenz S. Cederbaum

Cold atoms in optical lattices are described in real space by the multiorbital mean-field approach. We consider four typical systems: (i) spinless identical bosons, (ii) spinor identical bosons, (iii) Bose-Bose mixtures, and (iv) Bose-Fermi mixtures, and derive in each case the corresponding multiorbital mean-field energy functional and working equations. The general equations as well as those obtained by explicitly utilizing the translational symmetry of lattices are presented. We discuss the effects of particle-particle interactions and translational symmetry on properties of the solutions.