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We present a mathematically rigorous analysis of the ground state of a dilute, interacting Bose gas in a three-dimensional trap that is strongly confining in one direction so that the system becomes effectively two-dimensional. The…
A ground state energy density of an interacting dilute Bose gas system is studied in the canonical transformation scheme. It is shown that the transformation scheme enables us to calculate a higher order correction of order $n a^3$ in the…
We present results of computer simulations at low temperature of a two-dimensional system of dipolar bosons, with dipole moments aligned at an arbitrary angle with respect to the direction perpendicular to the plane. The phase diagram…
We study the physics of soft-core bosons at zero temperature in two dimensions for a class of potentials that could be realised in experiments with Rydberg dressed Bose-Einstein condensates. We analyze the ground state properties of the…
Thermodynamical properties of an interacting boson system at finite temperatures and zero chemical potential are studied within the framework of the Skyrme-like mean-field toy model. It is assumed that the mean field contains both…
We use a non-perturbative renormalization-group technique to study interacting bosons at zero temperature. Our approach reveals the instability of the Bogoliubov fixed point when $d\leq 3$ and yields the exact infrared behavior in all…
The ground state of a spinor Bose liquid is ferromagnetic, while the softest excitation above the ground state is the magnon mode. The dispersion relation of the magnon in a one-dimensional liquid is periodic in the wavenumber q with the…
Motivated by the recent experimental observation of an intermediate bosonic metallic state in the two-dimensional superconductor-insulator transition at $T=0$, we study an extended Bose Hubbard model in the limit of large number of…
We demonstrate rigorously that in the absence of explicit spin-dependent forces one of the ground states of interacting bosons with spin is always fully polarized -- however complicated the many-body interaction potential might be.…
We study Bose-Einstein gas for an arbitrary power low interaction $C_{\alpha}r^{-\alpha}$. This is done by the Hartree Fock Bogoliubov (HFB) approach at $T \le T_{c}$ and the mean field approach at $T>T_{c}$. Especially, we investigate the…
We study a one-dimensional disordered Bose fluid using bosonization, the replica method and a nonperturbative functional renormalization-group approach. The Bose-glass phase is described by a fully attractive strong-disorder fixed point…
A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density $\rho$ and temperature $T$. In the dilute regime, i.e., when $a^3\rho \ll 1$, where $a$ denotes the scattering length of the pair-interaction…
We obtain the superfluid hydrodynamic equations of a multi-component Bose gas with short-ranged interactions at zero temperature under the local equilibrium assumption and show that the quantum pressure is generally present in the…
We consider ground states of rotating Bose-Einstein condensates with attractive interactions in non-radially harmonic traps $V(x)=x_1^2+\Lambda ^2x_2^2 $, where $0<\Lambda \not =1$ and $x=(x_1, x_2)\in R^2$. For any fixed rotational…
We investigate the fragmented many-body ground states of a spin-2 Bose gas in zero magnetic field.\ We point out that the exact ground state is not simply an average over rotationally-invariant mean-field states, in contrast to the spin-1…
This paper is concerned with ground states of attractive Bose gases confined in an anharmonic trap $V(x)=\omega(|x|^2+k|x|^4)$ rotating at the velocity $\Omega>0$, where $\omega>0$ denotes the trapping frequency, and $k>0$ represents the…
The doubts concerning validity of gas approximation for strong interaction (for example, hard spheres) are expressed. A contradictory example - a Bose system in a lattice model - is considered. Namely, the X-Y model for spin 1/2 is taken. A…
We analyze the scattering problem of identical bosonic particles confined on a spherical surface. At low scattering energies and for a radius much larger than the healing length, we express the contact interaction strength in terms of the…
We investigate the zero-temperature phase diagram of interacting Bose gases in the presence of a simple cubic optical lattice, going beyond the regime where the mapping to the single-band Bose-Hubbard model is reliable. Our computational…
Motivated by the fundamental question of the fate of interacting bosons in flat bands, we consider a two-dimensional Bose gas at zero temperature with an underlying quartic single-particle dispersion in one spatial direction. This type of…