相关论文: Weakly-Interacting Bosons in a Trap within Approxi…
We consider a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of…
By using the Hartree-Fock-Bogoliubov equations within the Popov approximation, we investigate the thermodynamic properties of a dilute binary Bose-Fermi mixture confined in an isotropic harmonic trap. For mixtures with an attractive…
Developing Bogoliubov theory of weakly interacting Bose gas in uncompacted three-dimension space, quantum fluctuation energy of one component dilute gas of Bose-Einstein condensate (BEC) confined to two parallel plates investigated at…
The thermodynamics of a homogeneous dilute Bose gas with an arbitrary strong repulsion between particles is investigated on the basis of the exact relation connecting the pair correlation function with the in-medium pair wave functions and…
We introduce a family of correlated trial wave functions for the $N$-particle ground state of an interacting Bose gas in a harmonic trap. For large $N$, the correlations lead to a relative energy decrease of a fraction $3/5N$, compared to…
The present short note is simply intended to communicate that I have analytically diagonalized the Bogoliubov truncated Hamiltonian $H_c$~\cite{Bogo1,Bogo2}, in an interacting bosonic gas. This is the natural prosecution of my…
On top of the mean-field analysis of a Bose-Einstein condensate, one typically applies the Bogoliubov theory to analyze quantum fluctuations of the excited modes. Therefore, one has to diagonalize the Bogoliubov Hamiltonian in a symplectic…
We study the stability and dynamics of an ultra-cold bosonic gas trapped in a toroidal geometry and driven by rotation, in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the…
We calculate the density profiles and density correlation functions of the one-dimensional Bose gas in a harmonic trap, using the exact finite-temperature solutions for the uniform case, and applying a local density approximation. The…
We study the quantum dynamics of the Bose-Hubbard model on a ladder formed by two rings coupled by tunneling effect. By implementing the Bogoliubov approximation scheme, we prove that, despite the presence of the inter-ring coupling term,…
The lowest-lying collective modes of a trapped Bose gas in an optical lattice are studied in the Bose-Hubbard model. An exact diagonalization of the Hamiltonian is performed in a one-dimensional five-particle system in order to find the…
The macroscopic quantum states of a condensed neutral Bose gas in one-dimensional power-law traps are obtained by solving the Gross-Pitaevskii equation numerically. A suitable candidate for a trial wave function for the variational…
Quantum mechanical few-body systems in reduced dimensionalities can exhibit many interesting properties such as scale-invariance and universality. Analytical descriptions are often available for integer dimensionality, however, numerical…
The WKB-approximation for the Bogoliubov-equations of the quasi-particle excitations in Bose-gases with condensate is worked out in the case of spherically symmetric trap potentials on the basis of the resulting quantization rule. The…
The Bogoliubov approximation and the Gross-Pitaevskii equation characterize the effect of repulsive interactions on a dilute ideal Bose-Einstein gas in a spherical harmonic trap. For large $N$, the interactions expand the condensate…
We study the collapse in a coupled Bose-Einstein condensate of two types of bosons 1 and 2 under the action of a trap using the time-dependent Gross-Pitaevskii equation. The system may undergo collapse when one, two or three of the…
We investigate the dynamic behavior of a Bose-condensed gas of alkali atoms interacting with repulsive forces and confined in a magnetic trap at zero temperature. Using the Thomas-Fermi approximation, we rewrite the Gross-Pitaevskii…
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 two-parametric fractional statistics is proposed, which can be used to model a weakly-interacting Bose-system. It is shown that the parameters of the introduced weakly nonadditive Polychronakos statistics can be linked to effects of…
We study the problem of disordered interacting bosons within grand-canonical thermodynamics and Bogoliubov theory. We compute the fractions of condensed and non-condensed particles and corrections to the compressibility and the speed of…