相关论文: Low-energy excitations of a one-dimensional Bose g…
We investigate the low-energy excitation spectrum of a Bose gas confined in a trap, with weak long-range repulsive interactions. In particular, we prove that the spectrum can be described in terms of the eigenvalues of an effective…
We consider systems of bosons trapped in a box, in the Gross-Pitaevskii regime. We show that low-energy states exhibit complete Bose-Einstein condensation with an optimal bound on the number of orthogonal excitations. This extends recent…
We exploit a few- to many-body approach to study strongly interacting dipolar bosons in the quasi-one-dimensional system. The dipoles attract each other while the short range interactions are repulsive. Solving numerically the multi-atom…
We consider systems of $N$ bosons in a box with volume one, interacting through a repulsive two-body potential of the form $\kappa N^{3\beta-1} V(N^\beta x)$. For all $0 < \beta < 1$, and for sufficiently small coupling constant $\kappa >…
We present a novel approach to the Bogoliubov theory of dilute Bose gases, allowing for an elementary derivation of the celebrated Lee-Huang-Yang formula in the Gross-Pitaevskii regime. Furthermore, we identify the low lying excitation…
In a one-dimensional weakly interacting Bose-Fermi mixture one branch of elementary excitations is well described by the Bogoliubov spectrum. Here we use the microscopic theory to study the decay of such quasiparticle excitations. The main…
We consider a system of $N$ bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which…
We have studied the phase diagram of a quasi-two-dimensional interacting Bose gas at zero temperature in the presence of random potential created by laser speckles. The superfluid fraction and the fraction of particles with zero momentum…
We consider the ground-state properties of an extended one-dimensional Bose gas with pointwise attractive interactions. We take the limit where the interaction strength goes to zero as the system size increases at fixed particle density. In…
We develop a theory of damping of low energy, collective excitations in a quasi-2D, homogenous, dipolar Bose gas at zero temperature, via processes whereby an excitation decays into two excitations with lower energy. We find that owing to…
A modified Gross-Pitaevskii approximation was introduced recently for bosons in dimension $d\le2$ by Kolomeisky {\it et al.} (Phys. Rev. Lett. {\bf 85} 1146 (2000)). We use the density functional approach with sixth-degree interaction…
We study the dynamics of a Bose-Einstein condensate in the quasiperiodic kicked rotor described by a Gross-Pitaevskii equation with periodic boundary conditions. As the interactions are increased, Bogoliubov excitations appear and deplete…
We consider weakly interacting bosonic gases with local and non-local multi-body interactions. By using the Bogoliubov approximation, we first investigate contact interactions, studying the case in which the interparticle potential can be…
We consider systems of $N$ bosons in $\mathbb{R}^3$, trapped by an external potential. The interaction is repulsive and has a scattering length of the order $N^{-1}$ (Gross-Pitaevskii regime). We determine the ground state energy and the…
A one-dimensional model of bosons with repulsive short-range interactions, solved analytically by Lieb and Liniger many years ago, predicts existence of two branches of elementary excitations. One of them represents Bogoliubov phonons, the…
We have numerically solved the low-energy excitation spectra of ferromagnetic Bose-Einstein condensates subject to dipolar interparticle interactions. The system is assumed to be harmonically confined by purely optical means, thereby…
I consider general interacting systems of quantum particles in one spatial dimension. These consist of bosons or fermions, which can have any number of components, arbitrary spin or a combination thereof, featuring low-energy two- and…
We consider the low density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii…
This thesis is devoted to a rigorous study of interacting quantum gases. The main objects of interest are the closely related concepts of excitation spectrum and quasiparticles. The immediate motivation of this work is to propose a spectral…
The stochastic Gross-Pitaevskii equation is shown to be an excellent model for quasi-one-dimensional Bose gas experiments, accurately reproducing the in situ density profiles recently obtained in the experiments of Trebbia et al. [Phys.…