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We consider a gas of N bosons with interactions in the mean-field scaling regime. We review a recent proof of the asymptotic expansion of its spectrum and eigenstates and two applications of this result, namely the derivation of an…
We derive a new damping mechanism in the open quantum systems description of Bose-Einstein condensates. It stems from previously neglected terms in the derivation of the stochastic projective Gross-Pitaevskii equation (SPGPE), accounting…
The non-equilibrium dynamics of integrable systems are special: there is substantial evidence that after a quantum quench they do not thermalize but their asymptotic steady state can be described by a Generalized Gibbs Ensemble (GGE). Most…
Self-consistent hydrodynamic one-loop quantum corrections to the Gross-Pitaevskii equation due to the interaction of the condensate with collective excitations are calculated. It is done by making use a formalism of effective action and…
We propose and analyze a new numerical method for computing the ground state of the modified Gross-Pitaevskii equation for modeling the Bose-Einstein condensate with a higher order interaction by adapting the density function formulation…
The achievement of Bose-Einstein condensation (BEC) in ultracold vapors of alkali atoms has given enormous impulse to the theoretical and experimental study of dilute atomic gases in condensed quantum states inside magnetic traps and…
We present a theory for the linear dynamics of a weakly interacting Bose gas confined inside a harmonic trap at finite temperature. The theory treats the motions of the condensate and of the non-condensate on an equal footing within a…
Dilute Bose gases, cooled down to low temperatures below the Bose-Einstein condensation temperature, form coherent ensembles described by the Gross-Pitaevskii equation. Stationary solutions to the latter are topological coherent modes. The…
We consider a dilute homogeneous Bose gas with both an isotropic short-range contact interaction and an anisotropic long-range dipole-dipole interaction in a weak random potential at low temperature in three dimensions. Within the realm of…
We analyze the ground state of a Bose-Einstein condensate in the presence of higher-order interaction (HOI), modeled by a modified Gross-Pitaevskii equation (MGPE). In fact, due to the appearance of HOI, the ground state structures become…
We verify Bogoliubov's approximation for translation invariant Bose gases in the mean field regime, i.e. we prove that the ground state energy $E_N$ is given by $E_N=Ne_\mathrm{H}+\inf \sigma\left(\mathbb{H}\right)+o_{N\rightarrow…
The ground-state energy per particle $E/N$ and condensate density $n_0$ of a dilute Bose gas are studied with a self-consistent perturbation expansion satisfying the Hugenholtz-Pines theorem and conservation laws simultaneously. A class of…
We show that the spreading of the center-of-mass density of ultracold attractively interacting bosons can become superballistic in the presence of decoherence, via single-, two- and/or three-body losses. In the limit of weak decoherence, we…
We derive and analyze the coupled equations of quadratic approximation of the Bogoliubov model for a weakly interacting Bose gas. The first equation determines the condensate density as a variational parameter and ensures the minimum of the…
We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical…
In 1963, a Simple Approach was developed to study the ground state energy of an interacting Bose gas. It consists in the derivation of an Equation, which is not based on perturbation theory, and which gives the exact expansion of the energy…
In the mean-field approximation, the number density \rho(r) for the ground state of a Bose-Einstein condensate trapped by an external potential V(r) satisfies a classical field equation called the Gross-Pitaevskii equation. We show that…
We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This…
We describe a quantum droplet of a Bose-Bose mixture squeezed by an external harmonic forces in one spatial direction. Our approach is based on the self-consistent method formulated in [1]. The true spatial droplet profile in the direction…
We develop a quantum many-body theory of the Bose-Hubbard model based on the canonical quantization of the action derived from a Gutzwiller mean-field ansatz. Our theory is a systematic generalization of the Bogoliubov theory of…