Related papers: Taming the entanglement in the dynamical theory of…
We consider a homogeneous Bose gas of particles with an attractive interaction. Mean field theory predicts for this system a spontaneous symmetry breaking at a certain value of the interaction strength. We show that at this point a…
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 provide a detailed description of the nonequilibrium time evolution of an interacting homogeneous Bose-Einstein condensate. We use a nonperturbative in-medium quantum field theory approach as a microscopic model for the Bose gas. The…
We develop an approach for characterizing non-local quantum correlations in spin systems with exactly or nearly degenerate ground states. Starting with linearly independent degenerate eigenfunctions calculated with exact diagonalization we…
This is a book about Lieb's Simplified approach to the Bose gas, which is a family of effective single-particle equations to study the ground state of many-body systems of interacting Bosons. It was introduced by Lieb in 1963, and recently…
We present a complete analysis of the dynamics of a Bose-Einstein condensate trapped in a symmetric triple-well potential. Our classical analogue treatment, based on a time-dependent variational method using SU(3) coherent states, includes…
We define a formalism of a self-consistent description of the ground state of a weakly interacting Bose system, accounting for higher order terms in expansion of energy in the diluteness parameter. The approach is designed to be applied to…
We study the quench of a degenerate ultracold Bose gas to the unitary regime, where interactions are as strong as allowed by quantum mechanics. We lay the foundations of a cumulant theory able to capture simultaneously the three-body Efimov…
A well-isolated system often shows relaxation to a quasi-stationary state before reaching thermal equilibrium. Such a prethermalization has attracted considerable interest recently in association with closely related fundamental problems of…
The density of states of a Bose-condensed gas confined in a harmonic trap is investigated. The predictions of Bogoliubov theory are compared with the ones of Hartree-Fock theory and of the hydrodynamic model. We show that the Hartree-Fock…
The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
The Simplified approach to the Bose gas was introduced by Lieb in 1963 to study the ground state of systems of interacting Bosons. In a series of recent papers, it has been shown that the Simplified approach exceeds earlier expectations,…
We study entanglement entropy of boundary states in a free bosonic conformal field theory. A boundary state can be thought of as composed of a particular combination of left and right-moving modes of the two-dimensional conformal field…
We reconsider the non-equilibrium dynamics of closed quantum systems. In particular we focus on the thermalization of integrable systems. Here we show how the generalized Gibbs Ensemble (GGE) can be constructed as the best approximation to…
We consider the dynamics of a 2D Bose gas with an interaction potential of the form $N^{2\beta-1}w(N^\beta\cdot)$ for $\beta\in (0,3/2)$. The interaction may be chosen to be negative and large, leading to the instability regime where the…
The structure of the thermal equilibrium state of a weakly interacting Bose gas is of current interest. We calculate the density matrix of that state in two ways. The most effective method, in terms of yielding a simple, explicit answer, is…
Considering an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a toroidal trap, we find that the system undergoes a phase transition from a uniform to a localized state, as the magnitude of the…
As is well-known, in Bogoliubov's theory of an interacting Bose gas the ground state of the Hamiltonian $\hat{H}=\sum_{\bf k\neq 0}\hat{H}_{\bf k}$ is found by diagonalizing each of the Hamiltonians $\hat{H}_{\bf k}$ corresponding to a…
We study the entanglement dynamics and relaxation properties of a system of two interacting qubits in the two cases (I) two independent bosonic baths and (II) one common bath, at temperature T. The entanglement dynamics is studied in terms…