Related papers: Quantum many-body fluctuations around nonlinear Sc…
Quantum computers could potentially simulate the dynamics of systems such as polyatomic molecules on a much larger scale than classical computers. We investigate a general quantum computational algorithm that simulates the time evolution of…
We consider the quantum many-body evolution of a homogeneous Fermi gas in three dimensions in the coupled semiclassical and mean-field scaling regime. We study a class of initial data describing collective particle-hole pair excitations on…
This article gives a rigorous analysis of the fluctuations of the Bose-Einstein condensate for a system of non-interacting bosons in an arbitrary potential, assuming that the system is governed by the canonical ensemble. As a result of the…
In this work, we study the quantum fluctuation dynamics in a Bose gas on a torus $\Lambda=(L\mathbb{T})^3$ that exhibits Bose-Einstein condensation, beyond the leading order Hartree-Fock-Bogoliubov (HFB) fluctuations. Given a Bose-Einstein…
Coherent states play an important role in quantum mechanics because of their unique properties under time evolution. Here we explore this concept for one-dimensional repulsive nonlinear Schr\"odinger equations, which describe weakly…
We combine theoretical and experimental efforts to propose a method for studying energy fluctuations, in particular, to obtain the related bi-stochastic matrix of transition probabilities by means of simple measurements at the end of a…
Simulations of purely self-gravitating N-body systems are often used in astrophysics and cosmology to study the collisionless limit of such systems. Their results for macroscopic quantities should then converge well for sufficiently large…
A pendulum prepared perfectly inverted and motionless is a prototype of unstable equilibria and corresponds to an unstable hyperbolic fixed point in the dynamical phase space. Unstable fixed points are central to understanding Hamiltonian…
We investigate the dephasing suffered by a nonrelativistic quantum particle within a conformally fluctuating spacetime geometry. Starting from a minimally coupled massive Klein-Gordon field, the low velocity limit yields an effective…
Advancing our understanding of non-equilibrium phenomena in quantum many-body systems remains among the greatest challenges in physics. Here, we report on the experimental observation of a paradigmatic many-body problem, namely the…
We present a generalized Gross-Pitaevskii equation that describes also the dissipative dynamics of a trapped partially Bose condensed gas. It takes the form of a complex nonlinear Schr\"odinger equation with noise. We consider an…
We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behaviour is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87 (2001) 180601]. By…
The oscillator bases expansion stands as an efficient approximation method for the time-independent Schr\"odinger equation. The method, originally formulated with one non-linear variational parameter, can be extended to incorporate two such…
Correlated classical and quantum many-particle systems out of equilibrium are of high interest in many fields, including dense plasmas, correlated solids, and ultracold atoms. Accurate theoretical description of these systems is challenging…
In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun. Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied the joint dynamics of a classical point particle and a wave type generalization of…
The dynamics of a Bose-Einstein condensate of atoms having attractive interactions is studied using quantum many-body simulations. The collapse of the condensate by quantum tunneling is numerically demonstrated and the tunneling rate is…
We consider the time evolution of $N$ bosons in the mean field regime for factorized initial data. In the limit of large $N$, the many body evolution can be approximated by the non-linear Hartree equation. In this paper we are interested in…
The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrodinger equation for potentials V that can be any function of the…
We study quantum dynamics of bosonic atoms that are excited to form a phase kink, or several kinks, by an imprinting potential in a one-dimensional trap. We calculate dissipation due to quantum and thermal fluctuations in soliton…
Fluctuations of the number of condensed atoms in a finite-size, weakly interacting Bose gas confined in a box potential are investigated for temperatures up to the critical region. The canonical partition functions are evaluated using a…