Related papers: Analysis of fluctuations around non linear effecti…
We report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical…
We report on recent results concerning the derivation of effective evolution equations starting from many body quantum dynamics. In particular, we obtain rigorous derivations of nonlinear Hartree equations in the bosonic mean field limit,…
The development of powerful numerical techniques has drastically improved our understanding of quantum matter out of equilibrium. Inspired by recent progress in the area of noisy intermediate-scale quantum devices, this paper highlights…
We study the dynamics of a Bose-Einstein condensate in a one-dimensional optical lattice in the limit of weak atom-atom interactions, including an approximate model for quantum fluctuations. A pulsating dynamical instability in which atoms…
We review recent progress in the nonequilibrium dynamics of thermally isolated many-body quantum systems, evolving with an ensemble of Hamiltonians as opposed to deterministic evolution with a single time-dependent Hamiltonian. Such…
We show that any non-relativistic quantum N-body dynamics problem with pairwise interactions can be exactly reformulated in terms of N well behaved 1-body stochastic density equations. Specifically, the time evolving N-body density matrix…
The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two…
We show in detail how three one-body fluctuation profiles, namely the local compressibility, the local thermal susceptibility, and the reduced density, can be obtained from a statistical mechanical many-body description of classical…
We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical…
We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time…
We use dynamic equations to derive a relation between correlation functions and response or relaxation functions in many-body systems. The relation is very general and holds both in equilibrium, when the usual fluctuation-dissipation…
There has been recent interest in the relaxational modes of small-scale fully connected systems of aligning self-propelled particles (Spera et al., Phys. Rev. Lett. {\bf 132}: 078301 (2024)). We revisit the classical connection between…
Nonequilibrium dynamics in quantum field theory has been studied extensively using truncations of the 2PI effective action. Both 1/N and loop expansions beyond leading order show remarkable improvement when compared to mean-field…
We consider the dynamics of $N$ bosons in three dimensions. We assume the pair interaction is given by $N^{3\beta -1}V(N^{\beta }\cdot )$ . By studying an associated many-body wave operator, we introduce a BBGKY hierarchy which takes into…
In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this…
The quantum dynamics of a one-dimensional bosonic Josephson junction is studied by solving the time-dependent many-boson Schr\"odinger equation numerically exactly. Already for weak interparticle interactions and on short time scales, the…
We present a new proof of the convergence of the N-particle Schroedinger dynamics for bosons towards the dynamics generated by the Hartree equation in the mean-field limit. For a restricted class of two-body interactions, we obtain…
We introduce and investigate an open many-body quantum system in which kinetically constrained coherent and dissipative processes compete. The form of the incoherent dissipative dynamics is inspired by that of epidemic spreading or…
This work reviews recent advances in the analytical treatment of the continuum spectrum of correlated few-body non-relativistic Coulomb systems. The exactly solvable two-body problem serves as an introduction to the non-separable…
We have investigated S-wave bound states composed of three identical bosons interacting via regulated delta function potentials in non-relativistic quantum mechanics. For low-energy systems, these short-range potentials serve as an…