Related papers: Mean field limit for Bosons with compact kernels i…
We propose a new approach for the study of the time evolution of a factorized $N$-particle bosonic wave function with respect to a mean-field dynamics with a bounded interaction potential. The new technique, which is based on the control of…
The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized N-boson states, in the limit of large N. In this paper we provide estimates on the rate of convergence of the microscopic quantum mechanical evolution…
In this report we are aiming at introducing a global measure of non-classicality of the state space of $N$-level quantum systems and estimating it in the limit of large $N$. For this purpose we employ the Wigner function negativity as a…
We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…
I present recent results in quantum statistical mechanics, obtained in joint works with Mathieu Lewin and Phan Th{\`a}nh Nam. We consider a certain mean-field limit of the grand-canonical ensemble for a Bose gas at positive temperature. In…
We prove that Gibbs measures based on 1D defocusing nonlinear Schr{\"o}dinger functionals with sub-harmonic trapping can be obtained as the mean-field/large temperature limit of the corresponding grand-canonical ensemble for many bosons.…
We study the evolution of a many-particle system whose wave function obeys the N-body Schroedinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the absence of an external potential. We…
The detailed mean-field treatment of the Bose polaron problem in two and three dimensions is presented. Particularly, assuming that impurity is immersed in the dilute Bose gas and interacts with bosons via the hard-sphere two-body…
Quantum many-body interactions can induce quantum entanglement among particles, rendering them valuable resources for quantum-enhanced sensing. In this work, we derive a universal and fundamental bound for the growth of the quantum Fisher…
In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case.…
We show that the time-dependent nonlinear Schrodinger equation of mean-field theory has limited utility for a one-dimensional condensate of impenetrable bosons. Mean-field theory with its associated order parameter predicts interference…
A study of the integrability of one-dimensional quantum mechanical many-body systems with general point interactions and boundary conditions describing the interactions which can be independent or dependent on the spin states of the…
A multi-branch quantum circuit is considered from the viewpoint of coherent electron or wave transport. Starting with the closed system, we give analytical conditions for the appearance of two isolated localized states out of the energy…
A unified theory for the current through a nanoscale region of interacting electrons connected to two leads which can be either ferromagnet or superconductor is presented, yielding Meir-Wingreen-type formulas when applied to specific…
Transport properties of the multicomponent quantum many-body systems obeying Haldane's fractional exclusion statistics are studied in one dimension. By computing the finite-size spectrum under twisted boundary conditions, we explicitly…
We present a probabilistic proof of the mean field limit and propagation of chaos $N$-particle systems in three dimensions with positive (Coulomb) or negative (Newton) $1/r$ potentials scaling like $1/N$ and an $N$-dependent cut-off which…
The effect of scattering with non-zero impact parameters between consituents in relativistic heavy ion collisions is investigated. In solving the relativistic Boltzmann equation, the characteristic range of the collision kernel is varied…
We consider a gas of weakly interacting bosons in three dimensions subject to an external potential in the mean field regime. Assuming that the initial state of our system is a product state, we show that in the trace topology of one-body…
We develop a protocol for learning a class of interacting bosonic Hamiltonians from dynamics with Heisenberg-limited scaling. For Hamiltonians with an underlying bounded-degree graph structure, we can learn all parameters with root mean…
The mean-field pictures based on the standard time-dependent variational approach have widely been used in the study of nonlinear many-boson systems such as the Bose-Hubbard model. The mean-field schemes relevant to Gutzwiller-like trial…