Related papers: Mean field limit for bosons and propagation of Wig…
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…
We study the mean-field limit for a class of agent-based models describing flocking with nonlinear velocity alignment. Each agent interacts through a communication protocol $\phi$ and a non-linear coupling of velocities given by the power…
Realistic effective interparticle interactions of quantum many-body systems are widely seen as being short-range. However, the rigorous mathematical analysis of this type of model turns out to be extremely difficult, in general, with many…
We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for \emph{metastable states} in \emph{finite size systems}. In particular, we…
We present a probabilistic proof of the mean-field limit and propagation of chaos of a classical N-particle system in two dimensions with Coulomb interaction force of the form $f^N(q)=\pm\frac{q}{|q|^2}$ and $N$-dependent cut-off at…
In this paper we derive a two dimensional spray model with gyroscopic effects as the mean-field limit of a system modeling the interaction between an incompressible fluid and a finite number of solid particles. This spray model has been…
I review the quantum theory of the electron moving in a random environment. First, the quantum mechanics of individual particles scattered on a random potential is discussed. The quantum-mechanical description is extended to many-body…
We consider one-dimensional, interacting spinless bosons on a tight-binding lattice described by the Bose-Hubbard model. Besides attractive on-site two-body interactions, we include a three-body repulsive term such that the competition…
We study the mean-field dynamics of a system of $N$ interacting bosons starting from an initially condensated state. For a broad class of mean-field Hamiltonians, including models with arbitrary bounded interactions and models with…
We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner…
We study the interplay of superfluidity and glassy ordering of hard core bosons with random, frustrating interactions. This is motivated by bosonic systems such as amorphous supersolid, disordered superconductors with preformed pairs, and…
An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit…
We study the stationary nonlinear Schr\"odinger equation, or Gross-Pitaevskii equation, for a one--dimensional finite square well potential. By neglecting the mean--field interaction outside the potential well it is possible to discuss the…
Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization…
The evaluation and consideration of the mean flow in wave evolution equations are necessary for the accurate prediction of fluid particle trajectories under wave groups, with relevant implications in several domains, from the transport of…
We study the effective time evolution of a large quantum system consisting of a mixture of different species of identical bosons in interaction. If the system is initially prepared so as to exhibit condensation in each component, we prove…
In this work, we use a mixed quantum-classical (mean-field) many-body approach for simulating the quantum dynamics of excitons and exciton-polaritons beyond the single-excitation subspace. We combine the multitrajectory Ehrenfest approach,…
We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger (J. Chem. Phys. 65, 3968 (1976)), behaves like a weakly correlated ``mean field fluid'' over a…
Mean field theory is applied to nonequilibrium thermal energy transport in a model molecular junction. An approximation to the total time-dependent heat current in the junction is constructed using an ensemble of Ehrenfest trajectories, and…
Families of $N$ interacting curves are considered, with long range, mean field type, interaction. A family of curves defines a 1-current, concentrated on the curves, analog of the empirical measure of interacting point particles. This…