Related papers: Mean Field Limits in Strongly Confined Systems
The stationary one dimensional Schr\"odinger-Poisson system on a bounded interval is considered in the limit of a small Debye length (or small temperature). Electrons are supposed to be in a mixed state with the Boltzmann statistics. Using…
Neutral atoms interact through a van der Waals potential which asymptotically falls off as r^{-6}. In ultracold gases, this interaction can be described to a good approximation by the atom-atom scattering length. However, corrections arise…
We prove that the complex Euclidean field theory with local quartic self-interaction in two dimensions arises as a limit of an interacting Bose gas at positive temperature, when the density of the gas becomes large and the range of the…
We study the dynamics of non-aligning, non-interacting self-propelled particles confined to a box in two dimensions. In the strong confinement limit, when the persistence length of the active particles is much larger than the size of the…
One of quantum physics' fundamental, but largely unsolved, problems is the computation of the correlation functions in many-body systems. In this paper we address this problem in the case of one-dimensional spinor gases with repulsive…
We use a mean-field (Hartree-like) approach to study the conductance of a strongly localized electron system in two dimensions. We find a crossover between a regime where Coulomb interactions modify the conductance significantly to a regime…
The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle…
We report on a simple strategy to treat mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. Extending the method of counting, introduced in [Lett. Math.…
Understanding non-equilibrium quantum dynamics of many-body systems is one of the most challenging problems in modern theoretical physics. While numerous approximate and exact solutions exist for systems in equilibrium, examples of…
The spectrum and properties of quantum bound states is strongly dependent on the dimensionality of space. How this comes about and how one may theoretically and experimentally study the interpolation between different dimensions is a topic…
We prove that the grand canonical Gibbs state of an interacting quantum Bose gas converges to the Gibbs measure of a nonlinear Schr\"odinger equation in the mean-field limit, where the density of the gas becomes large and the interaction…
We consider the three-dimensional time-dependent Gross-Pitaevskii equation arising in the description of rotating Bose-Einstein condensates and study the corresponding scaling limit of strongly anisotropic confinement potentials. The…
We investigate bound states of a non-relativistic scalar particle in a three-dimensional helically twisted (torsional) geometry, considering both the free case and the presence of external radial interactions. The dynamics is described by…
We review some recent results on the norm approximation to the Schr\"odinger dynamics. We consider $N$ bosons in $\mathbb{R}^3$ with an interaction potential of the form $N^{3\beta-1}w(N^{\beta}(x-y))$ with $0\le \beta<1/2$, and show that…
We study the limiting behavior of a singularly perturbed Schr\"odinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane $(x,y)$ and subject to a strong uniform magnetic field in the plane…
We formulate a kinetic theory of self-interacting meson fields with an aim to describe the freezeout stage of the space-time evolution of matter in ultrarelativistic nuclear collisions. Kinetic equations are obtained from the Heisenberg…
Systems consisting of cold interacting bosons show interesting collective phenomena such as Bose-Einstein condensation or superfluidity and are currently studied in condensed matter and atomic physics. Of particular interest are nonideal…
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 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…
In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of $N$ $d$-dimensional bosons for large $N$. The…