Related papers: Second-order corrections to mean-field evolution o…
We formulate a method to study two-body correlations in a system of N identical bosons interacting via central two-body potentials. We use the adiabatic hyperspherical approach and assume a Faddeev-like decomposition of the wave function.…
We study the full time evolution of one- and two-mode bosonic quantum systems that interact through single- and two-mode squeezing Hamiltonians. We establish that the single- and two-mode cases are formally equivalent, leading to the same…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
The disorder-induced localization of few bosons interacting via a contact potential is investigated through the analysis of the level-spacing statistics familiar from random matrix theory. The model we consider is defined in a continuum and…
We consider the many-body time evolution of weakly interacting bosons in the mean field regime for initial coherent states. We show that bounded k-particle operators, corresponding to dependent random variables, satisfy both, a law of large…
We consider a few number of identical bosons trapped in a 2D isotropic harmonic potential and also the $N$-boson system when it is feasible. The atom-atom interaction is modelled by means of a finite-range Gaussian interaction. The spectral…
The mean field approximation is numerically validated in the bosonic case by considering the time evolution of quantum states and their associated reduced density matrices by many-body Schr\"odinger dynamics. The model phase-space is…
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 second order twist corrections to a toy model of a dipole-dipole interaction in the context of a both deterministic and stochastic effects. This work is done in the high $N_C$ limit in the Bjorken picture. We show that the…
Mean field theory for the time evolution of quantum meson fields is studied in terms of the functional Schroedinger picture with a time-dependent Gaussian variational wave functional. We first show that the equations of motion for the…
Few-body correlations often express the distinguishing characteristic features of a many-body system. This thesis studies such correlations within dilute Bose-Einstein condensates in the case of arbitrary negative s-wave scattering length.…
We study the many body Schr\"odinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling, that emerges naturally for initially confined particles.…
Zero-range effective interactions are commonly used in nuclear physics and in other domains to describe many-body systems within the mean-field model. If they are used within a beyond-mean-field framework, contributions to the total energy…
In this paper, we consider a class of second-order evolution differential inclusions in Hilbert spaces. This paper deals with the approximate controllability for a class of second-order control systems. First, we establish a set of…
In these lectures we review the simplest gauge extensions of the standard model, and the present and future limits on new weak interactions.
We analyze the Poisson structure of the time-dependent mean-field equations for bosons and construct the Lie-Poisson bracket associated to these equations. The latter follow from the time-dependent variational principle of Balian and…
We consider a system of $N\gg 1$ interacting fermionic particles in three dimensions, confined in a periodic box of volume $1$, in the mean-field scaling. We assume that the interaction potential is bounded and small enough. We prove upper…
This paper explores a system of interacting `soft core' bosons in the Gross-Pitaevskii mean-field approximation in a random Bernoulli potential. First, a condition for delocalization of the ground state wave function is proved which depends…
This article surveys a number of theoretical problems and open questions in the field of two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three dimensions, in two dimensions the formation of long-range…
Using the Funtional Integrals Formulation is developes a self-consistent mean field expansion to evolution operators of a system composed by two subsystems. This is a general expansion and can be generalized for more of two subsystems,…