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Quantum-field-theoretic descriptions of interacting condensed bosons have suffered from the lack of self-consistent approximation schemes satisfying Goldstone's theorem and dynamical conservation laws simultaneously. We present a procedure…
We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for…
Starting from the two-dimensional Boussinesq equation without rotation, we derive a kinetic equation for weak interaction of internal waves using non-canonical variables. We follow a formalism introduced by P. Ripa in the 80's. The…
We investigate the dynamical instability of Bose-Einstein condensates (BECs) with higher-order interactions immersed in an optical lattice with weak driving harmonic potential. For this, we compute both analytically and numerically a…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…
The constrained consensus problem considered in this paper, denoted interval consensus, is characterized by the fact that each agent can impose a lower and upper bound on the achievable consensus value. Such constraints can be encoded in…
We analyze the properties of the contact process with long-range interactions by the use of a kinetic ensemble in which the total number of particles is strictly conserved. In this ensemble, both annihilation and creation processes are…
A model is proposed of an infinite population of entities immigrating to a noncompact habitat, in which the newcomers are repelled by the already existing population. The evolution of such a population is described at micro- and mesoscopic…
We consider interacting multi-agent systems where the interaction is not only pairwise but involves simultaneous interactions among multiple agents (multiple-wise interaction). By passing through the mesoscopic and macroscopic limits with a…
We consider an interacting unbounded spin system, with conservation of the mean spin. We derive quantitative rates of convergence to the hydrodynamic limit provided the single-site potential is a bounded perturbation of a strictly convex…
We consider a system of particles experiencing diffusion and mean field interaction, and study its behaviour when the number of particles goes to infinity. We derive non-asymptotic large deviation bounds measuring the concentration of the…
A simple "trick" is proposed, which allows to perform exactly the site-averaging procedure required when developing integral equation theories of interaction site models of macromolecular fluids. It shows that no approximation is involved…
This note studies a network of agents having continuous-time dynamics with quantized interactions and time-varying directed topology. Due to the discontinuity of the dynamics, solutions of the resulting ODE system are intended in the sense…
We consider interacting particle systems with unbounded interaction range on general countably infinite graphs $S$ and prove explicit non-asymptotic error bounds for approximations of the infinite-volume dynamics by systems of finitely many…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
This paper studies a class of consensus dynamics where the interactions between agents are affected by a time-varying unknown scaling factor. This situation is encountered in the control of robotic fleets over a wireless network or in…
An approach based on a lattice version of the Boltzmann kinetic equation for describing multi-phase flows in nano- and micro-corrugated devices is proposed. We specialize it to describe the wetting/dewetting transition of fluids in presence…