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Starting from a Caldeira-Leggett model for the interaction of a system with an environment, Joichi, Matsumoto, and Yoshimura have reconsidered the derivation of the quantum Boltzmann equation. They find an extra term that accounts for the…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
We derive the hydrodynamic limit of the Kawasaki dynamics for the one-dimensional conservative system of unbounded real-valued spins with arbitrary strong, quadratic and finite-range interactions. This extends prior results for…
We investigate the long-time behaviour of solutions to a nonlocal partial differential equation on smooth Riemannian manifolds of bounded sectional curvature. The equation models self-collective behaviour with intrinsic interactions that…
A kinetic equation is derived for the phase density of a system of point particles, generating a system of integro-differential equations for distribution functions that have a deterministic meaning. The derivation took into account the…
We study the interaction between a pair of particles suspended in a uniform oscillatory flow. The time-averaged behavior of particles under these conditions, driven by inertial and viscous effects, is explored through a theoretical…
We study the equilibrium fluctuations of an interacting particle system evolving on the discrete ring with $N\in\mathbb N$ points, denoted by $\mathbb T_N$, and with three species of particles that we name $A,B$ and $C$, but such that at…
The variance and uncertainty product of the position and momentum many-particle operators of structureless bosons interacting by a long-range inter-particle interaction and trapped in a single-well potential are investigated. In the first…
In this set of lecture notes we review the mode-coupling theory of the glass transition from several perspectives. First, we derive mode-coupling equations for the description of density fluctuations from microscopic considerations with the…
We develop a unified kinetic theory for ordered fluids, which systematically extends the phase space with the appropriate generalized angular momenta. Our theory yields a uniquely determined mesoscopic model for any continuum with…
We examine the problem of a repulsive, weakly-interacting and harmonically trapped Bose-Einstein condensate under rotation. We derive a simple analytic expression for the energy incorporating the interactions when the angular momentum per…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
Homogeneous Boltzmann-type equations are an established tool for modelling interacting multi-agent systems in sociophysics by means of the principles of statistical mechanics and kinetic theory. A customary implicit assumption is that…
In this paper, we propose a numerical investigation of topological interactions in flocking dynamics. Starting from a microscopic description of the phenomena, mesoscopic and macroscopic models have been previously derived under specific…
We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally…
In this paper, how to successfully and efficiently condition a target population of agents towards consensus is discussed. To overcome the curse of dimensionality, the mean field formulation of the consensus control problem is considered.…
We study the dynamics of a Bose-Einstein condensate in a one-dimensional optical lattice in the limit of weak atom-atom interactions, including an approximate model for quantum fluctuations. A pulsating dynamical instability in which atoms…
The Rosen-Zener model for association of atoms in a Bose-Einstein condensate is studied. Using a nonlinear Volterra integral equation, we obtain an analytic formula for final probability of the transition to the molecular state for weak…
The hypothesis of molecular chaos plays the central role in kinetic theory, which provides a closure leading to the Boltzmann equation for quantitative description of classic fluids. Yet how to properly extend it to active systems is still…
The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions are derived. It is shown that interactions retardation leads to irreversible behaviour of many-body…