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A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov process that originally arises as the limit of the mean-field interacting particle system. The weighted empirical measure of this…
This paper investigates the parabolic scaling limit of a damped stochastic wave map from the real line into the two-dimensional sphere, perturbed by multiplicative Gaussian noise of co-normal type. We prove that under this rescaling, the…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…
Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In this spirit, we study the dynamical generation of entanglement as a signature of chaos in a system…
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic processes with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary…
The parametric variation of the eigenfrequencies of a chaotic plate is measured and compared to random matrix theory using recently calculated universal correlation functions. The sensitivity of the flexural modes of the plate to pressure…
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…
This study discusses the quantum behavior of a particle, which is controlled by fluctuations in the physical space-time (ST) variables, rather than provides a novel interpretation of quantum theory. The fluctuations, i.e., inhomogeneities…
We compare the statistical fluctuation properties of the baryon and meson experimental mass spectra with those obtained from theoretical models (quark models and lattice QCD). We find that for the experimental spectra the statistical…
We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…
It was recently pointed out (and demonstrated experimentally) by Lundeen et al. that the wave function of a particle (more precisely, the wave function possessed by each member of an ensemble of identically-prepared particles) can be…
The fluctuations of the work done by an external Gaussian random force on a harmonic oscillator that is also in contact with a thermal bath is studied. We have obtained the exact large deviation function as well as the complete asymptotic…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
A fundamental principle of chaotic quantum dynamics is that local subsystems eventually approach a thermal equilibrium state. Large subsystems thermalize slower: their approach to equilibrium is limited by the hydrodynamic build-up of…
We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…
Three-wave interactions form the basis of our understanding of many pattern forming systems because they encapsulate the most basic nonlinear interactions. In problems with two comparable length scales, it is possible for two waves of the…
One attractive interpretation of quantum mechanics is the ensemble interpretation, where Quantum Mechanics merely describes a statistical ensemble of objects and not individual objects. But this interpretation does not address why the…
Here we discuss some issues concerning the statistical properties of ocean surface waves. We show that, using the approach of weak turbulence theory, deviations from Gaussian statistics can be naturally included. In particular we discuss…
The autocorrelation function of spectral determinants is proposed as a convenient tool for the characterization of spectral statistics in general, and for the study of the intimate link between quantum chaos and random matrix theory, in…
We study the Schr\"odinger equation driven by a weak Brownian forcing, and derive Gaussian fluctuations in the form of a time-inhomogeneous Ornstein-Uhlenbeck process. As a result, when evaluated at a fixed frequency, the intensity of the…