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We introduce a new simple hierarchically constrained model of slow relaxation. The configurational energy has a simple form as there is no coupling among the spins defining the system; the associated stationary distribution is an…
In an effort to better understand collisionless relaxation processes in gravitational systems, we investigate one-dimensional models. Taking advantage of a Hermite-Legendre expansion of relevant distribution functions, we present analytical…
In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic…
The connection between domain relaxations at individual scales and the collective heterogeneous response in non-equilibrium systems is a topic of profound interest in recent times. In a model sys- tem of constantly driven oppositely charged…
We study the dynamics of a class of Hamiltonian systems with dissipation, coupled to noise, in a singular (small mass) limit. We derive the homogenized equation for the position degrees of freedom in the limit, including the presence of a…
This paper deals with a one--dimensional model for granular materials, which boils down to an inelastic version of the Kac kinetic equation, with inelasticity parameter $p>0$. In particular, the paper provides bounds for certain distances…
We study analytically and by computer simulations a complex system of adaptive agents with finite memory. Borrowing the framework of the Minority Game and using the replica formalism we show the existence of an equilibrium phase transition…
A variational coarse-graining framework for heterogeneous media is developed that allows for a seamless transition from the traditional static scenario to a arbitrary loading conditions, including inertia effects and body forces. The…
We describe a simple and flexible method for implementing semi-definite programming relaxations for bounding the set of quantum correlations. The method relies on obtaining equality constraints from randomly sampled moment matrices and…
We address the question whether observables of an exactly solvable model of electrons coupled to (optical) phonons relax into large time stationary state values and investigate if the asymptotic expectation values can be computed using a…
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently…
We start with a rather detailed, general discussion of recent results of the replica approach to statistical mechanics of a single classical particle placed in a random $N (\gg 1)$-dimensional Gaussian landscape and confined by a…
Relaxation processes in collisionless dynamics lead to peculiar behavior in systems with long-range interactions such as self-gravitating systems, non-neutral plasmas and wave-particle systems. These systems, adequately described by the…
We study a class of diffusion processes arising from random perturbations of conservative Hamiltonian systems. Under a set of abstract hypotheses -- including basic structural assumptions on the Hamiltonian, a weak Lyapunov structure, and a…
The evolution of physical systems are often modeled by simple Markovian processes. When settled into stationary states, the probability distributions of such systems are time independent, by definition. However, they do not necessarily fall…
We prove that quantum many-body systems on a one-dimensional lattice locally relax to Gaussian states under non-equilibrium dynamics generated by a bosonic quadratic Hamiltonian. This is true for a large class of initial states - pure or…
We study the steady state of a multiply-connected system that is driven out of equilibrium by a sparse perturbation. The prototype example is an $N$-site ring coupled to a thermal bath, driven by a stationary source that induces transitions…
We investigate early-time equilibration rates of observables in closed many-body quantum systems and compare them to those of two correlation functions, first introduced by Kubo and Srednicki. We explore whether these different rates…
We study nonequilibrium dynamics of relativistic $N$-component scalar field theories in Minkowski space-time in a classical-statistical regime, where typical occupation numbers of modes are much larger than unity. In this strongly…
The presence of nonanalyticity in observables is a manifestation of phase transitions. Through the study of two paradigmatic topological models in one and two dimensions, in this work we show that the circuit complexity based on our…