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We investigate the non-equilibrium dynamics of a class of isolated one-dimensional systems possessing two degenerate ground states, initialized in a low-energy symmetric phase. We report the emergence of a time-scale separation between fast…
We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by…
Topological defects play a prominent role in the physics of two-dimensional materials. When driven out of equilibrium in active nematics, disclinations can acquire spontaneous self-propulsion and drive self-sustained flows upon…
Many-body localized phases retain memory of their initial conditions in disordered interacting systems with unitary dynamics. The stability of the localized phase due to the breakdown of unitarity is of relevance to experiment in the…
We here describe the possibility of a synthetic description of the onset of Chaos in many degrees of freedom dynamical systems within the framework of the geometric description of dynamics. We show how this approach to instability helps to…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective…
Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on…
In this brief review we introduce the methods of quantum field theory out of equilibrium and study the non-equilibrium aspects of phase transitions. Specifically we critically study the picture of the ``slow-roll'' phase transition in the…
We review the non-equilibrium dynamics of many-body quantum systems after a quantum quench with spatial inhomogeneities, either in the Hamiltonian or in the initial state. We focus on integrable and many-body localized systems that fail to…
Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting these bifurcations…
The time evolution of O(N) symmetric lambda Phi^4 scalar field theory is studied in the large N limit. In this limit the <Phi> mean field and two-point correlation function <Phi Phi> evolve together as a self-consistent closed Hamiltonian…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
The dynamics of a dense relativistic quantum fluid out of thermodynamic equilibrium is studied in the framework of the Phi^4 scalar field theory in the large N limit. The time evolution of a particle distribution in momentum space (the…
A major open question in studies of nonequilibrium quantum dynamics is the identification of the time scales involved in the relaxation process of isolated quantum systems that have many interacting particles. We demonstrate that long time…
We formulate the statistical dynamics of topological defects in the active nematic phase, formed in two dimensions by a collection of self-driven particles on a substrate. An important consequence of the non-equilibrium drive is the…
Dynamical systems methods are used to investigate global behavior of the spatially flat Friedmann-Robertson-Walker cosmological model in gravitational theory with a non-minimally coupled scalar field and a constant potential function. We…
Non-Bloch topological invariants preserve the bulk-boundary correspondence in non-Hermitian topological systems, and are a key concept in the contemporary study of non-Hermitian topology. Here we report the dynamic detection of non-Bloch…
We develop an analysis pipeline for characterizing the topology of large scale structure and extracting cosmological constraints based on persistent homology. Persistent homology is a technique from topological data analysis that quantifies…
In quantum many-body theory no generic microscopic principle at the origin of complex dynamics is known. Quite opposed, in classical mechanics the theory of non-linear dynamics provides a detailed framework for the distinction between…