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Continuous time crystals, i.e., nonequilibrium phases with a spontaneously broken continuous time-translational symmetry, have been studied and recently observed in the long-time dynamics of open quantum systems. Here, we investigate a…
We study the long-time behavior of two run-and-tumble particles on the real line subjected to an attractive interaction potential and jamming interactions, which prevent the particles from crossing. We provide the explicit invariant…
The dynamical behavior of interacting systems plays a fundamental role for determining quantum correlations, such as entanglement. In this Letter, we describe temporal quantum effects of the inseparable evolution of composite quantum states…
We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or…
Repeated measurements can induce entanglement phase transitions in the dynamics of quantum systems. Interacting models, both chaotic and integrable, generically show a stable volume-law entangled phase at low measurement rates which…
In this work we develop a general formalism that categorizes the action of broken scale invariance on the non-equilibrium dynamics of non-relativistic quantum systems. This approach is equally applicable to both strongly and weakly…
Recent work on stochastic interacting particle systems with two particle species (or single-species systems with kinematic constraints) has demonstrated the existence of spontaneous symmetry breaking, long-range order and phase coexistence…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
A system of $N$ particles in a chemical medium in $\mathbb{R}^{d}$ is studied in a discrete time setting. Underlying interacting particle system in continuous time can be expressed as \begin{eqnarray} dX_{i}(t) &=&[-(I-A)X_{i}(t) +…
As in arXiv: math. 0809.2365 we consider classical system of interacting particles $\mathcal{P}_1, ..., \mathcal{P}_n$ on the line with only neighboring particles involved in interaction. On the contrast to arXiv: math. 0809.2365 now {\it…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
We assume that the properties of nonequilibrium stationary states of systems of particles can be expressed in terms of weighted orbital measures, i.e. through periodic orbit expansions. This allows us to derive the Onsager relations for…
We study the long-time behaviour of a class of piecewise-deterministic Markov processes which are an extension of some recent works. These $d$-dimensional processes, d>=1, can especially be used to model the motion of a bacterium in…
Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such…
We show that a collection of independent Ising spins evolving stochastically can display surprisingly large fluctuations towards ordered behaviour, as quantified by certain types of time-integrated plaquette observables, despite the…
There has been significant progress recently in our understanding of the stationary measures of the exclusion process on $Z$. The corresponding situation in higher dimensions remains largely a mystery. In this paper we give necessary and…
Some models allowing explicit calculation of periodic instantons and evaluation of their action are studied with regard to transitions from classical to quantum behaviour as the temperature is lowered and tunneling sets in. It is shown that…
The interplay between unitary dynamics and local quantum measurements results in unconventional non-unitary dynamical phases and transitions. In this paper we investigate the dynamics of $(d+1)$-dimensional hybrid stabilizer circuits, for…
This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment…