Related papers: Dynamical phase transitions in certain non-ergodic…
Dynamical phase transitions can occur in isolated quantum systems that are brought out of equilibrium by sudden parameter changes. We discuss the characterization of such dynamical phase transitions based on the statistics of produced…
Over the last few years it was pointed out that certain observables of time-evolving quantum systems may have singularities at certain moments in time, mimicking the singularities physical systems have when undergoing phase transitions.…
We consider a model of active Brownian particles with velocity-alignment in two spatial dimensions with passive and active fluctuations. Hereby, active fluctuations refers to purely non-equilibrium stochastic forces correlated with the…
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 large deviation theory has recently been applied to open quantum systems to uncover dynamical crossovers in the space of quantum trajectories associated to Markovian evolutions. Such dynamical crossovers are characterized by qualitative…
We study the occupation fluctuations of drifted Brownian motion in a closed interval, and show that they undergo a dynamical phase transition in the long-time limit without an additional low-noise limit. This phase transition is similar to…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
Recently, a class of stochastic processes known as piecewise deterministic Markov processes has been used to define continuous-time Markov chain Monte Carlo algorithms with a number of attractive properties, including compatibility with…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
We investigate the dynamics of kinetically constrained models of glass formers by analysing the statistics of trajectories of the dynamics, or histories, using large deviation function methods. We show that, in general, these models exhibit…
The Fredkin spin chain serves as an interesting theoretical example of a quantum Hamiltonian whose ground state exhibits a phase transition between three distinct phases, one of which violates the area law. Here we consider a classical…
We address the general problem of formulating the dynamical large deviations of non-Markovian systems in a closed form. Specifically, we consider a broad class of ``self-interacting'' jump processes whose dynamics depends on the past…
As a main example for the superstatistics approach, we study a Brownian particle moving in a d-dimensional inhomogeneous environment with macroscopic temperature fluctuations. We discuss the average occupation time of the particle in…
Large fluctuations have received considerable attention as they encode information on the fine-scale dynamics. Large deviation relations known as fluctuation theorems also capture crucial nonequilibrium thermodynamical properties. Here we…
The dynamical behaviour of many-body systems is often richer than what can be anticipated from their static properties. Here we show that in closed quantum systems this becomes evident by considering time-integrated observables as order…
In this paper we consider the controllability of certain class of non-autonomous neutral evolution stochastic functional differential equations, with time varying delays, driven by a fractional Brownian motion in a separable real Hilbert…
This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic differential equations with random coefficients. Similar to Gao and Liu \cite{GL}, this extends the corresponding results collected in…
We present an exact solution for one-dimensional overdamped dynamics near a hard wall, allowing us to connect steady-state distributions under confinement with the extreme value statistics of unconfined stochastic processes. This mapping…
In this thesis, we develop analytical methods to study out-of-equilibrium stochastic processes driven by colored noise, i.e., noise with temporal correlations. These non-Markovian processes pose significant analytical challenges compared to…
Dynamical phase transitions are defined as non-analytic points of the large deviation function of current fluctuations. We show that for boundary driven systems, many dynamical phase transitions can be identified using the geometrical…