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The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph.…
Quantum transitions are described semiclassically as motions of systems along (complex) trajectories. We consider the cases when the semiclassical trajectories are unstable and find that durations of the corresponding transitions are large.…
Robust statistical features have emerged from the microscopic analysis of dense pedestrian flows through a bottleneck, notably with respect to the time gaps between successive passages. We pinpoint the mechanisms at the origin of these…
Spontaneous symmetry breaking is well understood under equilibrium conditions as a consequence of the singularity of the thermodynamic limit. How a single global orientation of the order parameter dynamically emerges from an initially…
Cyclic transitions between active and passive states are central to many natural and synthetic systems, ranging from light-driven active particles to animal migrations. Here, we investigate a minimal model of self-propelled Brownian…
Polymer translocation in crowded environments is a ubiquitous phenomenon in biological systems. We studied polymer translocation through a pore in free, one-sided (asymmetric), and two-sided (symmetric) crowded environments. Extensive…
We study the disruption process of hierarchical 3-body systems with bodies of comparable mass. Such systems have long survival times that vary by orders of magnitude depending on the initial conditions. By comparing with 3-body numerical…
In human crowds as well as in many animal societies, local interactions among individuals often give rise to self-organized collective organizations that offer functional benefits to the group. For instance, flows of pedestrians moving in…
We introduce oscillatory analogues of fractional Brownian motion, sub-fractional Brownian motion and other related long range dependent Gaussian processes, we discuss their properties, and we show how they arise from particle systems with…
In this work we propose a model to describe the statistical fluctuations of the self-driven objects (species A) walking against an opposite crowd (species B) in order to simulate the regime characterized by stop-and-go waves in the context…
Symmetry-breaking phase transitions are ubiquitous in condensed matter systems and in quantum field theories. There is also good reason to believe that they feature in the very early history of the Universe. At many such transitions…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
Consider a discrete-time quantum walk on the $N$-cycle subject to decoherence both on the coin and the position degrees of freedom. By examining the evolution of the density matrix of the system, we derive some new conclusions about the…
We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
The evolution of many dynamical systems that describe relationships or interactions between objects can be effectively modeled by temporal networks, which are typically represented as a sequence of static network snapshots. In this paper,…
The emergence of collective motion, also known as flocking or swarming, in groups of moving individuals who orient themselves using only information from their neighbors is a very general phenomenon that is manifested at multiple spatial…
We analyse the motion of a system of particles subjected a random force fluctuating in both space and time, and experiencing viscous damping. When the damping exceeds a certain threshold, the system undergoes a phase transition: the…
Experimental studies of the diffusion of biomolecules in the environment of biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule…