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Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
Space-time modulation of refractive index can produce synthetically moving interfaces with arbitrary apparent velocities, including superluminal motion, offering new ways to control light in dynamic media. On the other hand, space-time wave…
We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks on the simplex of probability measures over a finite set. Due to a reinforcement mechanism, the increments of the walks are…
Space and time are crucial twins in physics. In quantum mechanics, spatial correlations already reveal nonclassical features, such as entanglement, and have bred many quantum technologies. However, the nature of quantum temporal…
We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…
We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying…
Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…
For the modelling of pedestrian dynamics we treat persons as self-driven objects moving in a continuous space. On the basis of a modified social force model we qualitatively analyze the influence of various approaches for the interaction…
The time-dependent pair correlation functions for a degenerate ideal quantum gas of charged particles in a uniform magnetic field are studied on the basis of equilibrium statistics. In particular, the influence of a flat hard wall on the…
Quantum walks constitute a rich area of quantum information science, where multipartite entanglement plays a central role in the dynamics and scalability of quantum advantage over classical simulators. In this work, we study the…
High Reynolds numbers Navier-Stokes equations are believed to break self-similarity concerning both spatial and temporal properties: correlation functions of different orders exhibit distinct decorrelation times and anomalous spatial…
Although the paradigm of criticality is centred around spatial correlations and their anomalous scaling, not many studies of Self-Organised Criticality (SOC) focus on spatial correlations. Often, integrated observables, such as avalanche…
When a particle moves through a spatially-random force field, its momentum may change at a rate which grows with its speed. Suppose moreover that a thermal bath provides friction which gets weaker for large speeds, enabling high-energy…
Several papers have recently calculated the contribution to pulsar timing array overlap reduction functions (ORFs) induced by our peculiar velocity with respect to the rest frame of the stochastic gravitational-wave background. Here we show…
Measurements of the peculiar velocities of large samples of galaxies enable new tests of the standard cosmological model, including determination of the growth rate of cosmic structure that encodes gravitational physics. With the size of…
Synchronization is one of the emerging collective phenomena in interacting particle systems. Its ubiquitous presence in nature, science, and technology has fascinated the scientific community over the decades. Moreover, a great deal of…
The temporal Talbot effect refers to the periodic revivals of a pulse train propagating in a dispersive medium, and is a temporal analog of the spatial Talbot effect with group-velocity dispersion in time replacing diffraction in space.…
In this paper we consider a class of one-dimensional interacting particle systems in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied/vacant sites has a local drift to the…
We review data analysis techniques that can be used to study temporal correlations among conductance traces in break junction measurements. We show that temporal histograms are a simple but efficient tool to check the temporal homogeneity…
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…