Related papers: Crossover from Diffusive to Ballistic Transport in…
We investigate the ballistic spreading behavior of the one-dimensional discrete time quantum walks whose time evolution is driven by any balanced quantum coin. We obtain closed-form expressions for the long-time variance of position of…
Consider a particle whose position evolves along the edges of a network. One definition for the displacement of a particle is the length of the shortest path on the network between the current and initial positions of the particle. Such a…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
Transport phenomena play a crucial role in modern physics and applied sciences. Examples include the dissipation of energy across a large system, the distribution of quantum information in optical networks, and the timely modeling of…
Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions, $\phi$, in the vicinity of the jamming transition at $\phi_{c}$. Various diffusion properties are computed…
Recently a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other non-linear theories the new approach has the advantage that it provides a full time-dependent description of the…
We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves…
Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement $\overline{\delta^2}$ of individual particles remains a random variable while indicating that the particle…
We calculate the system-size-over-wave-length ($M$) dependence of sample-to-sample conductance fluctuations, using the open kicked rotator to model chaotic scattering in a ballistic quantum dot coupled by two $N$-mode point contacts to…
We characterize a transition from normal to ballistic diffusion in a bouncing ball dynamics. The system is composed of a particle, or an ensemble of non-interacting particles, experiencing elastic collisions with a heavy and periodically…
We consider a continuous random walk model for describing normal as well as anomalous diffusion of particles subjected to an external force when these particles diffuse in a uniformly expanding (or contracting) medium. A general equation…
We show that a quantum particle in $\mathbb{R}^d$, for $d \geq 1$, subject to a white-noise potential, moves super-ballistically in the sense that the mean square displacement $\int \|x\|^2 \langle \rho(x,x,t) \rangle ~dx$ grows like…
Continuous-time random walks combining diffusive scattering and ballistic propagation on lattices model a class of L\'evy walks. The assumption that transitions in the scattering phase occur with exponentially-distributed waiting times…
Two models are first presented, of one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a phase-flip channel, and (ii) a model with…
We study a general class of translation invariant quantum Markov evolutions for a particle on $\bbZ^d$. The evolution consists of free flow, interrupted by scattering events. We assume spatial locality of the scattering events and…
It has been conjectured that transport in integrable one-dimensional (1D) systems is necessarily ballistic. The large diffusive response seen experimentally in nearly ideal realizations of the S=1/2 1D Heisenberg model is therefore puzzling…
We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…
We study single-file diffusion on a one-dimensional lattice with a random fractal distribution of hopping rates. For finite lattices, this problem shows three clearly different regimes, namely, nearly independent particles, highly…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of…