Related papers: Quantum diffusion of a relativistic particle in a …
We show analytically that there is anomalous diffusion when the diffusion constant depends on the concentration as a power law with a positive exponent or a negative exponent with absolute value less than one and the initial condition is a…
We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…
I study a relativistic open string coupling through its endpoints to a plane wave with arbitrary temporal profile. The string's transverse oscillations respond linearly to the external field. This makes it possible to solve the classical…
With the help of the methods developed in our previous article [Schmitz, to appear in "Annales de l'I.H.P. Prob. & Stat.], we highlight condition (T) as a source of new examples of 'ballistic' diffusions in a random environment when d>1…
We derive a general upper bound on the spreading rate of wavepackets in the framework of Schr\"odinger time evolution. Our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically…
We analyze statistical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. We study particle dynamics with discrete time. We show that a quantum-like interference pattern could appear as a statistical…
Quantum diffusion, as developed in the 1990s, could explain how a system, subject to measurement, goes into an eigenstate of the measured observable. Here it is shown that quantum diffusion theory can be interpreted as a result within…
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…
Resonant scattering of fast particles off low frequency plasma waves is a major process determining transport characteristics of energetic particles in the heliosphere and contributing to their acceleration. Usually, only Alfv\'en waves are…
The motion of a particle is studied in a random space-time. It is assumed that the velocity is small enough for the non-relativistic approximation to be valid. The randomness of the metric induces a diffusion in coordinate space. Hence it…
We conjecture that the random walk and the corresponding diffusion in the relativistic velocity space is an adequate method for describing the acceleration process in relativistic jets. Considering a simple toy model, the main features of…
We study a stochastic particle system which models the time evolution of the ranking of books by online bookstores (e.g., Amazon). In this system, particles are lined in a queue. Each particle jumps at random jump times to the top of the…
The wave instability acts in astrophysical plasmas to redistribute energy and momentum in the absence of frequent collisions. There are many different types of waves, and it is important to quantify the wave energy density and growth rate…
A relativistic bounce-averaged quasilinear diffusion equation is derived to describe stochastic particle transport associated with arbitrary-frequency electromagnetic fluctuations in a nonuniform magnetized plasma. Expressions for the…
We study the asymptotic behavior of branching diffusion processes in periodic media. For a super-critical branching process, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the…
We obtain a limit when mass tends to zero of the relativistic diffusion of Schay and Dudley. The diffusion process has the log-normal distribution. We discuss Langevin stochastic differential equations leading to an equilibrium…
We study the dynamics of cold atoms subjected to {\em pairs} of closely time-spaced $\delta$-kicks from standing waves of light. The classical phase space of this system is partitioned into momentum cells separated by trapping regions. In a…
We study the spatio-temporal evolution of wave packets in one-dimensional quasiperiodic lattices which localize linear waves. Nonlinearity (related to two-body interactions) has destructive effect on localization, as recently observed for…
We examine an extension to the theory of Gaussian wave packet dynamics in a one-dimensional potential by means of a sequence of time dependent displacement and squeezing transformations. Exact expressions for the quantum dynamics are found,…
Exact solutions of two-particle relativistic equations of quantum field theory describing the scattering $s$-states and the bound $s$-states are found in the cases of delta-shell potential and superposition of delta-shell potentials. Some…