Related papers: Power-law distributions in nonequilibrium open qua…

It has long been observed that the number of weak lines from many-electron atoms follows a power law distribution of intensity. While computer simulations have reproduced this dependence, its origin has not yet been clarified. Here we…

We address the question of how a non-equilibrium steady state (NESS) is reached in the Linbdladian dynamics of an open quantum system. We develop an expansion of the density matrix in terms of the NESS-excitations, each of which has its own…

Power-law (PL) distribution functions (DF) are prevalent in highly diverse systems. The systems range in size from nanometer to mega light years, in complexity from dust grains to living organisms, and characterize the distribution of…

A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…

For many driven-nonequilibrium systems, the probability distribution functions of magnitude and recurrence-time of large events follow a powerlaw indicating a strong temporal correlation. In this paper we argue why these probability…

We establish an explicit correspondence between ergodicity breaking in a system described by power-law tail distributions and the divergence of the moments of these distributions.

Supersonic turbulence generates distributions of shock waves. Here, we analyse the shock waves in three-dimensional numerical simulations of uniformly driven supersonic turbulence, with and without magnetohydrodynamics and self-gravity. We…

We investigate a stationary random coefficient autoregressive process. Using renewal type arguments tailor-made for such processes, we show that the stationary distribution has a power-law tail. When the model is normal, we show that the…

We propose an analytically tractable neural connectivity model with power-law distributed synaptic strengths. When threshold neurons with biologically plausible number of incoming connections are considered, our model features a continuous…

We consider the problem of probabilistic quantification of dynamical systems that have heavy-tailed characteristics. These heavy-tailed features are associated with rare transient responses due to the occurrence of internal instabilities.…

We study the large-time asymptotic of renewal-reward processes with a heavy-tailed waiting time distribution. It is known that the heavy tail of the distribution produces an extremely slow dynamics, resulting in a singular large deviation…

In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise…

Extreme events have an important role which is sometime catastrophic in a variety of natural phenomena including climate, earthquakes and turbulence, as well as in man-made environments like financial markets. Statistical analysis and…

We consider the atom-optical delta-kicked accelerator when the initial momentum distribution is symmetric. We demonstrate the existence of quantum-resonant dynamics, and derive analytic expressions for the system evolution. In particular,…

We consider an overdamped particle with a general physical mechanism that creates noisy active movement (e.g., a run-and-tumble particle or active Brownian particle etc.), that is confined by an external potential. Focusing on the limit in…

A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda…

The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in…

Fluctuation properties of the Langevin equation including a multiplicative, power-law noise and a quadratic potential are discussed. The noise has the Levy stable distribution. If this distribution is truncated, the covariance can be…

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…

Power law potentials dictate interactions across scales and matter, controlling the structure and dynamics of inanimate, and living systems. Though the equilibrium distributions of particles with a power law repulsion were extensively…