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10 papers · 2 filters
Infinite Invariant Density Determines Statistics of Time Averages for Weak Chaos
N. Korabel, E. Barkai
Weakly chaotic non-linear maps with marginal fixed points have an infinite invariant measure. Time averages of integrable and non-integrable observables remain random even in the l…
A fractional Feynman-Kac equation for weak ergodicity breaking
Shai Carmi, Eli Barkai
Continuous-time random walk (CTRW) is a model of anomalous sub-diffusion in which particles are immobilized for random times between successive jumps. A power-law distribution of t…
Solution of the Fokker-Planck equation with a logarithmic potential
A. Dechant, E. Lutz, E. Barkai +1
We investigate the diffusion of particles in an attractive one-dimensional potential that grows logarithmically for large using the Fokker-Planck equation. An eigenfunction e…
The combined effect of connectivity and dependency links on percolation of networks
Amir Bashan, Shlomo Havlin
Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However, the research is focused on systems with only one type…
Towards designing robust coupled networks
Christian M. Schneider, Nuri Yazdani, Nuno A. M. Araujo +2
Natural and technological interdependent systems have been shown to be highly vulnerable due to cascading failures and an abrupt collapse of global connectivity under initial failu…
Fluctuations of time averages for Langevin dynamics in a binding force field
A. Dechant, E. Lutz, D. A. Kessler +1
We derive a simple formula for the fluctuations of the time average around the thermal mean for overdamped Brownian motion in a binding potential U(x). Using a backward Fokker-Plan…