Lévy Flights over Quantum Paths

Lévy flights in binary optimization

There are many optimization heuristics which involves mutation operator. Reducing them to binary optimization allows to study properties of binary mutation operator. Modern heuristics yield from Lévy flights behavior, which is a bridge between local search and random shooting in binary space. The paper is oriented to statistical analysis of binary mutation with Lévy flight inside and Quantum Tu...

The Symmetric Stable Lévy Flights and the Feynman Path Integral

We determine the solution of the fractional spatial diffusion equation in n-dimensional Euclidean space for a “free” particle by computing the corresponding propagator. We employ both the Hamiltonian and Lagrangian approaches which produce exact results for the case of jumps governed by symmetric stable Lévy flights.

Lévy Flights in Quantum Transport in Quasiballistic Wires

Conductance fluctuations, localization, and statistics of Lyapunov exponents are studied numerically in pure metallic wires with rough boundaries (quasiballistic wires). We find that the correlation energy of conductance fluctuations scales anomalously with the sample dimensions, indicating the role of Lévy flights. Application of a magnetic field deflects the Lévy flights which reduces the loc...

Lévy flights and Lévy-Schrödinger semigroups

We analyze two different confining mechanisms for Lévy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Lévy-Schrödinger semigroups which induce so-called topological Lévy processes (Lévy flights with locally modified jump rates in the master equation). Given a stationary probability func...

Microscopic characterization of Lévy flights of light in atomic vapors