Thermalization of Lévy Flights : Path-Wise Picture in 2D
Joint Authors
Garbaczewski, Piotr
Żaba, Mariusz
Source
International Journal of Statistical Mechanics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-10-03
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We analyze two-dimensional (2D) random systems driven by a symmetric Lévy stable noise which in the presence of confining potentials may asymptotically set down at Boltzmann-type thermal equilibria.
In view of the Eliazar-Klafter no-go statement, such dynamical behavior is plainly incompatible with the standard Langevin modeling of Lévy flights.
No explicit path-wise description has been so far devised for the thermally equilibrating random motion we address, and its formulation is the principal goal of the present work.
To this end we prescribe a priori the target pdf ρ∗ in the Boltzmann form ~exp[−Φ(x)] and next select the Lévy noise (e.g., its Lévy measure) of interest.
To reconstruct random paths of the underlying stochastic process we resort to numerical methods.
We create a suitably modified version of the time honored Gillespie algorithm, originally invented in the chemical kinetics context.
A statistical analysis of generated sample trajectories allows us to infer a surrogate pdf ρ(x,t) dynamics which sets down at a predefined target, in consistency with the associated kinetic (master) equation.
American Psychological Association (APA)
Żaba, Mariusz& Garbaczewski, Piotr. 2013. Thermalization of Lévy Flights : Path-Wise Picture in 2D. International Journal of Statistical Mechanics،Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-494757
Modern Language Association (MLA)
Żaba, Mariusz& Garbaczewski, Piotr. Thermalization of Lévy Flights : Path-Wise Picture in 2D. International Journal of Statistical Mechanics No. 2013 (2013), pp.1-11.
https://search.emarefa.net/detail/BIM-494757
American Medical Association (AMA)
Żaba, Mariusz& Garbaczewski, Piotr. Thermalization of Lévy Flights : Path-Wise Picture in 2D. International Journal of Statistical Mechanics. 2013. Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-494757
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-494757