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- Title
Spectral Decomposition of a Fokker-Planck Equation at Criticality.
- Authors
Bologna, M.; Beig, M.; Svenkeson, A.; Grigolini, P.; West, B.
- Abstract
The mean field for a complex network consisting of a large but finite number of random two-state elements, $$M$$ , has been shown to satisfy a nonlinear Langevin equation. The noise intensity is inversely proportional to $$\sqrt{M} $$ . In the limiting case $$M = \infty $$ , the solution to the Langevin equation exhibits a transition from exponential to inverse power law relaxation as criticality is approached from above or below the critical point. When $$M < \infty $$ , the inverse power law is truncated by an exponential decay with rate $$\varGamma $$ , the evaluation of which is the main purpose of this article. An analytic/numeric approach is used to obtain the lowest-order eigenvalues in the spectral decomposition of the solution to the corresponding Fokker-Planck equation and its equivalent Schrödinger equation representation.
- Subjects
FOKKER-Planck equation; MODULAR arithmetic; LANGEVIN equations; EXPONENTS; NUMERICAL calculations
- Publication
Journal of Statistical Physics, 2015, Vol 160, Issue 2, p466
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-015-1262-5