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Collective behavior of coupled mesoscopic cylinders
Author(s) -
Dajka J.,
Łuczka J.,
Szopa M.,
Hänggi P.
Publication year - 2005
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200460022
Subject(s) - mesoscopic physics , physics , thermal fluctuations , fokker–planck equation , nonlinear system , phase transition , limit (mathematics) , phase diagram , langevin equation , thermal , phase (matter) , statistical physics , condensed matter physics , quantum mechanics , thermodynamics , mathematics , mathematical analysis , differential equation
We address the objective of the generation of finite magnetic flux out of unbiased thermal current fluctuations in a collection of identical mesoscopic cylinders which are coupled via mutual inductances. The influence of thermal Nyquist fluctuations are described in terms of a set of Langevin equations or a corresponding Fokker–Planck equation, respectively. In the limit of infinitely many constituents, the steady‐state of the system is determined by an effective, nonlinear Fokker–Planck equation. The system exhibits in this thermodynamic limit a second‐order phase transition: the average flux through each cylinder changes continuously from zero to non‐zero value and the phase diagram depicts a critical line. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)