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Linear response, persistent currents and related problems
Author(s) -
Janßen Martin,
Gummich Ute,
Hajdu János,
Viehweger Olaf
Publication year - 1993
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19935050406
Subject(s) - mesoscopic physics , canonical ensemble , ergodicity , grand canonical ensemble , microcanonical ensemble , physics , context (archaeology) , statistical physics , current (fluid) , equipartition theorem , canonical form , theoretical physics , quantum mechanics , mathematics , magnetic field , pure mathematics , thermodynamics , paleontology , statistics , monte carlo method , biology
Based on a general linear response approach we provide a systematic and unified survey of existing theories on persistent currents. The central notions in this context are equilibrium and dynamic persistent currents which are analyzed with respect to their similarities and differences in the canonical and grand canonical ensemble. We present criteria which relate the existence of persistent currents to the equipartition law and ergodicity for current correlators. We find that in additive Fermion systems at low temperatures both kinds of persistent currents coincide in the canonical ensemble whereas they differ in the grand canonical ensemble. Comparing different works on averaged persistent currents in diffusive mesoscopic rings within our framework and discussing several methods of calculating canonical currents with the help of grand canonical ensembles, we clarify some misunderstandings which have arisen in methodologically different approaches to the phenomenon of persistent currents. Finally, we relate the presence of dynamic persistent currents to the Hall conductivity on a finite cylinder and the center coordinate Kubo formula for the Hall conductivity.