Physics – Condensed Matter
Scientific paper
1995-03-15
Phys. Rev. B 52 (1995) 2728
Physics
Condensed Matter
19 pages, postscript (uuencoded, compressed)
Scientific paper
10.1103/PhysRevB.52.2728
We show by means of simple exact manipulations that the thermodynamic persistent current $I ( \phi , N )$ in a mesoscopic metal ring threaded by a magnetic flux $\phi$ at constant particle number $N$ agrees even beyond linear response with the dynamic current $I_{dy} ( \phi , N )$ that is defined via the response to a time-dependent flux in the limit that the frequency of the flux vanishes. However, it is impossible to express the disorder average of $I_{dy} ( \phi , N )$ in terms of conventional Green's functions at flux-independent chemical potential, because the part of the dynamic response function that involves two retarded and two advanced Green's functions is not negligible. Therefore the dynamics cannot be used to map a canonical average onto a more tractable grand canonical one. We also calculate the zero frequency limit of the dynamic current at constant chemical potential beyond linear response and show that it is fundamentally different from any thermodynamic derivative.
Fricke Jens
Kopietz Peter
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