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 TMF, 1991, Volume 86, Number 3, Pages 353–366 (Mi tmf5452)

Aharonov-Bohm problem on a square lattice

S. Ya. Zhitomirskaya, V. A. Mandel'shtam

Abstract: An explicit expression is obtained for the Green's function of the Schrödinger operator describing the motion of an electron on a square lattice in a magnetic field with flux that pierces a single cell it is show that the nontrivial component of the Green's function, equal to the contribution from the paths that pass round the singularity, is a compact operator. The method can also be used to find the partition functions for the ensembles of paths on the lattice that are associated with the numbers of turns around the fixed point.

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English version:
Theoretical and Mathematical Physics, 1991, 86:3, 241–251

Bibliographic databases:

Citation: S. Ya. Zhitomirskaya, V. A. Mandel'shtam, “Aharonov-Bohm problem on a square lattice”, TMF, 86:3 (1991), 353–366; Theoret. and Math. Phys., 86:3 (1991), 241–251

Citation in format AMSBIB
\Bibitem{ZhiMan91} \by S.~Ya.~Zhitomirskaya, V.~A.~Mandel'shtam \paper Aharonov-Bohm problem on a~square lattice \jour TMF \yr 1991 \vol 86 \issue 3 \pages 353--366 \mathnet{http://mi.mathnet.ru/tmf5452} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1107937} \transl \jour Theoret. and Math. Phys. \yr 1991 \vol 86 \issue 3 \pages 241--251 \crossref{https://doi.org/10.1007/BF01028421} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991GJ55400005}