Geodesic
Aharonov-Bohm problem on a~square lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 86 (1991) no. 3, pp. 353-366

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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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     author = {S. Ya. Zhitomirskaya and V. A. Mandel'shtam},
     title = {Aharonov-Bohm problem on a~square lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {353--366},
     publisher = {mathdoc},
     volume = {86},
     number = {3},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_86_3_a4/}
}
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S. Ya. Zhitomirskaya; V. A. Mandel'shtam. Aharonov-Bohm problem on a~square lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 86 (1991) no. 3, pp. 353-366. http://geodesic.mathdoc.fr/item/TMF_1991_86_3_a4/