Heat kernel of integrable billiards in a magnetic field

Details Heat kernel of integrable billiards in a magnetic field Heat kernel of integrable billiards in a magnetic field

1997-08-27

arxiv.org/abs/cond-mat/9708209v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

13 pages, Revtex

Scientific paper

10.1088/0305-4470/31/18/016

We present analytical methods to calculate the magnetic response of non-interacting electrons constrained to a domain with boundaries and submitted to a uniform magnetic field. Two different methods of calculation are considered - one involving the large energy asymptotic expansion of the resolvent (Stewartson-Waechter method) is applicable to the case of separable systems, and another based on the small time asymptotic behaviour of the heat kernel (Balian-Bloch method). Both methods are in agreement with each other but differ from the result obtained previously by Robnik. Finally, the Balian-Bloch multiple scattering expansion is studied and the extension of our results to other geometries is discussed.

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