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Heat trace asymptotics for quantum graphs

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arxiv 1212.2840 v1 pith:VWXSZ2RM submitted 2012-12-12 math.AP

Ralf Rueckriemen This is my paper · ORCID
classification math.AP
keywords heatpotentialadmitscoefficientskerneloperatorquantumassumptions
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We consider a quantum graph where the operator contains a potential. We show that this operator admits a heat kernel. Under some assumptions on the potential, this heat kernel admits an asymptotic expansion at t=0 with coefficients that depend on the potential in a universal way. These coefficients are spectral invariants, we compute the first few of them.

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  1. Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons

    math.SP 2019-08 accept novelty 8.0 of 10

    Steklov eigenvalues of curvilinear polygons are asymptotically equal to explicit quasi-eigenvalues built from side lengths and angles, with errors tending to zero.

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