Vacuum energy, spectral determinant and heat kernel asymptotics of graph Laplacians with general vertex matching conditions

Details Vacuum energy, spectral determinant and heat kernel asymptotics of graph Laplacians with general vertex matching conditions Vacuum energy, spectral determinant and heat kernel asymptotics of graph Laplacians with general vertex matching conditions

2009-11-30

arxiv.org/abs/0912.0036v2

Quantum field theory under the influence of external conditions (QFEXT09) K. A. Milton and M. Bordag (ed.'s), (World Scientifi

Physics

Mathematical Physics

5 pages, submitted to proceedings of QFEXT09, minor corrections made.

Scientific paper

We consider Laplace operators on metric graphs, networks of one-dimensional line segments (bonds), with matching conditions at the vertices that make the operator self-adjoint. Such quantum graphs provide a simple model of quantum mechanics in a classically chaotic system with multiple scales corresponding to the lengths of the bonds. For graph Laplacians we briefly report results for the spectral determinant, vacuum energy and heat kernel asymptotics of general graphs in terms of the vertex matching conditions.

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