Kato's inequality and asymptotic spectral properties for discrete magnetic Laplacians

By J. Dodziuk, Varghese Mathai. 2003

78 citations recorded by the source corpus.

In this paper, a discrete form of the Kato inequality for discrete magnetic Laplacians on graphs is used to study asymptotic properties of the spectrum of discrete magnetic Schrodinger operators. We use the existence of a ground state with suitable properties for the ordinary combinatorial Laplacian and semigroup domination to relate the combinatorial Laplacian with the discrete magnetic Laplacian.

Subfields: Computational Theory and Mathematics, Materials Chemistry, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/30651501ba8d7566bac61871d5f9438d99dea233

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In Computational Theory and Mathematics

In Materials Chemistry

In Mathematical Physics

Citations in the corpus

Heat Kernel and Essential Spectrum of Infinite Graphs (2008, methodology): “MR 894523 (88h:58118) [7] Józef Dodziuk and Varghese Mathai, Kato’s inequality and asymptotic spectral properties for discrete magnetic Laplacians, The ubiquitous heat kernel, Contemp.”
Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation (2011, background): “This has already been observed by Dodziuk/Matthai [12] and Dodziuk [10] in that they show stochastic completeness for certain bounded operators on graphs.”
Heat kernels on regular graphs and generalized Ihara zeta function formulas (2013, unknown): “We refer to [4,10] as well as the heat kernel formula for trees in Proposition 3.”
On the conservativeness and the recurrence of symmetric jump-diffusions (2012, background): “The conservativeness of the process associated with the physical Laplacian was studied in [6,7,39,40,15].”