Quantum mechanics on Laakso spaces

DOI10.1063/1.3702099zbMath1275.81041arXiv1011.3567OpenAlexW2963872210MaRDI QIDQ2860760

Amanda G. Parshall, Robert Kesler, Benjamin A. Steinhurst, Evelyn A. Stamey, Christopher Kauffman

Publication date: 20 November 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.3567

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Casimir effect in quantum field theory (81T55)

Related Items (6)

Existence of a meromorphic extension of spectral zeta functions on fractals ⋮ Dirac and magnetic Schrödinger operators on fractals ⋮ Dual graphs and modified Barlow-Bass resistance estimates for repeated barycentric subdivisions ⋮ Spectral analysis on Barlow and Evans' projective limit fractals ⋮ Gaps in the spectrum of the Laplacian on \(3N\)-gaskets ⋮ Spectra of perfect state transfer Hamiltonians on fractal-like graphs

Cites Work

• Harmonic oscillators on infinite Sierpinski gaskets
• A fractal quantum mechanical model with Coulomb potential
• Ahlfors \(Q\)-regular spaces with arbitrary \(Q>1\) admitting weak Poincaré inequality
• Eigenmodes of the Laplacian on some Laakso spaces
• Vibration modes of 3n-gaskets and other fractals
• Mathematical aspects of vacuum energy on quantum graphs

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