Statistical Mechanics and Quantum Fields on Fractals

DOI10.1090/CONM/601/11962zbMath1321.81024arXiv1210.6763OpenAlexW2218482877MaRDI QIDQ2949958

Eric Akkermans

Publication date: 5 October 2015

Published in: Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.6763

zbMATH Keywords

fractalsstatistical mechanicsquantum fields

Mathematics Subject Classification ID

Quantum equilibrium statistical mechanics (general) (82B10) Self-similar stochastic processes (60G18) Fractals (28A80) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Renormalization of holomorphic dynamical systems (37F25) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (13)

Spectral decimation of a self-similar version of almost Mathieu-type operators ⋮ Explicit formulas for heat kernels on diamond fractals ⋮ Regularized Laplacian determinants of self-similar fractals ⋮ Fractal snowflake domain diffusion with boundary and interior drifts ⋮ Magnetic Laplacians of locally exact forms on the Sierpinski gasket ⋮ Gaps labeling theorem for the bubble-diamond self-similar graphs ⋮ Construction of free quantum fields on nested fractal space-times ⋮ Spectral decimation of piecewise centrosymmetric Jacobi operators on graphs ⋮ Breaking of continuous scale invariance to discrete scale invariance: a universal quantum phase transition ⋮ Spectral analysis on Barlow and Evans' projective limit fractals ⋮ Singularly continuous spectrum of a self-similar Laplacian on the half-line ⋮ Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted Z-graded graphs ⋮ Spectra of perfect state transfer Hamiltonians on fractal-like graphs

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