Heat Kernels and Zeta Functions on Fractals

Abstract

On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features, very different from their behaviour on regular smooth manifolds, and these can have important physical consequences for both classical and quantum physics in systems having fractal properties.

19 pages, invited contribution for JPhysA Special Issue in honour of J. S. Dowker

Cited by in corpus (30)

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• Emergence of the Circle in a Statistical Model of Random Cubic Graphs
• Continuous Time Quantum Walks in finite Dimensions
• Energy and Laplacian on Hanoi-type fractal quantum graphs
• Spectral dimensions and dimension spectra of quantum spacetimes
• Spectral dimension and Bohr's formula for Schrodinger operators on unbounded fractal spaces
• Log-periodic critical amplitudes: a perturbative approach
• Singularly continuous spectrum of a self-similar Laplacian on the half-line
• Fractal snowflake domain diffusion with boundary and interior drifts
• Wave equation on one-dimensional fractals with spectral decimation and the complex dynamics of polynomials
• Regularized Laplacian determinants of self-similar fractals
• Entanglement entropy on finitely ramified graphs
• Spectral dimension of bosonic string theory
• Spectral Action Models of Gravity on Packed Swiss Cheese Cosmology
• Emergent time, cosmological constant and boundary dimension at infinity in combinatorial quantum gravity
• Casimir energy of Sierpinski triangles
• Revisiting log-periodic oscillations
• Effective de Sitter space, quantum behaviour and large-scale spectral dimension (3+1)
• Quantum Vacuum Energy of Self-Similar Configurations
• Hamiltonian systems, Toda lattices, Solitons, Lax Pairs on weighted Z-graded graphs
• Entangling Fractals
• Evaluation of Spectral Zeta-Functions with the Renormalization Group
• Free Energy on a Cycle Graph and Trigonometric Deformation of Heat Kernel Traces on Odd Spheres
• Gaps in the spectrum of the Laplacian on $3N$-Gaskets
• The impact of a random metric upon a diffusing particle
• Response of a canonical ensemble of quantum oscillators to a random metric