Heat kernels and zeta functions on fractals. (English) Zbl 1258.81042
Summary: 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.
MSC:
81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
28A80 | Fractals |
35K08 | Heat kernel |
37C30 | Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. |
81T20 | Quantum field theory on curved space or space-time backgrounds |