title: Thermodynamics of photons on fractals.
abstract: A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PV(s) = U/d(s), where d(s) is the spectral dimension and V(s) defines the "spectral volume." For regular manifolds, V(s) coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.
authors.affiliation: Department of Physics, Technion Israel Institute of Technology, 32000 Haifa, Israel.
authors.forename: Eric
authors.initials: E
authors.lastname: Akkermans
authors.forename: Gerald V
authors.initials: GV
authors.lastname: Dunne
authors.forename: Alexander
authors.initials: A
authors.lastname: Teplyaev