Power-law energy level-spacing distributions in fractals
arXiv:1811.01659 · doi:10.1103/PhysRevB.99.075402
Abstract
In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise linear functions. We propose that such a behaviour is a general feature of fractals, which can not be described properly by random matrix theory. Several other arguments for the power-law behaviour of the energy level-spacing distributions are proposed.
References in corpus (11)
- Random-Matrix Theory of Quantum Transport
- Anderson Transitions
- Artificial graphene as a tunable Dirac material
- Engineering artificial graphene in a two-dimensional electron gas
- Transport and optical properties of an electron gas in a Sierpinski carpet
- Topology in the Sierpiński-Hofstadter problem
- Spectral zeta functions of fractals and the complex dynamics of polynomials
- Fractal plasmonic metamaterials for subwavelength imaging
- Plasmon confinement in fractal quantum systems
- Localization in random fractal lattices
- Optical conductivity of a quantum electron gas in a Sierpinski carpet
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