Fractal Universe & Quantum Chaos

Why the Universe is Fractal (by Chris King): Life exists in the universe because the laws of nature arising from cosmic symmetry-breaking are intrinsically fractal and embrace chaotic dynamics in a manner that permits new structure to emerge on increasing scales, as we move from the level of fundamental particles to organisms. In a fundamental sense this is a cosmological property of the universe, because complex living systems represent the most complete interactive consummation of the four fundamental forces of nature. If the laws of nature permitted only ordered periodic or stochastic solutions to molecular aggregation, as in crystals, or amorphous glasses, the complex structures of tissues and life would remain impossible.

Exploring Quantum, Classical and Semi-classical Chaos in the Stadium Billiard (by Chris King): This paper explores quantum and classical chaos in the stadium billiard using Matlab simulations to investigate the behavior of wave functions in the stadium and the corresponding classical orbits believed to underlie wave function scarring. The simulations use three complementary methods. The quantum wave functions are modeled using a cellular automaton (CA) simulating a Hamiltonian wave function with discrete (square pixel) boundary conditions approaching the stadium in the classical limit. The classical orbits are computed by solving the reflection equations at the classical boundary thus giving direct insights into the wave functions and eigenstates of the quantum stadium. Finally a simplified semi-classical algorithm is developed to show the comparison between this and the quantum wave function method.