Fractal Noise in Quantum Ballistic and Diffusive Lattice Systems

We demonstrate fractal noise in the quantum evolution of wave packets moving either ballistically or diffusively in periodic and quasiperiodic tight-binding lattices, respectively. For the ballistic case with various initial superpositions we obtain a space-time self-affine fractal $\Psi(x,t)$ which verify the predictions by Berry for "a particle in a box", in addition to quantum revivals. For the diffusive case self-similar fractal evolution is also obtained. These universal fractal features of quantum theory might be useful in the field of quantum information, for creating efficient quantum algorithms, and can possibly be detectable in scattering from nanostructures.