Subdiffusive quantum transport for 3D Hamiltonians with absolutely continuous spectra

摘要

We exhibit a class of Hamiltonians in dimension D greater than or equal to 3, describing a quantum particle in an aperiodic medium with absolutely continuous spectrum and subdiffusive behavior. The diffusion exponent, which characterizes the time growth of the mean square displacement, can be chosen slightly bigger than Guarneri's lower bound. These models are built out of 1D Hamiltonians with well-understood spectral and transport properties. [References: 32]