Localization and Anomalous Diffusion of a Damped Quantum Particle

H. Grabert, P. Schramm, and G.-L. Ingold

Phys. Rev. Lett. 58, 1285–1288 (1987) DOI: 10.1103/PhysRevLett.58.1285

The time evolution of an initially localized state of a quantum particle coupled to a dissipative environment with spectral density I(ω)∝ωα for low frequencies is discussed. At finite temperatures, the width of the state can grow subdiffusively or superdiffusively depending on α. For α>2, damping becomes ineffective for long times and the state spreads kinematically. At zero temperature the spreading is slower and for α<1 an initially localized state remains localized for all times.