Diffusion of a Quantum Particle in a Fluctuating Medium

Quantum motion of a particle in a fluctuating lattice is studied on the basis of a time-dependent Hamiltonian with site energies being randomly modulated by stochastic noises. The case of the two-state jump noise is studied in details. It is found that the particle moves diffusively on a long time scale. When the noise has a non-white spectrum, the diffusion constant is substantially enhanced in comparison with the white noise limit owing to the local coherence of the wavefunction of the particle. A numerical study is also carried out for one-dimensional cases. The analytical result is in rough agreement with the numerical calculation.