Quantum Brownian motion induced by thermal noise in the presence of disorder (Q2795580)

The authors study the motion of a quantum particle through the lattice \(\mathbb Z^d\) in the presence of a disordered potential landscape and under the influence of thermal noise. The dynamics of the particle is described by a Lindblad equation for the time evolution of its state, a one-particle density matrix. The Hamiltonian part in the total Lindblad generator is given by a random Schrödinger operator. Using similar arguments of the second author [Commun. Math. Phys. 339, No. 3, 859--901 (2015; Zbl 1335.82014)] it is shown that an arbitrary small amount of thermal noise suffices for the particle to have a diffusive motion, i.e., a quantum Brownian motion. Moreover, the behaviour of the diffusion constant in the limit, where the coupling with the heat bath tends to zero, is studied.