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Quantum Brownian motion induced by thermal noise in the presence of disorder. (English) Zbl 1342.82122

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.

MSC:

82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
82D25 Statistical mechanics of crystals
81S22 Open systems, reduced dynamics, master equations, decoherence
60J65 Brownian motion
82C44 Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics
35Q82 PDEs in connection with statistical mechanics

Citations:

Zbl 1335.82014
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References:

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