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Quantum diffusion with drift and the Einstein relation. I
3. L. Bruneau, S. De Bievre, and C.-A. Pillet, “Scattering induced current in a tight-binding band,” J. Math. Phys. 52(2), 022109 (2011).
5. E. B. Davies, Linear Operators and their Spectra (Cambridge University Press, 2007).
7. W. De Roeck, J. Fröhlich, and K. Schnelli, “Quantum diffusion with drift and the Einstein relation. II,” J. Math. Phys. 55, (2014).
8. J. Dereziński, Introduction to Representations of Canonical Commutation and Anticommutation Relations, Lecture Notes in Physics Vol. 695 (Springer-Verlag, 2006).
10. D. Egli, J. Fröhlich, Z. Gang, A. Shao, and I. M. Sigal, “Hamiltonian dynamics of a particle interacting with a wave field,” Communications in Partial Differential Equations 38(12), 2155–2198 (2013).
11. K.-J. Engel and R. Nagel, A Short Course on Operator Semigroups (Universitext) (Springer, 2006).
14. E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, AMS Colloquium Publications, Vol. XXXI (American Mathematical Society, 1957).
15. V. Jakšić and C.-A. Pillet, “On a model for quantum friction. ii: Fermi's golden rule and dynamics at positive temperature,” Commun. Math. Phys. 176, 619–644 (1996).
16. T. Kato, Perturbation Theory for Linear Operators, 2nd ed. (Springer, Berlin, 1976).
18. Y. C. Li, R. Sato, and S. Y. Shaw, “Convergence theorems and Tauberian theorems for functions and sequences in Banach spaces and Banach lattices,” Isr. J. Math. 162(1), 109–149 (2007).
19. M. Merkli, “Positive commutators in non-equilibrium statistical mechanics,” Commun. Math. Phys. 62, 223–327 (2001).
20. M. Reed and B. Simon, Methods of Modern Mathematical Physics (Academic Press, New York, 1972), Vol. 2.
23. M. Sassetti, P. Saracco, E. Galleani d'Agliano, and F. Napoli, “Linear mobility for coherent quantum tunneling in a periodic potential,” Z. Phys. B: Condens. Matter 77(3), 491–495 (1989).
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We study the dynamics of a quantum particle hopping on a simple cubic lattice and driven by a constant external force. It is coupled to an array of identical, independent thermal reservoirs consisting of free, massless Bose fields, one at each site of the lattice. When the particle visits a site x of the lattice it can emit or absorb field quanta of the reservoir at x. Under the assumption that the coupling between the particle and the reservoirs and the driving force are sufficiently small, we establish the following results: The ergodic average over time of the state of the particle approaches a non-equilibrium steady state describing a non-zero mean drift of the particle. Its motion around the mean drift is diffusive, and the diffusion constant and the drift velocity are related to one another by the Einstein relation.
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