2012-05-02
10:15 at HCI J 574

Microscopic theory of relaxation and decoherence for weakly coupled quantum open systems

David Taj

Politecnico di Torino

We shall revisit the conventional adiabatic or Markov approximation, which —contrary to the semiclassical case— does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally addressed by Davies and co-workers almost three decades ago [1], we shall propose an alternative more general adiabatic procedure, which (i) is physically justified under the same validity restrictions of the conventional Markov approach, (ii) in the semiclassical limit reduces to the standard Fermi’s golden rule, and (iii) describes a genuine Lindblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes in electronic quantum devices [2, 3, 4]. Unlike standard master-equation formulations, our procedure guarantees a positive evolution for a variety of choices for the subsystem (that include the common partial trace reduction), and quantum scattering rates are well defined even in case the subsystem is infinitely extended/has continuous spectrum. We shall compare the proposed Markov dissipation model with the conventional one also through basic simulations of energy-relaxation versus decoherence channels in prototypical semiconductor nanodevices, and show how the new approach could be used to model quantum transport for a toy model spatially resolved device.

[1] E.B. Davies, “Markovian Master Equations,” Commun. math. Phys., vol. 39, p. 91–110 (1974). [2] D.TajandF.Rossi,“CompletelypositiveMarkovianquantumdynamicsintheweak-couplinglimit,”Phys. Rev. A, vol. 78, 052113 (2008). [3] D. Taj, R.C. Iotti and F. Rossi, “Dissipation and decoherence in nanodevices: a generalized Fermi’s golden rule,” Semiconductor Science and Technology, pp. 6, Vol. 24. (2009) [4] D. Taj, ”Van Hove Limit for Infinite Systems, Ann. Henri Poincar, 11, 1303 (2010)