Quantum theory of dissipative processes: The Markov approximation revisited

G. F. Vincent-Smith

David Taj, Rita Claudia Iotti, Fausto Rossi

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, we shall propose an alternative more general adiabatic procedure, able to provide a reliable/robust treatment of energy-dissipation and dephasing processes in electronic quantum devices. Unlike standard master-equation formulations, our procedure guarantees a positive evolution for a variety of physical subsystem (including the common partial trace), and quantum scattering rates are well defined even for subsystems with internal structure/ continuous energy 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.

Ilya Prigogine

M. Courbage

Fausto Rossi

We shall revisit the conventional adiabatic or Markov approximation, showing its intrinsic failure in describing the proper quantum-mechanical evolution of a generic subsystem interacting with its environment. In particular, we shall show that -contrary to the semiclassical case- the Markov limit does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this problem, we shall propose an alternative adiabatic procedure which (i) in the semiclassical limit reduces to the standard Fermi's golden rule, and (ii) describes a genuine Limblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes.

David Taj, Rita Claudia Iotti, Fausto Rossi

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 pointed out and partially solved by Davies and co-workers almost three decades ago, 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. Unlike standard master-equation formulations, the dependence of our approximation on the specific choice of the subsystem (that include the common partial trace reduction) does not threaten positivity, and quantum scattering rates are well defined even in case the subsystem is infinitely extended/has continuous spectrum.