Decoherence effects in the Wigner function formalism

We demonstrate the ability of the phase space formulation of quantum mechanics to provide convenient means and intuitive notions for exploring the process of transition from a quantum to a classical state known as decoherence. The Wigner equation, which is usually relevant for electron transport in nanostructures, augmented by the Boltzmann scattering operator is now applied to the time dependent transport problems which may be considered as benchmark examples for the decoherence role of phonons in semiconductor devices. Simulation results maintained by theoretical analysis show how scattering effectively destroys the interference effects. The initial coherence in the wave vector distribution is pushed towards the equilibrium distribution. In particular scattering by phonons hinders the natural spread of the density with time and advances it towards P. Schwaha · M. Nedjalkov ( ) · S. Selberherr Institute for Microelectronics, TU Wien, 1040 Wien, Austria e-mail: [email protected] P. Schwaha e-mail: [email protected] S. Selberherr e-mail: [email protected] Present address: P. Schwaha AVL List GmbH, Hans-List-Platz 1, 8020 Graz, Austria D. Querlioz · P. Dollfus · J. Saint-Martin Institut d’Electronique Fondamentale, Université Paris-Sud, CNRS, 91405 Orsay, France D. Querlioz e-mail: [email protected] P. Dollfus e-mail: [email protected] J. Saint-Martin e-mail: [email protected] a classical localization. Furthermore, the decoherence effect due to phonons, is measured by the purity of the Wigner state, which decreases from its initial value of 1, with a rate depending on the lattice temperature, and by a functional comparing diagonal with off-diagonal elements of the density matrix.