Nano-scale devices provide a unique environment to probe the effects of decoherence on quantum systems.  In particular, the roles of molecular vibrations and disorder on charge transport between two conductive contacts have been studied for several decades.  However, these effects are usually discussed in terms of models which assume either entirely coherent or entirely decoherent charge transfer between the electrodes.  There have been comparatively few examples of methods that have effectively spanned both extremes from first principles with regard to interaction between scattering charges and their vibrational thermal environment.  In this work, the development of a new treatment based on scattering theory in the Liouville space formalism is discussed to unify the electron tunneling and electron hopping regimes of transport.   Expressions for the evolution of vibronic populations and coherences as a function of time are derived as well as the current transmission through the junction starting from a simple Newns-Anderson Hamiltonian and the Liouville equation.  Several instructive limits will be discussed spanning the assumption of isolated molecular resonances in the elastic limit to the effect of coupling to molecular vibrations without any assumptions placed on the location of charge states.  The behavior of the Liouville transition matrix elements will be contrasted with the Hilbert space scattering approaches previously employed and the limitations of the later will be elucidated.

Electron scattering in Liouville space: From coherence to decoherence to incoherence?

252nd National Meeting (2016)

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