Dissipative quantum transport in a nanowire

The coherence-to-decoherence transition is studied in a nanowire modeled as a one-dimensional tight-binding lattice in the presence of an external field and in linear interaction with a boson heat bath, characterized by Ohmic dissipation. The focus of attention is the probability propagator which quantifies the likelihood of a quantum particle, such as an electron to end up at an arbitrary site at a time t, given that it was at the origin initially-and from it-the particle-current and the mean-squared displacement. If the bath is absent, the probability operator exhibits quantum coherence as can be captured by say, Bloch oscillation and Wannier-Stark (dynamic) localization. The coupling with the bath-which can be weak or strong-leads to decoherence that will be quantified in the text. The Ohmic model of the spectral function of bath excitations contains a cutoff frequency, which if greater than the temperature (in energy units) defines the "low-temperature" regime, whereas the opposite limit implies "high temperatures." Results will be presented in both these regimes separately.