Dissipative quantum transport in a quantum wire

We have carried out a real-time path-integral calculation of quantum transport of an electron through a dissipative quantum wire, which is modeled by a parabolic potential in one of the directions. The interaction between the electron and the phonons is treated in terms of an ordered expansion. At the linear order the problem is solved exactly. We present a detailed derivation of the influence of functional formalism within this model. We study the quantum dynamics of the electron under an external force nonperturbatively with various initial conditions. The electron drifting velocity is found to depend on the external force linearly, and consists of a sum of two terms. One term is a time-independent constant while the other oscillates with time. The drifting velocity remains the same for different initial conditions and the oscillation has a characteristic period. We found that while the confinement does not appear to influence the long time drifting velocity within the linear model, it does have very complicated nontrivial effects when nonlinear terms are included. A formalism is established to include the confining potential within a general model of the electron-phonon coupling.