A DILUTE NEUTRAL-CLUSTER APPROXIMATION FOR THE QUANTUM WASHBOARD POTENTIAL

Abstract

We study the mobility of a quantum particle in a biased cosine potential V(x)= V0 cos (k0x)–Fx and subject to an Ohmic-like dissipation. It is found that for [Formula: see text], there exists a set of discrete points αp=2p/(2p–1) at which the series for the mobility in powers of V0 may be partially summed via a dilute neutral-cluster approximation (in the sense that the coefficients are viewed as 1-d Coulomb chains). Detailed analyses are carried out for p=1 and 2, with p=1 recovering the so-called dilute-dipole approximation in a general way. In addition, the zero-temperature coefficients of [Formula: see text] and [Formula: see text] for the linear mobility are proved to be rigorously zero for α<1.