Thermopower of single-channel disordered and chaotic conductors

We show (analytically and by numerical simulation) that the zero-temperature limit of the distribution of the thermopower S of a one-dimensional disordered wire in the localized regime is a Lorentzian, with a disorder-independent width of 4 pi(3)k(B)(2)T/3e Delta (where T is the temperature and Delta the mean level spacing). Upon raising the temperature the distribution crosses over to an exponential form alpha exp(-2\S\eT/Delta). We also consider the case of a chaotic quantum dot with two single-channel ballistic point contacts. The distribution of S then has a cusp at S = 0 and a tail alpha \S\(-1-beta) In \S\ for large S (with beta = 1, 2 depending on the presence or absence of time-reversal symmetry). (C) 1998 Academic Press Limited.