Thank Nanoscale for bringing to my attention a long standing puzzle in mesocopic scale condensed matter physics, the “0.7 anomaly”. The problem is the behavior of the conductance (inverse of resistance) for a quantum point contact (QPC). Two experimental papers showing the effect are 0706.0792 and cond-mat/0005082, which see. Shot noise decreases at the 0.7 anomaly just as it does at the integer conductance points, see cond-mat/0311435. A recent perturbation analysis of the situation is given by 0707.1989. This blog post gives a non perturbational calculation.
Such a point contact is a region which is so small that it can hold at most a single electron. One controls the size of the conductance region by applying a voltage to a gate. One expects that the conductance will be a multiple of G0 = 1/13K ohms; this works for high conductance values (increasing to saturation) but an anomaly appears near cutoff.
This really is basic physics and should be well understood. The computer that I (and you, assuming you’re reading this in 2008) are using are built from CMOS logic gates. The QPC effect occurs when such a gate is operated near its cutoff point. There are billions of billions of these gates currently in operation on this planet (operating in cutoff and saturation); by all expectations they should have been well understood many decades ago.
However, it turns out that the situation is difficult to analyze with the usual tools of quantum mechanics. One ends up with a highly nonlinear situation involving “quasibound” states. Since the density matrix formalism I work with is specifically designed to solve highly nonlinear bound state QFT problems without recourse to the usual perturbation theory, this is a natural place to explore its application. In addition, this could be a good first application of MUB (mutually unbiased bases) to quantum theory.