This third part continues the theme of wave mechanics of non-interacting particles. However attention shifts from closed to open systems, namely the transport of quasiparticles (in a 2D electron gas) though a general two-terminal mesoscopic electronic device, or `quantum point contact' (QPC) [20,65].
We model the conductance of a QPC, in linear response.
If the QPC is highly non-adiabatic or near to
scatterers in the open reservoir regions, then
the usual distinction between `leads' and `reservoirs' breaks down.
This situation arises in the recent experimental work of
Katine  and Topinka 
in the Westervelt group
here at Harvard, where open resonant and scattering geometries were studied.
In such systems the Landauer formula [129,130,41,55,65]
for the conductance
(including spin degeneracy),
The relation between the Landauer and the half-plane scattering formalism
is expressed by
We analyse an idealized, highly non-adiabatic slit QPC system in the extreme quantum, intermediate, and semiclassical regimes. We derive the counterintuitive result (first due to Heller) that an arbitrarily small (tunneling) QPC can reach a p-wave channel conductance of when coupled to a suitable resonant cavity. We also find that if two or more resonances coincide, the total conductance can in theory reach multiples of this value.
This leads to some thought-experiments on attempting to overcome the maximum conductance per quantum channel. We also discuss reciprocity (left-to-right symmetry) of conductance, and the possibility of its breakdown in a proposed QPC (which could exhibit `conductance' quantization) for atom waves. We emphasizes the importance of the thermal occupation of states in phase space (as is usual in 2D electron systems), for reciprocity to exist. An analogous atomic QPC in 3D need not have this thermal occupation, thus in this system reciprocity can be broken.
This work has been in collaboration with Areez Mody and Miriam Blaauboer, and at the earlier stages many contributions were made by Adam Lupu-Sax. Joseph Thywissen, and professors Charlie Marcus and Daniel Fisher also contributed via stimulating discussions.