Consider nano-dimensional quantum system
consisting of a resonator connected to infinity by finite number (three
for example) of channels
.
Electron beam is injected into the system along the right channel and is handled by the
electric field with potential V(x,y). This
field is induced due to charging the resonator's walls A1,
A2,A3 by potentials V1,
V2,V3, respectively; the handling is realized by variation of
values V1,2,3.
The whole system is shielded by three non-closed lines B1,
B2,B3 (see
dashed lines). Thus the potential V(x,y)
exponentially decays along the channels and can be approximated by the solution to the
auxiliary Laplace problem in a truncated domain (with the zero boundary condition at
lines crossing the channels). An example of the potential is shown as the
color inset (top). Given V1,2,3, we solve this Laplace problem. Next, given the electron energy E, we solve the scattering problem with potential V(x,y) and observe that there exist combinations of V1,2,3 and E such that the scattering probability is concentrated either in the 2nd or in the 3rd channel (i.e., either |s12|2 @ 1 or |s13|2 @ 1). Plot (solid line) shows the transporting loses |s11|2 + |s13|2 versus E (in normalized units) varying between the 1st and 2nd channel's threshold; intensity map of the electron beam for the first peak minimum of transporting loses is shown on color inset (bottom).
Details: quant-ph/0406019 (in Russian: Pis'ma v Zhurnal Teknicheskoi Fiziki, vol.30 (2004), no.15, pp.69-76)
TO BE CONTINUED