  Earlier, in the CINT program at Los Alamos National Laboratory, we focused
ultrafast mode-locked lasers on the tip-sample junction of a scanning tunneling
microscope to generate currents at hundreds of harmonics of the laser pulse
repetition frequency. Each harmonic has a signal-to-noise ratio of 20 dB with a
10-dB linewidth of only 3 Hz. Now we model closed quantum nanocircuits with
rectangular, triangular, or delta-function barrier, shunted by a beryllium
filament for quasi-coherent electron transport over mean-free paths as great as
68 nm. The time-independent Schr\"odinger equation is solved with the boundary
conditions that the wavefunction and its derivative are continuous at both
connections. These four boundary conditions are used to form a four-by-four
complex matrix equation with only zeros in the right-hand column vector which
is required to have a non-trivial solution with each of the closed
nanocircuits. Each model has four parameters: (1) the barrier length, (2) the
height and shape of the barrier, (3) the length of the pre-barrier, and (4) the
electron energy. Any three of these may be specified and then the fourth is
varied to bring the determinant to zero to find the solutions on lines or
surfaces in the space defined by the four parameters. First, we use a
simplistic model having a rectangular barrier. The second model has a
triangular barrier as a first approximation to field emission, and we are
considering applying this approach for a self-contained nanoscale extension of
our earlier effort to generate the harmonics at Los Alamos. The third model has
a delta-function barrier, and the fourth model is an extension of the first one
where the width of the rectangular barrier is varied inversely with its height.
