| Abstract: |
| Recent developments in nanomanufacturing have produced molecular nanocars that roll on
(usually) gold surfaces. We formulate a mathematical model of one such nanocar, a rolling molecular wheelbarrow (a two-wheeled nanoscale molecular machine), informed by experiments on molecular machines recently synthesized in labs. The model is a nonholonomic system (briefly, a system with non-integrable velocity constraints), for which no general quantization procedure exists. Nonetheless, we successfully embed the system in a Hamiltonian one and then quantize the result using geometric quantization and other tools. We extract
from the result the quantum mechanics of the molecular wheelbarrow and derive explicit formulae
for the quantized energy spectrum. We also study a few variants of our model, some of which ignore
the model`s nonholonomic constraints. We show that these variants have different quantum energy
spectra, indicating that in such systems one should not ignore the nonholonomic constraints, since they
alter in a non-trivial way the energy spectrum of the molecule. |
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