Quantum or not? Mathematical equations shows whether electron transport in nanostructures follows quantum behavior

Understanding the transport of electrons in nanostructures and biological molecules
behavior of molecules. However, determining whether the electrons are behaving
according to the classical laws of motion or the quantum mechanical regime at the
nanoscale is challenging because many nanostructures fall in a grey area between
both regimes. Researchers from the RIKEN Advanced Science Institute in Wako,
with colleagues from Germany and Taiwan, have now devised a set of mathematical
equations that can distinguish classical from quantum mechanical behavior of
electrons in nanostructures.


On a macroscopic scale, objects follow the classical laws of motion. Golf or billiard
balls, for example, will follow exact, predictable paths. On a microscopic scale, objects
such as electrons move according to the laws of quantum mechanics, where processes
occur in a probabilistic manner (Fig. 1). Measuring the properties of quantum
mechanical systems, however, is challenging.
“In microscopic systems, it is very difficult to perform ideal measurements without
disturbing the system,” explains Neill Lambert from the research team. As a
consequence, measurements on quantum mechanical systems are difficult to
distinguish from invasive measurements on classical systems, says Franco Nori
from RIKEN and the University of Michigan, who led the research team. “It is important
to be confident that experimental results are not originating from a classical effect,
giving a false impression of quantum behavior.”
As a model system, the researchers chose the transport of electrons through
vanishingly small pieces of matter known as quantum dots. “Even measuring
the current passing through a quantum dot represents an invasive measurement
of the system,” Lambert notes. To identify quantum effects, he and his colleagues
developed a set of criteria expressed as a mathematical inequality relationship for
experimental data from these quantum dots. Any excess over a critical threshold
in the formula by a parameter represents a clear sign of quantum behavior. In
their simulations the researchers found several regimes at low temperatures
where quantum effects in the dynamics of electrons in the quantum dots
should occur.
The inequality relation derived by the researchers is based on fundamental principles
and therefore applies not only to the transport of electrons through quantum dots, but
also to many open, microscopic electron transport systems, says Nori. He believes that
it will soon be easier to determine whether electrons in nanostructures follow the
rules of quantum mechanics or take the classical route of their billiard-ball