Quantum or not? Mathematical equations resolve nanostructures behavior

Mathematical equations resolve nanostructures behavior
In a game of billiards, the path of each ball is determined by the classical laws of motion. At the microscopic scale, equivalent objects may be governed by quantum mechanics, such that their exact path of movement could take several directions. Credit: 2010 iStockphoto/JamesBrey

Understanding the transport of electrons in nanostructures and biological molecules is crucial to understanding properties such as electrical conductivity or the biochemical 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. Japanese 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 , objects follow the classical laws of motion. Golf or billiard balls, for example, will follow exact, predictable paths. On a , objects such as electrons move according to the laws of quantum mechanics, where processes occur in a probabilistic manner. 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 . “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 or take the classical route of their billiard-ball counterparts.

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More information: Lambert, N., et al. Distinguishing quantum and classical transport through nanostructures. Physical Review Letters 105, 176801 (2010) . See the article here: prl.aps.org/abstract/PRL/v105/i17/e176801 .
Provided by RIKEN
Citation: Quantum or not? Mathematical equations resolve nanostructures behavior (2010, December 17) retrieved 19 July 2019 from https://phys.org/news/2010-12-quantum-mathematical-equations-nanostructures-behavior.html
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Dec 17, 2010
I thought quantum mechanics applies to everything. However the weird quantum effects become negligible as mass and scale increases. One good example is that a pitched baseball (particle)has a wavelength however it is negligible due its mass/size.
Classical physics is an approximation which works well at the macro scale because quantum effects are negligible.
Isn't it also the case that quantum mechanics breaks down at the plank scale.

Dec 18, 2010

Quantum mechanics applies to everything at a very small scale, locally. Some systems function in a way where there is a wide-spread enough interaction between the macro and the micro scales in a dense enough space to enable a typically unusual effect at the macro level. A single quantum mechanical effect at the scales where those effects take place, has essentially no chance to manifest macroscopic effects, even though these events occur everywhere.

It's complicated to think about at first, but makes sense when you take the time to actually understand how technology is developed with applied physics.

Jan 19, 2011
If motion is discrete and not continuous, then as an object moves from place to place, it does not exist in the plank lenght space in between. Otherwise if- an object is pushed, then it does not compress and then stretch its full length.

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