The Quantum Mechanics of a Rolling Molecular “Nanocar”

Abstract We formulate a mathematical model of 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 w...

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Autores principales:	Oscar E. Fernandez, Mala L. Radhakrishnan
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2018
Materias:	Nonholonomic Systems Nonholonomic Constraints Wheelbarrow Nonholonomic Case Negative Ground State Energy Medicine R Science Q
Acceso en línea:	https://doaj.org/article/dd01ba56c1cd423290416af8f705adf4
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id	oai:doaj.org-article:dd01ba56c1cd423290416af8f705adf4
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spelling	oai:doaj.org-article:dd01ba56c1cd423290416af8f705adf42021-12-02T11:41:13ZThe Quantum Mechanics of a Rolling Molecular “Nanocar”10.1038/s41598-018-33023-82045-2322https://doaj.org/article/dd01ba56c1cd423290416af8f705adf42018-10-01T00:00:00Zhttps://doi.org/10.1038/s41598-018-33023-8https://doaj.org/toc/2045-2322Abstract We formulate a mathematical model of 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.Oscar E. FernandezMala L. RadhakrishnanNature PortfolioarticleNonholonomic SystemsNonholonomic ConstraintsWheelbarrowNonholonomic CaseNegative Ground State EnergyMedicineRScienceQENScientific Reports, Vol 8, Iss 1, Pp 1-11 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Nonholonomic Systems Nonholonomic Constraints Wheelbarrow Nonholonomic Case Negative Ground State Energy Medicine R Science Q
spellingShingle	Nonholonomic Systems Nonholonomic Constraints Wheelbarrow Nonholonomic Case Negative Ground State Energy Medicine R Science Q Oscar E. Fernandez Mala L. Radhakrishnan The Quantum Mechanics of a Rolling Molecular “Nanocar”
description	Abstract We formulate a mathematical model of 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.
format	article
author	Oscar E. Fernandez Mala L. Radhakrishnan
author_facet	Oscar E. Fernandez Mala L. Radhakrishnan
author_sort	Oscar E. Fernandez
title	The Quantum Mechanics of a Rolling Molecular “Nanocar”
title_short	The Quantum Mechanics of a Rolling Molecular “Nanocar”
title_full	The Quantum Mechanics of a Rolling Molecular “Nanocar”
title_fullStr	The Quantum Mechanics of a Rolling Molecular “Nanocar”
title_full_unstemmed	The Quantum Mechanics of a Rolling Molecular “Nanocar”
title_sort	quantum mechanics of a rolling molecular “nanocar”
publisher	Nature Portfolio
publishDate	2018
url	https://doaj.org/article/dd01ba56c1cd423290416af8f705adf4
work_keys_str_mv	AT oscarefernandez thequantummechanicsofarollingmolecularnanocar AT malalradhakrishnan thequantummechanicsofarollingmolecularnanocar AT oscarefernandez quantummechanicsofarollingmolecularnanocar AT malalradhakrishnan quantummechanicsofarollingmolecularnanocar
_version_	1718395431485964288

The Quantum Mechanics of a Rolling Molecular “Nanocar”

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