Abstract
In undulatory mechanics the rest mass of a particle is associated to a rest periodicity known as Compton periodicity. In carbon nanotubes the Compton periodicity is determined geometrically, through dimensional reduction, by the circumference of the curled-up dimension, or by similar spatial constraints to the charge carrier wave function in other condensed matter systems. In this way the Compton periodicity is effectively reduced by several orders of magnitude with respect to that of the electron, allowing for the possibility to experimentally test foundational aspects of quantum mechanics. We present a novel powerful formalism to derive the electronic properties of carbon nanotubes, in agreement with the results known in literature, from simple geometric and relativistic considerations about the Compton periodicity as well as a dictionary of analogies between particle and graphene physics.
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A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009).
M. Mecklenburg, B.C. Regan, Phys. Rev. Lett. 106, 116803 (2011).
D. Dolce, EPL 102, 31002 (2013).
D. Dolce, Ann. Phys. 327, 1562 (2012).
D. Dolce, Ann. Phys. 327, 2354 (2012).
D. Dolce, Found. Phys. 41, 178 (2011).
G. ’t Hooft, J. Phys: Conf. Ser. 67, 012015 (2007).
G. ’t Hooft, The Cellular Automaton Interpretation of Quantum Mechanics. A View on the Quantum Nature of our Universe, Compulsory or Impossible? (2014) arXiv:1405.1548.
L. de Broglie, Ann. Phys. 3, 22 (1925).
T.M. Rusin, W. Zawadzki, Phys. Rev. B 80, 045416 (2009).
R. Penrose, Cycles of Time. An Extraordinary View of The Universe (Knopf, New York, 2011) chapt. 2.3.
S.Y. Lan, P.C. Kuan, B. Estey, D. English, J.M. Brown, M.A. Hohensee, H. Müller, Science 339, 554 (2013).
J.C. Charlier, X. Blase, S. Roche, Rev. Mod. Phys. 79, 677 (2007).
J. de Woul, A. Merle, T. Ohlsson, Phys. Lett. B 714, 44 (2012).
D. Dolce, A. Perali, Found. Phys. 44, 9 (2014) arXiv:1307.5062.
J.W.M. C.T. White, Nature 6688, 29 (1998).
J. Zaanen, Nat. Phys. 10, 609 (2013).
K. Zou, X. Hong, J. Zhu, Phys. Rev. B 84, 085408 (2011).
A. Perali, D. Neilson, A.R. Hamilton, Phys. Rev. Lett. 110, 146803 (2013).
H. Margolis, Nat. Phys. 2, 82 (2014).
T.M. Rusin, W. Zawadzki, J. Phys.: Condens. Matter 26, 215301 (2014).
P. Catillon, N. Cue, M.J. Gaillard, R. Genre, M. Gouanère, R.G. Kirsch, J.C. Poizat, J. Remillieux, L. Roussel, M. Spighel, Found. Phys. 28, 659 (2008).
K.S. Novoselov, V.I. Fal’ko, L. Colombo, P.R. Gellert, M.G. Schwab, K. Kim, Nature 490, 192 (2012).
I. Kenyon, General relativity (Oxford Science Publications, 1990).
A. Perali, A. Bianconi, A. Lanzara, N.L. Saini, Solid State Commun 100, 181 (1996).
D. Dolce, A. Perali, Testing Cellular Automata Interpretation of Quantum Mechanics in Graphene and Superconducting Systems (2014) prepared for DICE2014, to be published in J. Phys.: Conf. Ser.
D.T. Son, M.A. Stephanov, Phys. Rev. D 69, 065020 (2004).
A. Chodos, R.L. Jaffe, K. Johnson, C.B. Thorn, V.F. Weisskopf, Phys. Rev. D 9, 3471 (1974).
E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998).
M.A.H. Vozmediano, M.I. Katsnelson, F. Guinea, Phys. Rep. 496, 109 (2010).
A. Iorio, J. Phys. Conf. Ser. 442, 012056 (2013).
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Dolce, D., Perali, A. On the Compton clock and the undulatory nature of particle mass in graphene systems. Eur. Phys. J. Plus 130, 41 (2015). https://doi.org/10.1140/epjp/i2015-15041-5
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DOI: https://doi.org/10.1140/epjp/i2015-15041-5