Elastic field causing noncommutativity

Abstract:We study how a uniform torsion background, modeling a continuous density of screw dislocations and induces effective spatial noncommutativity and reshapes the energy spectrum of a free quantum particle. Within the geometric theory of defects, the metric yields a first-order (magnetic-like) coupling in the transverse dynamics, equivalent to an effective magnetic field $B_{eff}$ proportional to $p_z Omega$, where $Omega$ encodes the torsion strength. In the strong-coupling (Landau) regime, the planar coordinates obey [x,y] != 0 and the spectrum organizes into Landau-like levels with a slight electric-field-driven tilt and a uniform shift. Thus, increasing $Omega$ drives the system continuously toward the familiar Landau problem in flat space, with torsion setting the noncommutativity scale and controlling the approach to the Landau limit.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2602.08604 [cond-mat.mes-hall]

(or arXiv:2602.08604v1 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2602.08604 Focus to learn more arXiv-issued DOI via DataCite

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