Elastic field causing noncommutativity

¹ Universidade Federal do Vale do São Francisco - 48902-300 Juazeiro, BA, Brazil
² Instituto de Física, Universidade Federal de Alagoas - 57072-970 Maceió, AL, Brazil
³ Centro de Ciências, Tecnologia e Saúde, Universidade Estadual da Paraíba - 58233-000 Araruna, PB, Brazil
⁴ Departamento de Física, Universidade Federal da Paraíba - 58051-970 João Pessoa, PB, Brazil

Received: 9 February 2026
Accepted: 31 March 2026

Abstract

We study how a uniform torsion background —modeling a continuous density of screw dislocations— 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 , where Ω encodes the torsion strength. In the strong-coupling (Landau) regime, the planar coordinates obey and the spectrum organizes into Landau-like levels with a slight electric-field–driven tilt and a uniform shift. Thus, increasing Ω 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.