Elastic field causing noncommutativity

TL;DR

This paper explores how a uniform torsion background, representing screw dislocations, induces effective spatial noncommutativity and modifies the energy spectrum of a free quantum particle, drawing parallels to Landau levels.

Contribution

It demonstrates how torsion causes noncommutative geometry effects and reshapes the quantum energy spectrum, connecting defect theory with magnetic-like phenomena.

Findings

Torsion induces an effective magnetic field proportional to momentum and torsion strength.

In strong coupling, coordinates obey noncommutative relations similar to Landau levels.

Increasing torsion drives the system towards the Landau problem in flat space.

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.