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arXiv:2602.08604

Elastic field causing noncommutativity

A. L. Silva Netto, A. M. de M. Carvalho, G. Q. Garcia, C. Furtado

cond-mat.mes-hallquant-phSubmitted Feb 9, 2026• Announced Feb 10, 2026
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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.

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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 BeffB_{eff}Beff​ proportional to pzOmegap_z Omegapz​Omega, where OmegaOmegaOmega 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 OmegaOmegaOmega 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.
We study a charged particle moving outside a spiral (screw) dislocation in a uniform magnetic field. Although the geometry is locally Euclidean, its global screw identification couples the conserved axial and azimuthal quantities through the combination J=ℓ−βk\mathcal{J}=\ell-βkJ=ℓ−βk After eliminating the cyclic coordinates, the radial motion is governed by an inverse-square term determined by J\mathcal{J}J and a harmonic confining term generated by the magnetic field. The corresponding reduced quantum problem is exactly solvable for qB0≠0q\mathcal{B}_0\neq0qB0​=0, yielding an equally spaced spectrum with an orientation-dependent energy shift. The radial probability density depends on J\mathcal{J}J, and opposite values of the screw-modified quantum number have identical spatial profiles but different energies for a fixed magnetic-field orientation. The radial size scales as ⟨r2⟩n∝∣qB0∣−1/2\sqrt{\langle r^2\rangle_n}\propto |q\mathcal{B}_0|^{-1/2}⟨r2⟩n​​∝∣qB0​∣−1/2, with the magnetic length setting the localization scale. At qB0=0q\mathcal{B}_0=0qB0​=0, the confining term vanishes, and the problem reduces to a scale-free inverse-square system. Thus, the screw parameter enters the dynamics through the global coupling of the conserved axial and azimuthal quantities, whereas the magnetic field provides radial confinement and its orientation determines the spectral asymmetry.
We study a single electron confined in a uniform-torsion medium, a continuum model of a screw dislocation density, in a perpendicular magnetic field, and in the presence of an Aharonov--Bohm flux. Torsion alone produces radial confinement without any \textit{ad hoc} potential, while the Aharonov--Bohm phase breaks the usual m↔−mm\leftrightarrow -mm↔−m symmetry. From the exact spectrum and wave functions, we find: (i) a torsion-controlled optical transition whose energy blue-shifts from ∼6.8\sim 6.8∼6.8 to ∼15.5\sim 15.5∼15.5~meV and whose saturation intensity varies by an order of magnitude, enabling geometry-programmable optical switching; (ii) an Aharonov--Bohm-tunable ``angular pseudospin'' formed by the m=±1m=\pm1m=±1 states, with flux-controlled level splitting and asymmetric oscillator strengths that allow selective optical addressability; and (iii) an approximately linear torsion dependence of the transition energy that enables nanoscale torsion metrology with an estimated resolution of ∼105 m−1\sim 10^{5}~\mathrm{m}^{-1}∼105 m−1. In this context, ``torsion'' refers to the experimentally relevant continuum limit of a uniform density of parallel screw dislocations, i.e., a crystal with finite torsion but vanishing curvature, which can, in practice, be engineered and probed in twisted nanowires and strained semiconductor heterostructures. We also show how torsion provides \textit{in situ} control of emitter--cavity detuning and light--matter coupling in cavity QED, in direct analogy with strain tuning of semiconductor quantum dots in nanocavities, but here arising from a purely geometric/topological parameter.
We investigate the optical response of a conduction electron in a helically twisted mesoscopic medium containing a screw dislocation and a uniform torsional background, in the presence of an axial magnetic field and an Aharonov--Bohm flux. We show that the coupling between longitudinal motion and the geometric background produces an effective in-plane confinement, allowing bound states to emerge without the need for an external radial potential. Exact analytical solutions are obtained for the energy spectrum and radial wave functions, and these results are used to evaluate linear and third-order nonlinear absorption, changes in the refractive index, the photoionization cross section, and the oscillator strength. The combined action of torsion, magnetic field, and topological defect increases the interlevel spacing, compresses the radial electronic distribution, and breaks the dynamical symmetry between opposite angular-momentum channels, leading to strongly asymmetric and state-resolved optical spectra. Under intense optical excitation, the nonlinear contribution can overcome linear absorption, driving the system into a negative-absorption regime and enabling geometry-controlled optical gain. These results establish torsion and defect engineering as effective tools for tuning confinement, resonant energies, and selective amplification in mesoscopic nanophotonic platforms operating in the mid-infrared and terahertz ranges.
We investigate the geometric phase for a two-level atom interacting with massless scalar field in the background spacetime of a cosmic string with torsion in the framework of open quantum systems. We show that the geometric phase depends on not only the inherent properties of this atom but also on the topological properties of the background spacetime. The correction to the geometric phase of the atom derives from a composite effect of the cosmic string and screw dislocation associated with the curvature and torsion, respectively. The numerical results of the correction to the geometric phase are also present. It is seen that the modification of the phase oscillates around zero and the amplitude of the correction decreases gradually, with the increase of the distance r between the atom and line defects. When the atom gets close to the line defects, the correction will increase significantly but finally tend to a finite value. The behavior of the geometric phase with the variation of the atomic position in three different types of topological defect spacetimes, i.e. , the cosmic string spacetime, screw dislocation spacetime and cosmic string spacetime with torsion, are also shown. We note that the geometric phase in the case of cosmic string spacetime is different from that of other two spacetimes, which suggests that the presence of torsion can significantly affect the geometric phase of the atom, especially in the region near the topological defects. In addition, the geometric phase for the two-level atom which results from the thermal fluctuation of the thermal bath is studied. It is shown that the geometric phase increases with the growth of the temperature T .
We investigate the effective dynamics of a particle confined near a space curve. In the strict thin-layer reduction of the nondegenerate transverse ground state, torsion does not enter the local effective Hamiltonian, which contains only the curvature-induced scalar geometric potential. In contrast, for a thin guide with finite transverse width, a leading-order adiabatic projection onto the twofold-degenerate first-excited transverse band renders the rotation of the Frenet normal frame dynamically relevant and generates a matrix-valued Abelian gauge potential. Using a projection-based derivation in a co-rotating Frenet-frame basis, we show that this effective gauge potential is directly determined by the local torsion of the curve. The resulting effective Hamiltonian takes a gauge-covariant form and produces two transverse-mode branches whose parabolic dispersions are shifted in opposite directions in momentum space. For closed curves, the associated holonomy is controlled by the integrated torsion and leads to geometric interference. These results provide a direct realization of a Wilczek--Zee-type connection induced purely by spatial geometry in curved quantum waveguides. We further construct a classical-wave analogue using the degenerate bending modes of an isotropic elastic rod, demonstrating that the same torsion-induced gauge structure appears in continuum wave physics.