Unified Exact Cylindrical Dirac Modes and Symmetry-Resolved Quantum Geometry

• URL: http://arxiv.org/abs/2608.10563v1
• Date: Tue, 11 Aug 2026 06:51:29 GMT
• Title: Unified Exact Cylindrical Dirac Modes and Symmetry-Resolved Quantum Geometry
• Abstract summary: Exact cylindrical solutions of the free Dirac equation provide natural single-particle modes for a broad class of relativistic fermion systems.<n>We show how the commonly used spin-polarized, separation, helicity, and transverse-helicity modes are embedded in the resulting two-dimensional solution space.
• Score: 2.1686432495639045
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Exact cylindrical solutions of the free Dirac equation provide natural single-particle modes for a broad class of axially symmetric relativistic fermion systems, including electron vortices, twisted-particle scattering, rotating matter, and cylindrical field quantization, but are commonly formulated in different internal bases. We derive the general regular positive-energy cylindrical solution at fixed energy, transverse and longitudinal momenta, and total angular momentum, and show how the commonly used spin-polarized, separation, helicity, and transverse-helicity modes are embedded in the resulting two-dimensional solution space. A conserved transverse operator resolves the residual doublet into two symmetry-defined branches. Their parameter-dependent eigenspaces admit a gauge-invariant quantum-geometric characterization, with opposite Berry curvatures, a common quantum metric, and saturation of the two-level metric--curvature relation. We further derive symmetry constraints on branch conversion and the corresponding reduced two-state dynamics. The resulting framework connects mode classification, symmetry resolution, quantum geometry, and dynamics across distinct cylindrical Dirac settings.

Related papers

• Scattering, bound states, and resonances in the one-dimensional Dirac equation via supersymmetric quantum mechanics [0.0]
  We develop a unified treatment of scattering and discrete spectra for the one-dimensional Dirac equation with scalar and vector interactions.<n>Under the spin-symmetry condition, the coupled first-order Dirac system maps exactly onto an effective Sturm--Liouville (Schr-din-ger-like) problem for a single spinor component.
  arXiv  Detail & Related papers  (2026-07-01T01:07:29Z)
• Generalized symmetries, invariant solutions and conservation laws in the Jaynes-Cummings model [41.99844472131922]
  We investigate the Jaynes--Cummings model (JCM) using Lie symmetry analysis and conservation-law theory.<n>The dynamics is formulated as a system of partial differential equations by projecting the von Neumann equation onto the atomic degrees of freedom.<n>We derive additional conserved currents involving atomic populations, coherence, reduced-state purity, and moments of the field characteristic function.
  arXiv  Detail & Related papers  (2026-06-14T01:42:11Z)
• Mean-field and fluctuation dynamics in off-resonant two-mode atom-field interactions [39.146761527401424]
  We study a two-level system coupled to two quantized electromagnetic modes within the Jaynes-Cummings framework.<n>While the single-mode model is exactly solvable due to its conserved excitation number, the two-mode model extension presents a fundamental challenge.<n>Our scheme separates the dynamics into a dominant, exactly solvable semiclassical component, the atom interacting with the mean fields of both modes.
  arXiv  Detail & Related papers  (2026-05-19T22:30:51Z)
• Dual Quantum Geometric Tensors and Local Topological Invariant [1.8205293871050265]
  We show that the Zeeman QGT is generically non-Hermitian and admits a natural decomposition into normal and anomalous metric-curvature sectors.<n>The results establish a unified framework connecting non-Hermitian Zeeman quantum geometry, local Dirac-node topology, and measurable transport signatures.
  arXiv  Detail & Related papers  (2026-04-09T08:00:50Z)
• Typical entanglement in anyon chains: Page curves beyond Lie group symmetries [41.99844472131922]
  We study bipartite entanglement statistics in one-dimensional anyon chains constrained by fusion rules of unitary pre-modular categories.<n>Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(sqrtL)$ or $O(1)$ symmetry-type corrections.<n> Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions.
  arXiv  Detail & Related papers  (2026-03-26T18:00:03Z)
• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Hilbert space geometry and quantum chaos [39.58317527488534]
  We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians. We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
  arXiv  Detail & Related papers  (2024-11-18T19:00:17Z)
• Exact solutions of a spin-orbit coupling model in two-dimensional central-potentials and quantum-classical correspondence [0.0]
  We present both the classical and quantum periodic-orbits of a neutral spinning particle constrained in two-dimensional central-potentials with a cylindrically symmetric electric-field. A non-Abelian anyon-model emerges in a natural way.
  arXiv  Detail & Related papers  (2023-08-20T12:49:30Z)
• Duality symmetry conjugates of the quantum Rabi model : effective bosonic, fermionic and coupling-only dynamical properties [0.0]
  In this article, two symmetry operators, characterized as "duality" symmetry operators, have been introduced which transform the quantum Rabi Hamiltonian into duality conjugates. The closed $SU(2)$ Lie algebra provides the standard eigenvalues and eigenstates of the parity symmetry operator. It is established that Jaynes-Cummings and anti-Jaynes-Cummings operators are duality symmetry conjugates.
  arXiv  Detail & Related papers  (2021-12-23T13:08:20Z)
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness [68.8204255655161]
  We compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls. We show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution.
  arXiv  Detail & Related papers  (2021-10-27T15:27:54Z)
• Rectification induced by geometry in two-dimensional quantum spin lattices [58.720142291102135]
  We address the role of geometrical asymmetry in the occurrence of spin rectification in two-dimensional quantum spin chains. We show that geometrical asymmetry, along with inhomogeneous magnetic fields, can induce spin current rectification even in the XX model.
  arXiv  Detail & Related papers  (2020-12-02T18:10:02Z)
• Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry [0.0]
  We develop a theory of symmetry-protected quantized invariants for topological phases defined on a lattice. We show how discrete rotational and translational symmetry fractionalization can be characterized by a discrete spin vector. The fractionally quantized charge polarization, which is non-trivial only on a lattice with $2$, $3$, and $4$-fold rotation symmetry, implies a fractional charge bound to lattice dislocations.
  arXiv  Detail & Related papers  (2020-05-20T18:00:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.