Numerical study of non-relativistic quantum systems and small oscillations induced in a helically twisted geometry

• URL: http://arxiv.org/abs/2602.16693v1
• Date: Wed, 18 Feb 2026 18:39:54 GMT
• Title: Numerical study of non-relativistic quantum systems and small oscillations induced in a helically twisted geometry
• Authors: C. F. S. Pereira, R. L. L. Vitória, A. R. Soares, B. B. Silva, H. Belich, Edilberto O. Silva,
• Abstract summary: We investigate bound states of a non-relativistic scalar particle in a three-dimensional helically twisted (torsional) geometry.<n>The dynamics is described by the Schrdinger equation on a curved spatial background.<n>We compute spectra and eigenfunctions numerically by formulating the radial equation as a self-adjoint Sturm--Liouville problem.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate bound states of a non-relativistic scalar particle in a three-dimensional helically twisted (torsional) geometry, considering both the free case and the presence of external radial interactions. The dynamics is described by the Schrödinger equation on a curved spatial background and, when included, by minimal coupling to a magnetic vector potential incorporating an Aharonov--Bohm flux. After separation of variables, the problem reduces to a one-dimensional radial eigenvalue equation governed by an effective potential that combines torsion-induced Coulomb-like and centrifugal-like structures with magnetic/flux-dependent terms and optional model interactions. Because closed-form analytic solutions are not reliable over the parameter ranges required for systematic scans, we compute spectra and eigenfunctions numerically by formulating the radial equation as a self-adjoint Sturm--Liouville problem and solving it with a finite-difference discretization on a truncated radial domain, with explicit convergence control. We analyze four representative scenarios: (i) no external potential, (ii) Cornell-type confinement, (iii) Kratzer-type interaction, and (iv) the small-oscillation regime around the minimum of a Morse potential. We present systematic trends of the low-lying levels as functions of the torsion parameter, magnetic field, and azimuthal sector, and we show that geometric couplings alone can produce effective confinement even in the absence of an external interaction.

Related papers

• 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)
• Planar Dirac equation with radial contact potentials [0.0]
  We investigate the most general time-independent contact potential supported on a circumference.<n>The problem is effectively reduced to a one-dimensional one (the radial)<n>We then investigate the bound and scattering solutions for several choices of the physical parameters.
  arXiv  Detail & Related papers  (2025-11-10T15:10:26Z)
• Non-relativistic Quantum Mechanics on a Twisted Cylindrical Surface [0.0]
  Twisted cylindrical tubes are important model systems for nanostructures, heterostructures, and curved quantum devices.<n>In this work, we investigate the quantum behavior of an electron confined to a twisted cylindrical surface.
  arXiv  Detail & Related papers  (2025-11-06T13:57:24Z)
• Parametric resonant enhancement of motional entanglement under optimal control: an analytical study [45.88028371034407]
  We study theoretically continuous-variable entanglement between the motional degrees of freedom of optically trapped massive particles coupled via the Coulomb interaction.<n>We perform a detailed analysis of the parametric resonance induced by temporal modulation of the coupling strength, based on the system's coupled nonlinear, nonhomogeneous dynamical equations.<n>We demonstrate that a stationary nonequilibrium entangled state is realized as a result of the competition between parametric gain and decoherence.
  arXiv  Detail & Related papers  (2025-10-21T09:01:19Z)
• Geometry-induced Coulomb-like potential in helically twisted quantum systems [0.0]
  We investigate the Schr"odinger equation in a three-dimensional helically twisted space characterized by a non-trivial torsion parameter.<n>The intrinsic coupling between angular and longitudinal momenta induced by the torsion gives rise to an attractive Coulomb-like potential term.<n>The interplay between the torsion parameter and the effective Coulomb-like interaction is analyzed in detail, showing how geometric deformation generates novel quantum confinement mechanisms.
  arXiv  Detail & Related papers  (2025-07-06T23:20:26Z)
• Spiral dislocation as a tunable geometric parameter for optical responses in quantum rings [0.562479170374811]
  We investigate the optical and quantum mechanical properties of a charged spinless particle confined in a two-dimensional quantum ring.<n>The dislocation is modeled by a torsion-induced metric that alters the spatial geometry without introducing curvature.<n>The geometric deformation leads to an energy-dependent effective potential, enabling a tunable control over the bound-state spectrum.
  arXiv  Detail & Related papers  (2025-06-29T15:52:36Z)
• Decoupling of External and Internal Dynamics in Driven Two-level Systems [49.96265870315999]
  We show how a laser driven two-level system can be decoupled into a set of equations acting only on the external degrees of freedom for each state.<n>We give a way of characterizing the solvability of this family of problems by appealing to a classical oscillator with time-dependent damping.<n>We show that chirping of the driving fields phase emerges naturally as a means of compensating the Ehrenfest/mean-value part of the detuning operator's dynamics.
  arXiv  Detail & Related papers  (2024-06-03T16:42:28Z)
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $λ\!φ^4$ model [44.99833362998488]
  A quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field. We show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs.
  arXiv  Detail & Related papers  (2023-05-10T12:59:07Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Dispersive readout of molecular spin qudits [68.8204255655161]
  We study the physics of a magnetic molecule described by a "giant" spin with multiple $d > 2$ spin states. We derive an expression for the output modes in the dispersive regime of operation. We find that the measurement of the cavity transmission allows to uniquely determine the spin state of the qudits.
  arXiv  Detail & Related papers  (2021-09-29T18:00:09Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Atomic self-organization emerging from tunable quadrature coupling [5.624813092014403]
  We propose a novel scheme to couple two density-wave degrees of freedom of a BEC to two quadratures of the cavity field. We unravel a dynamically unstable state induced by the cavity dissipation. Our work enriches the quantum simulation toolbox in the cavity-quantum-electrodynamics system.
  arXiv  Detail & Related papers  (2020-04-07T13:25:44Z)

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.