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arxiv: 1906.11000 · v1 · pith:SKJ2TV2Enew · submitted 2019-06-26 · 🪐 quant-ph · gr-qc

Aharonov-Bohm-type effect in the background of a distortion of a vertical line into a vertical spiral

W. C. F. da Silva , K. Bakke This is my paper

Pith reviewed 2026-05-25 15:49 UTC · model grok-4.3

classification 🪐 quant-ph gr-qc
keywords Aharonov-Bohm effecttopological defectspiral distortionbound statesquantum particlerotation effectsangular momentum shiftelastic medium
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0 comments X

The pith

A distortion turning a vertical line into a vertical spiral acts as a topological defect that shifts the angular momentum quantum number of a confined quantum particle, producing an Aharonov-Bohm effect for bound states.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how a specific topological defect in an elastic medium affects a spinless quantum particle confined to a cylindrical box. It shows that the defect causes a shift in the allowed angular momentum values, which in turn modifies the energy levels in a way analogous to the Aharonov-Bohm effect. This analogue persists even when the system is rotating, and rotation introduces an additional coupling between the particle's angular momentum and the frame's angular velocity. A sympathetic reader would care because this extends the Aharonov-Bohm phenomenon to bound states in a curved or defective geometry without needing magnetic fields.

Core claim

The topological defect corresponding to the distortion of a vertical line into a vertical spiral yields a shift in the angular momentum quantum number, producing an analogue of the Aharonov-Bohm effect for bound states in the confined system; the effect persists under rotation with an additional coupling between angular momentum and angular velocity.

What carries the argument

The topological defect from the line-to-spiral distortion, which modifies the quantum wave equation through a shift in the angular momentum quantum number.

If this is right

  • The allowed energies of the bound states are shifted due to the defect.
  • The Aharonov-Bohm analogue holds for the rotating case as well.
  • Rotation couples the angular momentum to the angular velocity of the frame.
  • The effect is independent of magnetic fields and arises purely from the topology.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar defects might produce measurable effects in condensed matter systems with spiral dislocations.
  • Experiments could involve particles in media with engineered spiral defects to observe the energy shifts.
  • This suggests that other line distortions could lead to different quantum phase effects.

Load-bearing premise

The distortion is modeled solely as causing a topological shift in the angular momentum without introducing additional potential terms or altering the metric in other ways.

What would settle it

Calculating or measuring the energy spectrum of a particle confined in a cylindrical region with an embedded spiral distortion and checking if the angular momentum labels are shifted by a constant amount independent of other parameters.

read the original abstract

It is analysed Aharonov-Bohm-type effects when a spinless quantum particle is in an elastic medium with the distortion of a vertical line into a vertical spiral. By confining the spinless particle to a cylindrical box, the analogue of the Aharonov-Bohm effect for bound states is observed due to influence of the topological defect on the allowed energies of the system. It corresponds to the shift in the angular momentum quantum number yielded by the effects of the topology of the distortion of a vertical line into a vertical spiral. In addition, it is analysed the effects of rotation. It is shown that the Aharonov-Bohm effect for bound states exists. Besides, there is an analogue of the coupling between the angular momentum and angular velocity of the rotating frame.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript analyzes Aharonov-Bohm-type effects for a spinless quantum particle in an elastic medium featuring the distortion of a vertical line into a vertical spiral. Confining the particle to a cylindrical box, the paper claims an analogue of the Aharonov-Bohm effect for bound states arising from a topological shift in the angular momentum quantum number. The analysis is extended to a rotating frame, where the bound-state AB analogue persists together with a coupling between angular momentum and angular velocity.

Significance. If the central claim of a constant angular-momentum shift holds, the work would furnish a concrete topological analogue of the AB effect for bound states in a defect background, extending earlier studies of line defects in elastic media and adding a rotating-frame extension. No machine-checked proofs or parameter-free derivations are present, but the setup is in principle falsifiable via the predicted energy spectrum.

major comments (1)
  1. [the section deriving the energy eigenvalues for the non-rotating cylindrical confinement] The metric for the vertical-spiral distortion is the standard screw-dislocation line element ds² = dr² + r² dϕ² + (dz + β dϕ)². Separation of the Schrödinger (or Laplace-Beltrami) equation on this background produces an effective angular-momentum quantum number m − β k_z rather than a constant offset m + α. Because the cylindrical confinement quantizes k_z, the radial spectrum mixes radial and axial quantum numbers and is not equivalent to the pure m-shift required for a direct AB analogue. This issue is load-bearing for the central claim and is not resolved by the stated treatment of the defect.
minor comments (1)
  1. Notation for the defect parameter β and the range of the cylindrical confinement (height, radius) should be stated explicitly at first use.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and insightful comments on our manuscript. We provide a point-by-point response to the major comment below, and we are prepared to revise the manuscript accordingly to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [the section deriving the energy eigenvalues for the non-rotating cylindrical confinement] The metric for the vertical-spiral distortion is the standard screw-dislocation line element ds² = dr² + r² dϕ² + (dz + β dϕ)². Separation of the Schrödinger (or Laplace-Beltrami) equation on this background produces an effective angular-momentum quantum number m − β k_z rather than a constant offset m + α. Because the cylindrical confinement quantizes k_z, the radial spectrum mixes radial and axial quantum numbers and is not equivalent to the pure m-shift required for a direct AB analogue. This issue is load-bearing for the central claim and is not resolved by the stated treatment of the defect.

    Authors: We agree that the effective quantum number is m - β k_z, with k_z quantized due to the finite length of the cylinder. This leads to an effective shift that depends on the axial quantum number. However, this does not invalidate the AB analogue; rather, it shows that the topological defect induces a k_z-dependent phase shift analogous to an AB flux that couples to the axial momentum. In the limit of large cylinder length or for fixed k_z, it reduces to a constant shift per mode. The central claim is that the topology affects the bound state spectrum via this mechanism, which is still a valid analogue, albeit with additional structure due to the screw dislocation. We will add a discussion clarifying this point and perhaps include a comparison to the standard AB case in the revised version. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation follows from metric geometry

full rationale

The paper obtains the angular-momentum shift and the resulting bound-state spectrum by substituting the given screw-dislocation line element into the Laplace-Beltrami operator (or Schrödinger equation) inside a cylindrical box and separating variables. The effective replacement m → m + β k_z (or equivalent) is an algebraic consequence of the cross term in the metric, not a quantity defined in terms of the final spectrum or fitted to it. No self-citation is invoked as a uniqueness theorem, no parameter is fitted on a subset and then relabeled a prediction, and the central claim is not presupposed by the inputs. The derivation is therefore self-contained from the stated geometry to the energy levels.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the spiral distortion can be treated as a topological defect inducing a specific angular momentum shift in the Schrödinger equation for a confined particle; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption The distortion of a vertical line into a vertical spiral acts as a topological defect that shifts the angular momentum quantum number in the confined particle's energy spectrum.
    This modeling choice is required for the Aharonov-Bohm analogue to appear and is invoked throughout the abstract description.

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Forward citations

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Reference graph

Works this paper leans on

42 extracted references · 42 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    Kleinert, Gauge fields in condensed matter, vol

    H. Kleinert, Gauge fields in condensed matter, vol. 2 , (World Scientific, Singapore, 1989)

    work page 1989

  2. [2]

    M. O. Katanaev and I. V. Volovich. Ann. Phys. (NY) 216, 1 (1992)

    work page 1992

  3. [3]

    D. L. Dexter and F. Seitz, Effects of Dislocations on Mobilities in Semiconductors , Phys. Rev. 86, 964 (1952). DOI: 10.1103/PhysRev.86.964

    work page doi:10.1103/physrev.86.964 1952

  4. [4]

    Figielski, Dislocations as electrically active centres in semiconduc tors?alf a century from the discovery, J

    T. Figielski, Dislocations as electrically active centres in semiconduc tors?alf a century from the discovery, J. Phys.: Condens. Matter 14, 12665 (2012). DOI: 10.1088/0953-8984/14/48/301

    work page doi:10.1088/0953-8984/14/48/301 2012

  5. [5]

    Jaszek, Carrier scattering by dislocations in semiconductors , J

    R. Jaszek, Carrier scattering by dislocations in semiconductors , J. Mater. Sci. Mater. Electron. 12, 1 (2001). DOI: 10.1023/A:1011228626077

    work page doi:10.1023/a:1011228626077 2001

  6. [6]

    Aurell, Torsion and electron motion in quantum dots with crystal lat tice dislocations, J

    E. Aurell, Torsion and electron motion in quantum dots with crystal lat tice dislocations, J. Phys. A: Math. Gen. 32, 571 (1999). DOI: 10.1088/0305-4470/32/4/004

    work page doi:10.1088/0305-4470/32/4/004 1999

  7. [7]

    K. C. Valanis e V. P. Panoskaltsis, Material metric, connectivity and dislocations in continu a, Acta Mech. 175, 77 (2005). DOI: 10.1007/s00707-004-0196-9. 10

    work page doi:10.1007/s00707-004-0196-9 2005

  8. [8]

    R. A. Puntigam and H. H. Soleng, Volterra Distortions, Spinning Strings, and Cosmic Defects , Class. Quantum Grav. 14, 1129 (1997). DOI: 10.1088/0264-9381/14/5/017

    work page doi:10.1088/0264-9381/14/5/017 1997

  9. [9]

    Furtado, V

    C. Furtado, V. B. Bezerra and F. Moraes, Quantum scattering by a magnetic flux screw dislocation, Phys. Lett. A 289, 160 (2001). DOI: 10.1016/S0375-9601(01)00615-6

    work page doi:10.1016/s0375-9601(01)00615-6 2001

  10. [10]

    A. L. Silva Netto, C. Chesman and C. Furtado, Influence of topology in a quantum ring , Phys. Lett. A 372, 3894 (2008). DOI: 10.1016/j.physleta.2008.02.060

    work page doi:10.1016/j.physleta.2008.02.060 2008

  11. [11]

    Dantas, C

    L. Dantas, C. Furtado and A. L. Silva Netto, Quantum ring in a rotating frame in the presence of a topological defect , Phys. Lett. A 379, 11 (2015). DOI:10.1016/j.physleta.2014.10.016

    work page doi:10.1016/j.physleta.2014.10.016 2015

  12. [12]

    Soheibi et al , Screw dislocation and external fields effects on the Kratzer p seudodot, Eur

    N. Soheibi et al , Screw dislocation and external fields effects on the Kratzer p seudodot, Eur. Phys. J. B 90, 212 (2017). DOI: 10.1140/epjb/e2017-80468-9

    work page doi:10.1140/epjb/e2017-80468-9 2017

  13. [14]

    Bakke and C

    K. Bakke and C. Furtado, One-qubit quantum gates associated with topological defec ts in solids , Quantum Inf. Process 12, 119 (2013). DOI: /10.1016/j.physleta.2015.06.035

    work page doi:10.1016/j.physleta.2015.06.035 2013

  14. [15]

    G. de A. Marques et al , Landau levels in the presence of topological defects , J. Phys. A: Math. Gen. 34, 5945 (2001). DOI:10.1088/0305-4470/34/30/306

    work page doi:10.1088/0305-4470/34/30/306 2001

  15. [16]

    Furtado and F

    C. Furtado and F. Moraes, Landau levels in the presence of a screw dislocation , Europhys. Lett. 45, 279 (1999). DOI:10.1209/epl/i1999-00159-8

    work page doi:10.1209/epl/i1999-00159-8 1999

  16. [17]

    A. L. Silva Netto and C. Furtado, Elastic Landau levels , J. Phys.: Condens. Matter 20, 125209 (2008). DOI: 10.1088/0953-8984/20/12/125209

    work page doi:10.1088/0953-8984/20/12/125209 2008

  17. [18]

    Filgueiras, M

    C. Filgueiras, M. Rojas, G. Aciole and E. O. Silva, Landau quantization, Aharonov-Bohm effect and two-dimensional pseudoharmonic quantum dot arou nd a screw dislocation , Phys. Lett. A 380, 3847 (2016). DOI: 10.1016/j.physleta.2016.09.025

    work page doi:10.1016/j.physleta.2016.09.025 2016

  18. [19]

    Bakke and C

    K. Bakke and C. Furtado, Abelian geometric phase due to the presence of an edge disloc ation, Phys. Rev. A 87, 012130 (2013). DOI: 10.1103/PhysRevA.87.012130

    work page doi:10.1103/physreva.87.012130 2013

  19. [20]

    A. V. D. M. Maia and K. Bakke, Harmonic oscillator in an elastic medium with a spiral dislocation, Physica B 531, 213 (2018). DOI: 10.1016/j.physb.2017.12.045

    work page doi:10.1016/j.physb.2017.12.045 2018

  20. [21]

    Aharonov and D

    Y. Aharonov and D. Bohm, Significance of Electromagnetic Potentials in the Quantum Th eory, Phys. Rev. 115, 485 (1959). DOI: 10.1103/PhysRev.115.485

    work page doi:10.1103/physrev.115.485 1959

  21. [22]

    Peshkin and A

    M. Peshkin and A. Tonomura, The Aharonov-Bohm Effect (Springer-Verlag, in: Lecture Notes in Physics, Vol. 340, Berlin, 1989). 11

    work page 1989

  22. [23]

    V. B. Bezerra, Global effects due to a chiral cone , J. Math. Phys. 38, 2553 (1997). DOI: 10.1063/1.531995

    work page doi:10.1063/1.531995 1997

  23. [24]

    J. de S. Carvalho et al , Eur. Phys. J. C 57, 817 (2008)

    work page 2008

  24. [25]

    Carvalho, A

    J. Carvalho, A. M. de M. Carvalho, E. Cavalcante and C. Fu rtado, Eur. Phys. J. C 76, 365 (2016)

    work page 2016

  25. [26]

    Hosseinpour, H

    M. Hosseinpour, H. Hassanabadi and M. de Montigny, Eur. Phys. J. C 79, 311 (2019)

    work page 2019

  26. [27]

    G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, sixth edition (Elsevier Academic Press, New York, 2005)

    work page 2005

  27. [28]

    Abramowitz and I

    M. Abramowitz and I. A. Stegum, Handbook of mathematical functions (Dover Publications Inc., New York, 1965)

    work page 1965

  28. [29]

    N. W. McLachlan, Theory and applications of Mathieu functions (Clarendon Press, Oxford, UK, 1947)

    work page 1947

  29. [30]

    H. J. W. M¨ uler-Kirsten, Introduction to quantum mechanics: Schr¨ odinger equation a nd path integral (Word Scientific, Singapure, 2006)

    work page 2006

  30. [31]

    D. J. Griffiths, Introduction to quantum mechanics, Second Edition , (Prentice Hall, 2004)

    work page 2004

  31. [32]

    L. D. Landau and E. M. Lifshitz, Mechanics, third edition (Pergamon Press, Oxford, 1980)

    work page 1980

  32. [33]

    L. D. Landau and E. M. Lifshitz, Statistical Physics - Part 1, 3rd. ed. (Pergamon Press, New York, 1980)

    work page 1980

  33. [34]

    Quantum Mechanics in a Rotating Frame

    J. Anandan and J. Suzuki in Relativity in Rotating Frames, Relativistic Physics in Rot at- ing Reference Frame, Edited by G. Rizzi and M. L. Ruggiero (Kluwer Academic Publi shers, Dordrecht, 2004) p 361-369; arXiv:quant-ph/0305081

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  34. [35]

    Tsai and D

    C.-H. Tsai and D. Neilson, New quantum interference effect in rotating systems , Phys. Rev. A 37, 619 (1988). DOI: 10.1103/PhysRevA.37.619

    work page doi:10.1103/physreva.37.619 1988

  35. [36]

    I. C. Fonseca and K. Bakke, Rotating effects on the Landau quantization for an atom with a magnetic quadrupole moment , J. Chem. Phys. 144, 014308 (2016). DOI: 10.1063/1.4939525

    work page doi:10.1063/1.4939525 2016

  36. [37]

    I. C. Fonseca and K. Bakke, Some aspects of the interaction of a magnetic quadrupole mo- ment with an electric field in a rotating frame , J. Math. Phys. 58, 102103 (2017). DOI: 10.1063/1.5001564

    work page doi:10.1063/1.5001564 2017

  37. [38]

    A. B. Oliveira and K. Bakke, Effects on a Landau-type system for a neutral particle with no permanent electric dipole moment subject to the Kratzer pot ential in a rotating frame , Proc. R. Soc. A 472, 20150858 (2016). DOI: 10.1098/rspa.2015.0858. 12

    work page doi:10.1098/rspa.2015.0858 2016

  38. [39]

    Y. M. Cho, D. H. Park, and G. G. Han, Gravitational anyon , Phys. Rev. D 43, 1421 (1991). DOI: 10.1103/PhysRevD.43.1421

    work page doi:10.1103/physrevd.43.1421 1991

  39. [40]

    Jensen and J

    B. Jensen and J. Kucera, On a gravitational Aharonov-Bohm effect , J. Math. Phys. 34, 4975 (1993). DOI: 10.1063/1.530335

    work page doi:10.1063/1.530335 1993

  40. [41]

    L. A. Page, Effect of Earth’s Rotation in Neutron Interferometry , Phys. Rev. Lett. 35, 543 (1975). DOI: 10.1103/PhysRevLett.35.543

    work page doi:10.1103/physrevlett.35.543 1975

  41. [42]

    S. A. Werner, J.-L. Staudenmann and R. Colella, Effect of Earth’s Rotation on the Quantum Mechanical Phase of the Neutron , Phys. Rev. Lett. 42, 1103 (1979). DOI: 10.1103/Phys- RevLett.42.1103

    work page doi:10.1103/phys- 1979

  42. [43]

    F. W. Hehl and W.-T. Ni, Inertial effects of a Dirac particle , Phys. Rev. D 42, 2045 (1990). DOI: 10.1103/PhysRevD.42.2045. 13

    work page doi:10.1103/physrevd.42.2045 2045