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Cited by 2Dust and Plasma Wave PhenomenaQuantum and Classical ElectrodynamicsNoncommutative and Quantum Gravity Theories

Study Zitterbewegung effect in a quasi one-dimensional relativistic quantum plasma by Dirac-Heisenberg-Wigner formalization

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Nematizadeh Juneghani, Safura, Bagheri, Mehran, Shokri, Babak·2021·Journal of Cosmology and Astroparticle Physics
DOI 10.1088/1475-7516/2021/09/002
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Abstract

The trembling motion of moving electrons, known as Zitterbewegung effect, in quasi-one-dimensional relativistic quantum plasma is theoretically investigated by using Dirac equation together with the Wigner distribution function. The relativistic Wigner matrix is used to calculate the mean values of the position and velocity operators for a Dirac gas of electrons. It is found that the oscillatory behavior of measurable quantities could be associated with the Zitterbewegung effect which manifests itself as a damping interference pattern stemming from mixing the positive and negative dispersion modes of Dirac particles.

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  • Zitterbewegung is a signature of the interference of particle and antiparticle states.

    “that is a signature of the interference of particle and antiparticle states”

    From Photonic cellular automaton simulation of relativistic quantum fields: Observation of <i>Zitterbewegung</i> (2024) · cites this paper as [78]

    The paper’s concluding discussion (page unavailable) describes Zitterbewegung as an interference pattern arising from mixing positive and negative dispersion branches, and its discussion of the oscillations attributes them to mixed components. It does not identify those branches as particle and antiparticle states, so that specific characterization is not established by our copy. (LLM, conf=0.78)

    Experimental — accuracy not yet measured

  • Zitterbewegung is the oscillation of the expected value of the position operator X.

    “namely the oscillation of the expected value of the position operator X [32-34, 77-91].”

    From Photonic cellular automaton simulation of relativistic quantum fields: Observation of <i>Zitterbewegung</i> (2024) · cites this paper as [78]

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Research works printed but not linked: 59

  1. Y. Shi, N.J. Fisch and H. Qin, Effective action approach to wave propagation in scalar QED plasmas, Phys. Rev. A 94 (2016) 012124 [arXiv:1603.03967] [INSPIRE]. · DOI
  2. M. Bonitz, A. Filinov, J. Bning and J.W. Dufty, Introduction to Quantum Plasmas, Springer-Verlag, Berlin (2010).
  3. S. Balberg and S.L. Shapiro, The Properties of Condensed Matter in White Dwarfs and Neutron Stars, Academic Press, London (2000). JCAP09(2021)002
  4. P.K. Shukla and B. Eliasson, Nonlinear interactions between electromagnetic waves and electron plasma oscillations in quantum plasmas, Phys. Rev. Lett. 99 (2007) 096401. · DOI
  5. S.A. Khan, Low frequency collective modes in dense relativistic-degenerate strongly coupled plasma, Astrophys. Space Sci. 340 (2012) 71. · DOI
  6. S.A. Khan, Coupled modes in magnetized dense plasma with relativistic-degenerate electrons, Phys. Plasmas 19 (2012) 014506. · DOI
  7. M. Jamil, A. Rasheed, C. Rozina, W.M. Moslem and M. Salimullah, Beam driven upper-hybrid-wave instability in quantized semiconductor plasmas, Phys. Plasmas 21 (2014) 020704. · DOI
  8. F. Haas, A magnetohydrodynamic model for quantum plasmas, Phys. Plasmas 12 (2005) 062117. · DOI
  9. P.K. Shukla and B. Eliasson, Colloquium: Nonlinear collective interactions in quantum plasmas with degenerate electron fluids, Rev. Mod. Phys. 83 (2011) 885. · DOI · Paper page
  10. P.K. Shukla, D.A. Mendis and S.I. Krasheninnikov, Wave propagation in the magnetized cores of white dwarf stars with ultra-relativistic degenerate electrons, J. Plasma Phys. 77 (2011) 571. · DOI
  11. P. Sharma, Modified dispersion properties of lower hybrid wave with exchange correlation potential in ultra-relativistic degenerate plasma, Phys. Lett. A 382 (2018) 1796. · DOI
  12. A.A. Mamun, P.K. Shukla and D.A. Mendis, Electromagnetic waves in self-gravitating, strongly coupled magnetized degenerate plasma, J. Plasma Phys. 78 (2012) 143. · DOI
  13. S. Chandrasekhar, The density of white dwarf stars, Phil. Mag. 11 (1931) 592. · DOI
  14. S. Chandrasekhar, The maximum mass of ideal white dwarfs, Astrophys. J. 74 (1931) 81. · DOI
  15. G. Sarri et al., Generation of neutral and high-density electron-positron pair plasmas in the laboratory, Nat. Commun. 6 (2015) 6747. · DOI
  16. A. Curtis et al., Micro-scale fusion in dense relativistic nanowire array plasmas, Nat. Commun. 9 (2018) 1077. · DOI
  17. M.D. Bustamante and S.A. Hojman, Lagrangian structures, integrability and chaos for 3-D dynamical equations, J. Phys. A 36 (2003) 151 [hep-th/0208189] [INSPIRE]. · DOI
  18. R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt and C.F. Roos, Quantum simulation of the dirac equation, Nature 463 (2010) 68. · DOI · Paper page
  19. L.J. Garay, J.R. Anglin, J.I. Cirac and P. Zoller, Black holes in Bose-Einstein condensates, Phys. Rev. Lett. 85 (2000) 4643 [gr-qc/0002015] [INSPIRE]. · DOI
  20. T.M. Rusin and W. Zawadzki, Zitterbewegung of electrons in graphene in a magnetic field, Phys. Rev. B 78 (2008) 125419. · DOI · Paper page
  21. A. Bermudez, M.A. Martin-Delgado and E. Solano, Exact mapping of the 2 + 1 dirac oscillator onto the jaynes-cummings model: Ion-trap experimental proposal, Phys. Rev. A 76 (2007) 041801. · DOI · Paper page
  22. E.S. Sedov, Y.G. Rubo and A.V. Kavokin, Zitterbewegung of exciton-polaritons, Phys. Rev. B 97 (2018) 245312. · DOI · Paper page
  23. Y. Wang et al., Acoustic Zitterbewegung in ordinary sonic crystals: A general classical description, Phys. Lett. A 374 (2010) 4933. · DOI · Paper page
  24. J. Schliemann, D. Loss and R.M. Westervelt, Zitterbewegungof electrons and holes in III-V semiconductor quantum wells, Phys. Rev. B 73 (2006) 085323. JCAP09(2021)002 · DOI · Paper page
  25. J.Y. Vaishnav and C.W. Clark, Observing Zitterbewegung with Ultracold Atoms, Phys. Rev. Lett. 100 (2008) 153002 [arXiv:0711.3270] [INSPIRE]. · DOI · Paper page
  26. J. Larson and S. Levin, Effective abelian and non-abelian gauge potentials in cavity QED, Phys. Rev. Lett. 103 (2009) 013602. · DOI
  27. G. Juzeliūnas, J. Ruseckas, M. Lindberg, L. Santos and P. Öhberg, Quasirelativistic behavior of cold atoms in light fields, Phys. Rev. A 77 (2008) 011802. · DOI · Paper page
  28. M. Merkl, F.E. Zimmer, G. Juzeliūnas and P. Öhberg, Atomic Zitterbewegung, Europhys. Lett. 83 (2008) 54002. · DOI · Paper page
  29. Q. Zhang, J. Gong and C.H. Oh, Driven Dirac-like equation via mirror oscillation: Controlled cold-atom Zitterbewegung, Phys. Rev. A 81 (2010) 023608. · DOI · Paper page
  30. W. Zawadzki and T.M. Rusin, Nature of electron Zitterbewegung in crystalline solids, Phys. Lett. A 374 (2010) 3533. · DOI · Paper page
  31. M. Trushin and J. Schliemann, Spin dynamics in rolled-up two-dimensional electron gases, New J. Phys. 9 (2007) 346. · DOI
  32. T. Biswas and T.K. Ghosh, Zitterbewegung of electrons in quantum wells and dots in the presence of an in-plane magnetic field, J. Phys. Condens. Matter 24 (2012) 185304. · DOI
  33. V. Achilleos, D.J. Frantzeskakis and P.G. Kevrekidis, Beating dark-dark solitons and Zitterbewegung in spin-orbit-coupled bose-einstein condensates, Phys. Rev. A 89 (2014) 033636. · DOI
  34. H. Deng, F. Ye, B.A. Malomed, X. Chen and N.C. Panoiu, Optically and electrically tunable dirac points and Zitterbewegung in graphene-based photonic superlattices, Phys. Rev. B 91 (2015) 201402. · DOI
  35. Q. Zhang and J. Gong, Perfect Zitterbewegung oscillations in the Kitaev chain system, Phys. Rev. A 93 (2016) 032117. · DOI
  36. A.V. Zhukov, R. Bouffanais, N.N. Konobeeva and M.B. Belonenko, Zitterbewegung near a Schwarzschild-type black hole, Mod. Phys. Lett. A 31 (2016) 1650168. · DOI
  37. A. Chaudhuri, T.J. Lerotholi, D.C. Jackson, D.P. Woodruff and R.G. Jones, (2 √ 3 × 3)rect. phase of alkylthiolate self-assembled monolayers on Au(111): A symmetry-constrained structural solution, Phys. Rev. B 79 (2009) 195439. · DOI
  38. F.A. Asenjo, J. Zamanian, M. Marklund, G. Brodin and P. Johansson, Semi-relativistic effects in spin-1/2 quantum plasmas, New J. Phys. 14 (2012) 073042. · DOI · Paper page
  39. Y. Hinschberger, G. Manfredi and P.-A. Hervieux, Coherent spin-light-induced mechanisms in the semirelativistic limit of the self-consistent dirac-maxwell equations, Phys. Rev. A 93 (2016) 042117. · DOI
  40. S. Varró and J. Javanainen, Gauge-invariant relativistic wigner functions, J. Opt. B 5 (2003) S402. · DOI
  41. A.G. Campos, R. Cabrera, D.I. Bondar and H.A. Rabitz, Violation of Hudson's theorem in relativistic quantum mechanics, Phys. Rev. A 90 (2014) 034102 [arXiv:1402.1768] [INSPIRE]. JCAP09(2021)002 · DOI
  42. I. Bialynicki-Birula, P. Gornicki and J. Rafelski, Phase space structure of the Dirac vacuum, Phys. Rev. D 44 (1991) 1825 [INSPIRE]. · DOI · Paper page
  43. R. Hakim and J. Heyvaerts, Covariant wigner function approach for relativistic quantum plasmas, Phys. Rev. A 18 (1978) 1250. · DOI
  44. V. Guidi, A. Mazzolari, D.D. Salvador and L. Bacci, Deflection of MeV protons by an unbent half-wavelength silicon crystal, Phys. Rev. Lett. 108 (2012) 014801. · DOI
  45. W. Zawadzki and T.M. Rusin, Zitterbewegung (trembling motion) of electrons in narrow-gap semiconductors, J. Phys. Condens. Matter 20 (2008) 454208. · DOI · Paper page
  46. R. Winkler, U. Zülicke and J. Bolte, Oscillatory multiband dynamics of free particles: The ubiquity of Zitterbewegung effects, Phys. Rev. B 75 (2007) 205314. · DOI · Paper page
  47. Y.A. Bychkov and E.I. Rashba, Oscillatory effects and the magnetic susceptibility of carriers in inversion layers, J. Phys. C 17 (1984) 6039. · DOI · Paper page
  48. W. Zawadzki and T.M. Rusin, Zitterbewegung (trembling motion) of electrons in semiconductors: a review, J. Phys. Condens. Matter 23 (2011) 143201. · DOI · Paper page
  49. T.M. Rusin and W. Zawadzki, Transient Zitterbewegung of charge carriers in mono-and bilayer graphene, and carbon nanotubes, Phys. Rev. B 76 (2007) 195439. · DOI · Paper page
  50. A.A. Deriglazov, Spinning-particle model for the Dirac equation and the relativistic Zitterbewegung, Phys. Lett. A 376 (2012) 309 [arXiv:1106.5228] [INSPIRE]. · DOI · Paper page
  51. S.M. Barnett, Optical dirac equation, New J. Phys. 16 (2014) 093008. · DOI · Paper page
  52. F. Haas, Quantum Plasmas, An Hydrodynamic Approach. Springer, NewYork (2011).
  53. B. Shokri and A.A. Rukhadze, Electrodaynamics of conductiong dispersive media, Springer, Berlin (2019).
  54. O.V. Bogdanov and Y.L. Pivovarov, Formation of spectral characteristics of channeling radiation from 800-MEV to 2000-MeV electrons and positrons in a thin silicon crystal, Nucl. Instrum. Meth. B 266 (2008) 3852 [INSPIRE]. · DOI
  55. H. Barber, Effective mass and intrinsic concentration in silicon, Solid State Electron. 10 (1967) 1039. · DOI
  56. R. Hakim, Introduction to Relativistic Statistical Mechanics: Classical and Quantum, World Scientific Pub. Co. Inc. (2011).
  57. Z. Haba, The Four-Dimensional Position Operator Coherent States and Representations of the Conformal Group, Nuovo Cim. A A 30 (1975) 567 [INSPIRE]. · DOI
  58. S. Choi, N.Y. Yao and M.D. Lukin, Dynamical engineering of interactions in qudit ensembles, Phys. Rev. Lett. 119 (2017) 183603. · DOI
  59. R.W. Spekkens, Negativity and contextuality are equivalent notions of nonclassicality, Phys. Rev. Lett. 101 (2008) 020401. · DOI

Cited by

Sorted by citations

Authors
Nematizadeh Juneghani, S., Bagheri, M., & Shokri, B.
Affiliations
Shahid Beheshti University (IR)
Venue
Journal of Cosmology and Astroparticle Physics
Publisher
IOP Publishing
Published
2021-09-01
Volume
2021
Issue
09
Pages
002
ISSN
  • 1475-7508 (ISSN-L)
  • 1475-7516
DOI
10.1088/1475-7516/2021/09/002
OpenAlex
W3004613345
Cited by
2
References
5
Citations by year
2024: 1 · 2022: 1
FWCI
0.22
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of Cosmology and Astroparticle Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Dust and Plasma Wave Phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
Keywords
Zitterbewegung, Dirac equation, Wigner function, oscillations

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