Advertisement

Quantum Time Entanglement of Electrons

  • J.H. McGuire
  • A.L. Godunov
Part of the Physics of Atoms and Molecules book series (PAMO)

Abstract

Correlation is often significant in electron scattering from atoms, nuclei and bulk matter. Mathematically, as well as conceptually, correlation and entanglement are defined in the same way. Both correlation and entanglement connote mixing. Both are described as a deviation from a product (uncorrelated) form. In quantum optics the term entanglement is used to describe the spatial mixing of states of a system by external electromagnetic fields. In static systems correlation arises from interparticle fields that mix wavefunctions. Correlation dynamics, intrinsic in scattering from few and many body systems, adds the dimension of time to the basic conceptual framework. Time correlation, described here, mixes the time evolution of the particles. This time entanglement, which is non-local, requires both spatial correlation and quantum time ordering.

Keywords

Time Correlation Total Cross Section Evolution Operator Asymptotic Condition Interaction Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    H. Knudsen and J. F. Reading, Phys. Reports 212, 107 (1992).CrossRefADSGoogle Scholar
  2. [2]
    N. Stolterfoht, Phys. Rev. A 48, 2980 (1993).CrossRefADSGoogle Scholar
  3. [3]
    J. H. McGuire, Electron Correlation Dynamics in Atomic Collisions, (Cambridge University Press, 1997).Google Scholar
  4. [4]
    J. H. McGuire at al., submitted to Phys. Rev. A. (2002).Google Scholar
  5. [5]
    A.L. Godunov et al., J. Phys. B. 34, 5055 (2001).CrossRefADSGoogle Scholar
  6. [6]
    A. L. Godunov and J. H. McGuire, J. Phys. B. 34, L223 (2001).CrossRefADSGoogle Scholar
  7. [7]
    J. H. McGuire et al., Phys. Rev. A63, 052706-1 (2001).ADSGoogle Scholar
  8. [8]
    H. Merabet et al., Phys. Rev A65, 010703(R) (2002).ADSGoogle Scholar
  9. [9]
    M. L. Goldberger and K. Watson, Collision Theory, (Wiley, NY, 1964), p. 48.MATHGoogle Scholar
  10. [10]
    W. Magnus, Commun. Pure and Applied Math, 7, 971 (1954). In some applications of the Magnus expansion, the leading term can give an infinite total cross section. In our application, the total cross sections are sensibly finite.MathSciNetGoogle Scholar
  11. [11]
    J.H. McGuire, Phys. Rev. A 36, 1114 (1987).CrossRefADSGoogle Scholar
  12. [12]
    R. Olson and A. Salop, Phys. Rev. A. 16, 531 (1977).CrossRefADSGoogle Scholar
  13. [13]
    G. B. Arfkin and G. B. Weber, Mathematical Methods for Physicists, (Academic Press, 1995), Problems 1.15.14.Google Scholar
  14. [14]
    J. R. Taylor, Scattering Theory, (John Wiley and Sons, NY, 1972).Google Scholar
  15. [15]
    J.H. McGuire et al., Phys. Rev. A26, 1109 (1982). Obtaining Γ from η is in general non-trivial.ADSGoogle Scholar
  16. [16]
    R. Balescu, Equilibrium and Non-equilibrium Statistical Mechanics, John Wiley, NY, 1975) Chap. 21, Sec. 1.Google Scholar
  17. [17]
    L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995).Google Scholar
  18. [18]
    H. Z. Zhao et al., Phys. Rev. Lett. 79, 613 (1997).CrossRefADSGoogle Scholar
  19. [19]
    A.L. Godunov et al., J. Phys B. 30, 5451 (1997).CrossRefADSGoogle Scholar
  20. [20]
    A.L. Godunov et al., J. Phys B. 30, 3227 (1997).CrossRefADSGoogle Scholar
  21. [21]
    D. H. Madison et al., J. Phys. B 24, 3861 (1991).CrossRefADSGoogle Scholar
  22. [22]
    T. Kirchner et al., Phys. Rev A 62, 042704 (2000).CrossRefADSGoogle Scholar
  23. [23]
    P. J. Marchalant et al., J. Phys. B 33, L749 (2000).CrossRefADSGoogle Scholar
  24. [24]
    Y. Fang and K. Bartschat, J. Phys. B 34, L19–25 (2001).CrossRefADSGoogle Scholar
  25. [25]
    A.L. Goodman and T. Jin, Phys. Rev. C 54, 1165 (1996).CrossRefADSGoogle Scholar
  26. [26]
    D. H. Madison, private communication.Google Scholar
  27. [28]
    H. Goldstein, Classical Mechanics, Addison-Wesley, Reading, Mass. (1959) Sec. 7-5.Google Scholar
  28. [29]
    A. Sommerfeld, Optics, (Academic Press, NY, 1955), p. 355.Google Scholar
  29. [30]
    A. Messiah, Quantum Mechanics, (Wiley, NY, 1961), p. 41 (action), p. 60 (time propagation).Google Scholar
  30. [31]
    Rubin H. Landau, Quantum Mechanics II, (Wiley Interscience, NY, 2nd Edition, 1996).MATHGoogle Scholar
  31. [32]
    H. Huang and J. H. Eberly, J. Mod. Optics 5, 915 (1993).ADSCrossRefGoogle Scholar
  32. [33]
    W. Kohn, Review of Modern Physics 71 1253, (1999).CrossRefADSGoogle Scholar
  33. [34]
    F. H. M. Faisal, Theory of Multiphoton Processes, (Plenum Press, NY) (1987).Google Scholar
  34. [35]
    L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms, (Dover, NY, 1987), Chap. 2.Google Scholar
  35. [36]
    R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics (Oxford University Press, NY, 1974).Google Scholar
  36. [37]
    C. H. Bennett et al, Quantum information science, Report of the NSF Workshop in Arlington, VA, Oct. 28–29, 1999.Google Scholar
  37. [38]
    M. Macucci et al. Nanotechnology 12, 136 (2001).CrossRefADSGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers, New York 2005

Authors and Affiliations

  • J.H. McGuire
    • 1
  • A.L. Godunov
    • 2
  1. 1.Tulane UniversityNew OrleansUSA
  2. 2.Old Dominion UniversityNorfolkUSA

Personalised recommendations