Advertisement

Edge states of a three dimensional kicked rotor

  • Alexandra BakmanEmail author
  • Hagar Veksler
  • Shmuel Fishman
Regular Article
  • 13 Downloads

Abstract

Edge localization is a fascinating quantum phenomenon. In this paper, the underlying mechanism generating it is presented analytically and verified numerically for a weakly kicked three-dimensional rotor. We expand the eigenstates of the one-kick propagator of the kicked rotor in the basis of the free rotor eigenstates, which are defined by the quantum number of angular momentum. Since this quantum number must be non-negative, there is an edge near zero angular momentum, and an edge state is created. Analogy to tight binding model in solid state physics is used.

Graphical abstract

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    A.P. Vinogradov, A.V. Dorofeenko, A.M. Merzlikin, A.A. Lisyansky, Physics – Uspekhi 53, 243 (2010) ADSCrossRefGoogle Scholar
  2. 2.
    R.D. Meade, K.D. Brommer, A.M. Rappe, J.D. Joannopoulos, Phys. Rev. B 44, 19 (1991) Google Scholar
  3. 3.
    V. Podzorov, E. Menard, A. Borissov, V. Kiryukhin, J.A. Rogers, M.E. Gershenson, Phys. Rev. Lett. 93, 8 (2004) CrossRefGoogle Scholar
  4. 4.
    H. Lin, R.S. Markiewicz, L.A. Wray, L. Fu, M.Z. Hasan, A. Bansil, Phys. Rev. Lett. 105, 036404 (2010) ADSCrossRefGoogle Scholar
  5. 5.
    J.C.Y. Teo, L. Fu, C.L. Kane, Phys. Rev. B 78, 045426 (2008) ADSCrossRefGoogle Scholar
  6. 6.
    D.X. Qu, Y.S. Hor, J. Xiong, R.J. Cava, N.P. Ong, Science 329, 821 (2010) ADSCrossRefGoogle Scholar
  7. 7.
    F. Xiu, L. He, Y. Wang, L. Cheng, L.T. Chang, M. Lang, G. Huang, X. Kou, Y. Zhou, X. Jiang, Z. Chen, J. Zou, A. Shailos, K.L. Wang, Nat. Nanotechnol. 6, 216 (2011) ADSCrossRefGoogle Scholar
  8. 8.
    R. Blümel, S. Fishman, U. Smilansky, J. Chem. Phys. 84, 2604 (1986) ADSCrossRefGoogle Scholar
  9. 9.
    J. Floß, I.Sh. Averbukh, Phys. Rev. A 86, 021401(R) (2012) ADSCrossRefGoogle Scholar
  10. 10.
    J. Floß, S. Fishman, I.Sh. Averbukh, Phys. Rev. A 88, 023426 (2013) ADSCrossRefGoogle Scholar
  11. 11.
    G. Casati, B. Chirikov, Quantum Chaos: Between Order and Disorder (Cambridge University Press, 1995) Google Scholar
  12. 12.
    J. Gong, P. Brumer, J. Chem. Phys. 115, 3590 (2001) ADSCrossRefGoogle Scholar
  13. 13.
    K.F. Lee, E.A. Shapiro, D.M. Villeneuve, P.B. Corkum, Phys. Rev A 73, 033403 (2006) ADSCrossRefGoogle Scholar
  14. 14.
    J. Floß, I.Sh. Averbukh, Phys. Rev. E 91, 052911 (2015) ADSCrossRefGoogle Scholar
  15. 15.
    F.M. Izrailev, D.L. Shepelyanskii, Theor. Math. Phys. 43, 553 (1980) CrossRefGoogle Scholar
  16. 16.
    F.M. Izrailev, G. Casati, J. Ford, B.V. Chirikov, in Proc. conf. on stochastic behavior in classical and quantum Hamiltonian systems, Como, Italy, 1977, Preprint 78-46 [in Russian], Institute of Nuclear Physics, Siberian Branch, USSR academy of sciences, Novosibirsk (1978) Google Scholar
  17. 17.
    S. Fishman, in Proc. of the International School of Physics Enrico Fermi, Varenna (1991) Google Scholar
  18. 18.
    J.C. Slater, G.F. Koster, Phys. Rev. 94, 6 (1954) CrossRefGoogle Scholar
  19. 19.
    W.A. Harrison, Electronic structure and the properties of solids: the physics of the chemical bond (Dover Publications, 1989) Google Scholar
  20. 20.
    F. Bloch, Z. Phys. 52, 555 (1928) ADSCrossRefGoogle Scholar
  21. 21.
    N.W. Ashcroft, N.D. Mermin, Solid state physics (Saunders, Philadelphia, 1976) Google Scholar
  22. 22.
    S. Fishman, D.R. Grempel, R.E. Prange, Phys. Rev. Lett. 49, 8 (1982) CrossRefGoogle Scholar
  23. 23.
    H.A. Mavromatis, R.S. Alassar, Appl. Math. Lett. 12, 101 (1999) MathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Alexandra Bakman
    • 1
    Email author
  • Hagar Veksler
    • 1
  • Shmuel Fishman
    • 1
  1. 1.Technion – Israel Institute of Technology, Technion CityHaifaIsrael

Personalised recommendations