Edge states of a three dimensional kicked rotor

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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.

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  1. 1.

    A.P. Vinogradov, A.V. Dorofeenko, A.M. Merzlikin, A.A. Lisyansky, Physics – Uspekhi 53, 243 (2010)

  2. 2.

    R.D. Meade, K.D. Brommer, A.M. Rappe, J.D. Joannopoulos, Phys. Rev. B 44, 19 (1991)

  3. 3.

    V. Podzorov, E. Menard, A. Borissov, V. Kiryukhin, J.A. Rogers, M.E. Gershenson, Phys. Rev. Lett. 93, 8 (2004)

  4. 4.

    H. Lin, R.S. Markiewicz, L.A. Wray, L. Fu, M.Z. Hasan, A. Bansil, Phys. Rev. Lett. 105, 036404 (2010)

  5. 5.

    J.C.Y. Teo, L. Fu, C.L. Kane, Phys. Rev. B 78, 045426 (2008)

  6. 6.

    D.X. Qu, Y.S. Hor, J. Xiong, R.J. Cava, N.P. Ong, Science 329, 821 (2010)

  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)

  8. 8.

    R. Blümel, S. Fishman, U. Smilansky, J. Chem. Phys. 84, 2604 (1986)

  9. 9.

    J. Floß, I.Sh. Averbukh, Phys. Rev. A 86, 021401(R) (2012)

  10. 10.

    J. Floß, S. Fishman, I.Sh. Averbukh, Phys. Rev. A 88, 023426 (2013)

  11. 11.

    G. Casati, B. Chirikov,Quantum Chaos: Between Order and Disorder (Cambridge University Press, 1995)

  12. 12.

    J. Gong, P. Brumer, J. Chem. Phys. 115, 3590 (2001)

  13. 13.

    K.F. Lee, E.A. Shapiro, D.M. Villeneuve, P.B. Corkum, Phys. Rev A 73, 033403 (2006)

  14. 14.

    J. Floß, I.Sh. Averbukh, Phys. Rev. E 91, 052911 (2015)

  15. 15.

    F.M. Izrailev, D.L. Shepelyanskii, Theor. Math. Phys. 43, 553 (1980)

  16. 16.

    F.M. Izrailev, G. Casati, J. Ford, B.V. Chirikov, inProc. 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)

  17. 17.

    S. Fishman, inProc. of the International School of Physics Enrico Fermi, Varenna (1991)

  18. 18.

    J.C. Slater, G.F. Koster, Phys. Rev. 94, 6 (1954)

  19. 19.

    W.A. Harrison,Electronic structure and the properties of solids: the physics of the chemical bond (Dover Publications, 1989)

  20. 20.

    F. Bloch, Z. Phys. 52, 555 (1928)

  21. 21.

    N.W. Ashcroft, N.D. Mermin,Solid state physics (Saunders, Philadelphia, 1976)

  22. 22.

    S. Fishman, D.R. Grempel, R.E. Prange, Phys. Rev. Lett. 49, 8 (1982)

  23. 23.

    H.A. Mavromatis, R.S. Alassar, Appl. Math. Lett. 12, 101 (1999)

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Correspondence to Alexandra Bakman.

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Bakman, A., Veksler, H. & Fishman, S. Edge states of a three dimensional kicked rotor. Eur. Phys. J. B 92, 236 (2019) doi:10.1140/epjb/e2019-100174-8

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  • Statistical and Nonlinear Physics