Abstract

Quantum billiards have attracted much interest in many fields. People have made a lot of researches on the two-dimensional (2D) billiard systems. Contrary to the 2D billiard, due to the complication of its classical periodic orbits, no one has studied the correspondence between the quantum spectra and the classical orbits of the three-dimensional (3D) billiards. Taking the cubic billiard as an example, using the periodic orbit theory, we find the periodic orbit of the cubic billiard and study the correspondence between the quantum spectra and the length of the classical orbits in 3D system. The Fourier transformed spectrum of this system has allowed direct comparison between peaks in such plot and the length of the periodic orbits, which verifies the correctness of the periodic orbit theory. This is another example showing that semiclassical method provides a bridge between quantum and classical mechanics.

© 2006 Chinese Optics Letters

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  2. H. J. Stockmann and J. Stein, Phys. Rev. Lett. 64, 2215 (1990).
  3. C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, Phys. Rev. Lett. 69, 506 (1992).
  4. N. Friedman, A. Kaplan, D. Carasso, and N. Davidson, Phys. Rev. Lett. 86, 1518 (2001).
  5. C. Zhang, J. Liu, M. G. Raizen, and Q. Niu, Phys. Rev. Lett. 93, 074101 (2004).
  6. P. Cvitanovic, Chaos 2, 1 (1992).
  7. D. L. Aronstein and C. R. Stroud, Phys. Rev. A 55, 4526 (1997).
  8. R. W. Robinett and S. Heppelmann, Phys. Rev. A 65, 062103 (2002).
  9. M. A. Doncheski and R. W. Robinett, Annals of Physics 299, 208 (2002).
  10. R. W. Robinett, Surface Rev. and Lett. 5, 519 (1998).
  11. R. W. Robinett, Am. J. Phys. 67, 67 (1999).
  12. S. M. Reimann, M. Brack, A. G. Magner, and M. V. N. Murthy, Phys. Rev. A 53, 39 (1996).
  13. R. W. Robinett, J. Math. Phys. 39, 278 (1998).
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  15. I. Zozoulenko, R. Schuster, K.-F. Berggren, and K. Ensslin, Phys. Rev. B 55, 10209 (1997).
  16. I. Sh. Averbukh, M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, Phys. Rev. Lett. 77, 3518 (1996).

2004 (1)

C. Zhang, J. Liu, M. G. Raizen, and Q. Niu, Phys. Rev. Lett. 93, 074101 (2004).

2002 (3)

R. W. Robinett and S. Heppelmann, Phys. Rev. A 65, 062103 (2002).

M. A. Doncheski and R. W. Robinett, Annals of Physics 299, 208 (2002).

J. Cserti, A. Kormanyos, Z. Kaufmann, and C. J. Lambert, Phys. Rev. Lett. 89, 057001 (2002).

2001 (1)

N. Friedman, A. Kaplan, D. Carasso, and N. Davidson, Phys. Rev. Lett. 86, 1518 (2001).

1999 (1)

R. W. Robinett, Am. J. Phys. 67, 67 (1999).

1998 (3)

R. W. Robinett, J. Math. Phys. 39, 278 (1998).

L. Christensson, H. Linke, and P. Omling, Phys. Rev. B 57, 12306 (1998).

R. W. Robinett, Surface Rev. and Lett. 5, 519 (1998).

1997 (2)

I. Zozoulenko, R. Schuster, K.-F. Berggren, and K. Ensslin, Phys. Rev. B 55, 10209 (1997).

D. L. Aronstein and C. R. Stroud, Phys. Rev. A 55, 4526 (1997).

1996 (2)

S. M. Reimann, M. Brack, A. G. Magner, and M. V. N. Murthy, Phys. Rev. A 53, 39 (1996).

I. Sh. Averbukh, M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, Phys. Rev. Lett. 77, 3518 (1996).

1992 (2)

P. Cvitanovic, Chaos 2, 1 (1992).

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, Phys. Rev. Lett. 69, 506 (1992).

1990 (1)

H. J. Stockmann and J. Stein, Phys. Rev. Lett. 64, 2215 (1990).

Aronstein, D. L.

D. L. Aronstein and C. R. Stroud, Phys. Rev. A 55, 4526 (1997).

Averbukh, I. Sh.

I. Sh. Averbukh, M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, Phys. Rev. Lett. 77, 3518 (1996).

Berggren, K.-F.

I. Zozoulenko, R. Schuster, K.-F. Berggren, and K. Ensslin, Phys. Rev. B 55, 10209 (1997).

Brack, M.

S. M. Reimann, M. Brack, A. G. Magner, and M. V. N. Murthy, Phys. Rev. A 53, 39 (1996).

Carasso, D.

N. Friedman, A. Kaplan, D. Carasso, and N. Davidson, Phys. Rev. Lett. 86, 1518 (2001).

Christensson, L.

L. Christensson, H. Linke, and P. Omling, Phys. Rev. B 57, 12306 (1998).

Cserti, J.

J. Cserti, A. Kormanyos, Z. Kaufmann, and C. J. Lambert, Phys. Rev. Lett. 89, 057001 (2002).

Cvitanovic, P.

P. Cvitanovic, Chaos 2, 1 (1992).

Davidson, N.

N. Friedman, A. Kaplan, D. Carasso, and N. Davidson, Phys. Rev. Lett. 86, 1518 (2001).

Doncheski, M. A.

M. A. Doncheski and R. W. Robinett, Annals of Physics 299, 208 (2002).

Ensslin, K.

I. Zozoulenko, R. Schuster, K.-F. Berggren, and K. Ensslin, Phys. Rev. B 55, 10209 (1997).

Friedman, N.

N. Friedman, A. Kaplan, D. Carasso, and N. Davidson, Phys. Rev. Lett. 86, 1518 (2001).

Gossard, A. C.

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, Phys. Rev. Lett. 69, 506 (1992).

Heppelmann, S.

R. W. Robinett and S. Heppelmann, Phys. Rev. A 65, 062103 (2002).

Hopkins, P. F.

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, Phys. Rev. Lett. 69, 506 (1992).

Kaplan, A.

N. Friedman, A. Kaplan, D. Carasso, and N. Davidson, Phys. Rev. Lett. 86, 1518 (2001).

Kaufmann, Z.

J. Cserti, A. Kormanyos, Z. Kaufmann, and C. J. Lambert, Phys. Rev. Lett. 89, 057001 (2002).

Kormanyos, A.

J. Cserti, A. Kormanyos, Z. Kaufmann, and C. J. Lambert, Phys. Rev. Lett. 89, 057001 (2002).

Lambert, C. J.

J. Cserti, A. Kormanyos, Z. Kaufmann, and C. J. Lambert, Phys. Rev. Lett. 89, 057001 (2002).

Linke, H.

L. Christensson, H. Linke, and P. Omling, Phys. Rev. B 57, 12306 (1998).

Liu, J.

C. Zhang, J. Liu, M. G. Raizen, and Q. Niu, Phys. Rev. Lett. 93, 074101 (2004).

Magner, A. G.

S. M. Reimann, M. Brack, A. G. Magner, and M. V. N. Murthy, Phys. Rev. A 53, 39 (1996).

Marcus, C. M.

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, Phys. Rev. Lett. 69, 506 (1992).

Murthy, M. V. N.

S. M. Reimann, M. Brack, A. G. Magner, and M. V. N. Murthy, Phys. Rev. A 53, 39 (1996).

Niu, Q.

C. Zhang, J. Liu, M. G. Raizen, and Q. Niu, Phys. Rev. Lett. 93, 074101 (2004).

Omling, P.

L. Christensson, H. Linke, and P. Omling, Phys. Rev. B 57, 12306 (1998).

Raizen, M. G.

C. Zhang, J. Liu, M. G. Raizen, and Q. Niu, Phys. Rev. Lett. 93, 074101 (2004).

Reimann, S. M.

S. M. Reimann, M. Brack, A. G. Magner, and M. V. N. Murthy, Phys. Rev. A 53, 39 (1996).

Rimberg, A. J.

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, Phys. Rev. Lett. 69, 506 (1992).

Robinett, R. W.

M. A. Doncheski and R. W. Robinett, Annals of Physics 299, 208 (2002).

R. W. Robinett and S. Heppelmann, Phys. Rev. A 65, 062103 (2002).

R. W. Robinett, Am. J. Phys. 67, 67 (1999).

R. W. Robinett, Surface Rev. and Lett. 5, 519 (1998).

R. W. Robinett, J. Math. Phys. 39, 278 (1998).

Schuster, R.

I. Zozoulenko, R. Schuster, K.-F. Berggren, and K. Ensslin, Phys. Rev. B 55, 10209 (1997).

Stein, J.

H. J. Stockmann and J. Stein, Phys. Rev. Lett. 64, 2215 (1990).

Stockmann, H. J.

H. J. Stockmann and J. Stein, Phys. Rev. Lett. 64, 2215 (1990).

Stolow, A.

I. Sh. Averbukh, M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, Phys. Rev. Lett. 77, 3518 (1996).

Stroud, C. R.

D. L. Aronstein and C. R. Stroud, Phys. Rev. A 55, 4526 (1997).

Villeneuve, D. M.

I. Sh. Averbukh, M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, Phys. Rev. Lett. 77, 3518 (1996).

Vrakking, M. J. J.

I. Sh. Averbukh, M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, Phys. Rev. Lett. 77, 3518 (1996).

Westervelt, R. M.

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, Phys. Rev. Lett. 69, 506 (1992).

Zhang, C.

C. Zhang, J. Liu, M. G. Raizen, and Q. Niu, Phys. Rev. Lett. 93, 074101 (2004).

Zozoulenko, I.

I. Zozoulenko, R. Schuster, K.-F. Berggren, and K. Ensslin, Phys. Rev. B 55, 10209 (1997).

Am. J. Phys. (1)

R. W. Robinett, Am. J. Phys. 67, 67 (1999).

Annals of Physics (1)

M. A. Doncheski and R. W. Robinett, Annals of Physics 299, 208 (2002).

Chaos (1)

P. Cvitanovic, Chaos 2, 1 (1992).

J. Math. Phys. (1)

R. W. Robinett, J. Math. Phys. 39, 278 (1998).

Phys. Rev. A (3)

S. M. Reimann, M. Brack, A. G. Magner, and M. V. N. Murthy, Phys. Rev. A 53, 39 (1996).

D. L. Aronstein and C. R. Stroud, Phys. Rev. A 55, 4526 (1997).

R. W. Robinett and S. Heppelmann, Phys. Rev. A 65, 062103 (2002).

Phys. Rev. B (2)

L. Christensson, H. Linke, and P. Omling, Phys. Rev. B 57, 12306 (1998).

I. Zozoulenko, R. Schuster, K.-F. Berggren, and K. Ensslin, Phys. Rev. B 55, 10209 (1997).

Phys. Rev. Lett. (6)

I. Sh. Averbukh, M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, Phys. Rev. Lett. 77, 3518 (1996).

J. Cserti, A. Kormanyos, Z. Kaufmann, and C. J. Lambert, Phys. Rev. Lett. 89, 057001 (2002).

H. J. Stockmann and J. Stein, Phys. Rev. Lett. 64, 2215 (1990).

C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, Phys. Rev. Lett. 69, 506 (1992).

N. Friedman, A. Kaplan, D. Carasso, and N. Davidson, Phys. Rev. Lett. 86, 1518 (2001).

C. Zhang, J. Liu, M. G. Raizen, and Q. Niu, Phys. Rev. Lett. 93, 074101 (2004).

Surface Rev. and Lett. (1)

R. W. Robinett, Surface Rev. and Lett. 5, 519 (1998).

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