Autocorrelation function of level velocities for ray-splitting billiards

Y. Hlushchuk; A. Kohler; Sz. Bauch; L. Sirko; R. Blümel; M. Barth; H.-J. Stöckmann

doi:10.1103/PhysRevE.61.366

Access by Xinjiang University

Autocorrelation function of level velocities for ray-splitting billiards

Y. Hlushchuk^1,2, A. Kohler³, Sz. Bauch¹, L. Sirko^1,2, R. Blümel⁴, M. Barth⁵, and H.-J. Stöckmann⁵

¹Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
²College of Science, Aleja Lotników 32/46, 02-668 Warszawa, Poland
³Sysdeco GIS AS, P.O. Box 433, 3601 Kongsberg, Norway
⁴Department of Physics, Wesleyan University, Middletown, Connecticut 06459-0155
⁵Fachbereich Physik, Universität Marburg, Renthof 5, D-35032 Marburg, Germany

PDF

Phys. Rev. E 61, 366 – Published 1 January, 2000

DOI: https://doi.org/10.1103/PhysRevE.61.366

Abstract

We study experimentally and theoretically the autocorrelation function of level velocities $c (x)$ and the generalized conductance $C (0)$ for classically chaotic ray-splitting systems. Experimentally, a Sinai ray-splitting billiard was simulated by a thin microwave rectangular cavity with a quarter-circle Teflon insert. For the theoretical estimates of the autocorrelator $c (x)$ and the conductance $C (0)$ we made parameter-dependent quantum calculations of eigenenergies of an annular ray-splitting billiard. Our experimental and numerical results are compared to theoretical predictions of systems based on the Gaussian orthogonal ensemble in random matrix theory.

References (35)

F.J. Dyson, J. Math. Phys. 3, 140 (1962).
M.L. Mehta, Random Matrices (Academic Press, New York, 1991).
A. Szafer and B.L. Altshuler, Phys. Rev. Lett. 70, 587 (1993).
B.D. Simons and B.L. Altshuler, Phys. Rev. Lett. 70, 4063 (1993).
B.D. Simons and B.L. Alshuler, Phys. Rev. B 48, 5422 (1993).
M. Faas, B.D. Simons, X. Zotos, and B.L. Altshuler, Phys. Rev. B 48, 5439 (1993).
B.D. Simons, A. Hashimoto, M. Courtney, D. Klepner, and B.L. Alshuler, Phys. Rev. Lett. 71, 2899 (1993).
M.V. Berry and J.P. Keating, J. Phys. A 27, 6167 (1994).
H. Bruus, C.H. Lewenkopf, and E.R. Mucciolo, Phys. Rev. B 53, 9968 (1996).
H. Bruus, C.H. Lewenkopf, and E.R. Mucciolo, Phys. Scr. T69, 13 (1997).
D. Delande and J. Zakrzewski, J. Phys. Soc. Jpn. 63, 101 (1994).
J. Zakrzewski, Z. Phys. B: Condens. Matter 98, 273 (1995).
I. Guarneri, K. Życzkowski, J. Zakrzewski, L. Molinari, and G. Casati, Phys. Rev. E 52, 2220 (1995).
P. Kunstman, K. Życzkowski, and J. Zakrzewski, Phys. Rev. E 55, 2446 (1997).
X. Yang and J. Burgdörfer, Phys. Rev. A 46, 2295 (1992).
L. Couchman, E. Ott, and T.M. Antonsen, Jr., Phys. Rev. A 46, 6193 (1992).
R.E. Prange, E. Ott, T.M. Antonsen, Jr., B. Georgeot, and R. Blümel, Phys. Rev. E 53, 207 (1996).
R. Blümel, T.M. Antonsen, B. Georgeot, E. Ott, and R.E. Prange, Phys. Rev. Lett. 76, 2476 (1996); Phys. Rev. E 53, 3284 (1996).
R.N. Oerter, E. Ott, T.M. Antonsen, Jr., and P. So, Phys. Lett. A 216, 59 (1996).
A. Kohler, G.H.M. Killesreiter, and R. Blümel, Phys. Rev. E 56, 2691 (1997).
A. Kohler and R. Blümel, Phys. Lett. A 238, 271 (1998).
L. Sirko, P.M. Koch, and R. Blümel, Phys. Rev. Lett. 78, 2940 (1997).
Sz. Bauch, A. Błȩdowski, L. Sirko, P.M. Koch, and R. Blümel, Phys. Rev. E 57, 304 (1998).
A. Kohler and R. Blümel, Phys. Lett. A 247, 87 (1998).
K. Schaadt, M.Sc. thesis, University of Copenhagen, 1997, p. 50; T. Bertelsen, C. Ellegaard, T. Guhr, K. Lindemann, M. Oxborrow, and K. Schaadt (unpublished).
M. Barth, U. Kuhl, and H.-J. Stöckmann, Phys. Rev. Lett. 82, 2026 (1999).
J.D. Jackson, Classical Electrodynamics (John Wiley, New York, 1975).
M.C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
H.-J. Stöckmann and J. Stein, Phys. Rev. Lett. 64, 2215 (1990).
S. Sridhar, Phys. Rev. Lett. 67, 785 (1991).
K.H. Breeden and A.P. Sheppard, Microwave J. 10, 59 (1967); Radio Sci. 3, 205 (1968).
O. Bohigas, D. Boosé, R. Egydio de Carvalho, and V. Marvulle, Nucl. Phys. A 560, 197 (1993).
H. Bruus and A.D. Stone, Phys. Rev. B 50, 18 275 (1994); Physica B 189, 43 (1993).
M. Kollmann, J. Stein, U. Stoffregen, H.-J. Stöckmann, and B. Eckhardt, Phys. Rev. E 49, R1 (1994).
E. Born and E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1964).

[c1] F.J. Dyson, J. Math. Phys. 3, 140 (1962).

[c2] M.L. Mehta, Random Matrices (Academic Press, New York, 1991).

[c3] A. Szafer and B.L. Altshuler, Phys. Rev. Lett. 70, 587 (1993).

[c4] B.D. Simons and B.L. Altshuler, Phys. Rev. Lett. 70, 4063 (1993).

[c5] B.D. Simons and B.L. Alshuler, Phys. Rev. B 48, 5422 (1993).

[c6] M. Faas, B.D. Simons, X. Zotos, and B.L. Altshuler, Phys. Rev. B 48, 5439 (1993).

[c7] B.D. Simons, A. Hashimoto, M. Courtney, D. Klepner, and B.L. Alshuler, Phys. Rev. Lett. 71, 2899 (1993).

[c8] M.V. Berry and J.P. Keating, J. Phys. A 27, 6167 (1994).

[c9] H. Bruus, C.H. Lewenkopf, and E.R. Mucciolo, Phys. Rev. B 53, 9968 (1996).

[c10] H. Bruus, C.H. Lewenkopf, and E.R. Mucciolo, Phys. Scr. T69, 13 (1997).

[c11] D. Delande and J. Zakrzewski, J. Phys. Soc. Jpn. 63, 101 (1994).

[c12] J. Zakrzewski, Z. Phys. B: Condens. Matter 98, 273 (1995).

[c13] I. Guarneri, K. Życzkowski, J. Zakrzewski, L. Molinari, and G. Casati, Phys. Rev. E 52, 2220 (1995).

[c14] P. Kunstman, K. Życzkowski, and J. Zakrzewski, Phys. Rev. E 55, 2446 (1997).

[c15] X. Yang and J. Burgdörfer, Phys. Rev. A 46, 2295 (1992).

[c16] L. Couchman, E. Ott, and T.M. Antonsen, Jr., Phys. Rev. A 46, 6193 (1992).

[c17] R.E. Prange, E. Ott, T.M. Antonsen, Jr., B. Georgeot, and R. Blümel, Phys. Rev. E 53, 207 (1996).

[c18] R. Blümel, T.M. Antonsen, B. Georgeot, E. Ott, and R.E. Prange, Phys. Rev. Lett. 76, 2476 (1996); Phys. Rev. E 53, 3284 (1996).

[c19] R.N. Oerter, E. Ott, T.M. Antonsen, Jr., and P. So, Phys. Lett. A 216, 59 (1996).

[c20] A. Kohler, G.H.M. Killesreiter, and R. Blümel, Phys. Rev. E 56, 2691 (1997).

[c21] A. Kohler and R. Blümel, Phys. Lett. A 238, 271 (1998).

[c22] L. Sirko, P.M. Koch, and R. Blümel, Phys. Rev. Lett. 78, 2940 (1997).

[c23] Sz. Bauch, A. Błȩdowski, L. Sirko, P.M. Koch, and R. Blümel, Phys. Rev. E 57, 304 (1998).

[c24] A. Kohler and R. Blümel, Phys. Lett. A 247, 87 (1998).

[c25] K. Schaadt, M.Sc. thesis, University of Copenhagen, 1997, p. 50; T. Bertelsen, C. Ellegaard, T. Guhr, K. Lindemann, M. Oxborrow, and K. Schaadt (unpublished).

[c26] M. Barth, U. Kuhl, and H.-J. Stöckmann, Phys. Rev. Lett. 82, 2026 (1999).

[c27] J.D. Jackson, Classical Electrodynamics (John Wiley, New York, 1975).

[c28] M.C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).

[c29] H.-J. Stöckmann and J. Stein, Phys. Rev. Lett. 64, 2215 (1990).

[c30] S. Sridhar, Phys. Rev. Lett. 67, 785 (1991).

[c31] K.H. Breeden and A.P. Sheppard, Microwave J. 10, 59 (1967); Radio Sci. 3, 205 (1968).

[c32] O. Bohigas, D. Boosé, R. Egydio de Carvalho, and V. Marvulle, Nucl. Phys. A 560, 197 (1993).

[c33] H. Bruus and A.D. Stone, Phys. Rev. B 50, 18 275 (1994); Physica B 189, 43 (1993).

[c34] M. Kollmann, J. Stein, U. Stoffregen, H.-J. Stöckmann, and B. Eckhardt, Phys. Rev. E 49, R1 (1994).

[c35] E. Born and E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1964).

Physical Review E

Export citation

Export citation

Autocorrelation function of level velocities for ray-splitting billiards

Abstract

References (35)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation