Abstract
We study a model of complex band random matrices capable of describing the transitions between three different ensembles of Hermitian matrices: Gaussian orthogonal, Gaussian unitary and Poissonian. Analyzing numerical data we observe new scaling relations based on the generalized localization length of eigenvectors. We show that during transitions between canonical ensembles of random matrices the changes of statistical properties of eigenvalues and eigenvectors are correlated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Berry M.V., Tabor, M.: Proc. R. Soc. Lond. A356, 375 (1977)
Haake, F.: Quantum signatures of chaos. Berlin, Heidelberg, New York: 1991
Reichl, L.E.: The transition to chaos. Berlin, Heidelberg, New York: 1992
Bohigas, O., Giannoni, M.J., Schmit, C.: Phys. Rev. Lett.52, 1 (1984)
Porter, C.E.: Statistical theory of spectra. New York: Academic Press 1965
Brody, T.A., Flores, J., French, J.B., Mello, P.A., Pandey A., Wong S.S.M.: Rev. Mod. Phys.53, 385 (1981)
Mehta, M.L.: Random matrices, 2 edn. New York: Academic Press 1990
Seligman, T.H., Verbaarschot, J.J., Zirnbauer M.R.: J. Phys. A18, 2751 (1985)
Casati, G., Guarneri, I., Scharf, R., Izrailev, F.: Phys. Rev. Lett.64, 5 (1990)
Casati, G., Molinari, L., Izrailev, F.: Phys. Rev. Lett.64, 1851 (1990)
Grammaticos, B., Ramani, A., Caurier, E.: J. Phys. A23, 5855 (1990); Caurier, E., Ramani, A. Grammaticos, B.: ibid J. Phys. A26, 3845 (1993)
Wilkinson, M., Feingold M., Leitner, D.M.: J. Phys. A24, 175 (1991)
Casati, G., Izrailev, F., Molinari, L.: J. Phys. A24, 4755 (1991)
Życzkowski, K., Lewenstein M., Kuś, M., Izrailev, F.: Phys. Rev. A45, 811 (1992)
Fyodorov, Y.V., Mirlin, A.D.: Phys. Rev. Lett.67, 2405 (1991)
Kuś, M., Lewenstein, M., Haake, F.: Phys. Rev. A44, 2800 (1991)
Casati, G., Girko, V.L.: Rand. Oper. Stoch. Eqs.1, 1 (1992)
Serwicki, R.: Master Thesis, Kraków (1992)
Życzkowski, K.: Acta Phys. Pol. B24, 967 (1983)
Pandey, A., Mehta, M.L.: Commun. Math. Phys.87, 449 (1983)
French, J.B., Kota, V.K.B., Pandey, A., Tomsovic, S.: Ann. Phys. (N.Y.)181, 198 (1988)
Lenz, G., Haake, F.: Phys. Rev. Lett.67, 1 (1991)
Evangelou, N., Economou, E.N.: Phys. Lett. A151, 345 (1990)
Cheon, T.: Phys. Rev. A42, 6227 (1990)
Izrailev, F.M.: Phys. Rep.196, 299 (1990)
Haake, F., Życzkowski, K.: Phys. Rev. A42, 1013 (1990)
Fyodorov, Y.V., Mirlin, A.D.: Phys. Rev. Lett.71, 412 (1993)
Jones, K.R.W.: J. Phys. A23, L1247 (1990)
Spanier, J., Oldham, K.B.: An atlas of functions. Washington: Hemisphere 1987
Fyodorov, Y.V., Mirlin, A.D.: Phys. Rev. Lett.69, 1093 (1992) with errata, ibid. Phys. Rev. Lett.69, 8832 (1992)
Bohigas, O., Giannoni, M.J.: Ann. Phys. (N.Y.)89, 393 (1975)
Camarda, H.S.: Phys. Rev. A45, 597 (1992)
Dupuis, N., Montambaux, G.: Phys. Rev. B43, 14390 (1991)
Pichard, J.-L., Sanquer, M., Slevin, K., Debray, P.: Phys. Rev. Lett.65, 1812 (1990)
Życzkowski, K., Lenz, G.: Z. Phys. B82, 299 (1991)
Sommers, H.-J., Iida, S.: Phys. Rev. E49, R2513, (1994)
Izrailev, F., Molinari, L., Życzkowski, K.: (to be published)
Blümel, R., Smilansky, U.: Phys. Rev. Lett.69, 217 (1992)
Thaha, M., Blümel, R., Smilansky, U.: Phys. Rev. E48, 1764 (1993)
Thaha, M., Blümel; Phys. Rev. Lett.72, 72 (1994)
Mirlin, A.D.: Phys. Rev. Lett72, 3437 (1994)
Lenz, G., Życzkowski, K.: J. Phys. A25, 5539 (1992)
Życzkowski, K., Kuś, K.: J. Phys. A27, 4235 (1994)
Feingold, M., Leitner, D. and Wilkinson, M.: Phys. Rev. Lett.66, 986 (1991)
Gioletta, A., Feingold, M., Izrailev, F., Molinari, L.: Phys. Rev. Lett.70, 2936 (1993)
Casati, G., Chirikov, B.V., Guarneri, I., Izrailev, F.: Phys. Rev. E48, R1613 (1993)