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[1] A. Bäcker and R. Schubert, Chaotic eigenfunctions in momentum space, J. Phys. A 32 (1999), 4795-4815. [2] A. H. Barnett, Dissipation in Deforming Chaotic Billiards, Harvard Uni-versity 2000_10. [3] Sz. Bauch, A. Bledowski, L. Sirko, P.M. Koch, and R. Blümel, Signature of non-Newtonian orbits in ray-splitting cavities, Phys. Rev. E (accepted for publication, 1997). [4] M. V. Berry, Quantizing a classically ergodic system: Sinai billiard and the KKR method, Ann. Phys., 131:163-216, 1981. [5] M. V. Berry and M. Wilkinson, Diabolical points in the spectra of trian-gles, Proc. Roy. Soc. London A, 392:15, 1984. [6] P. A. Boasman, Nonlinearity, 7:485, 1994. [7] E. B. Bogomolny, Nonlinearity, 5:805-866, 1992. [8] A. Bulgac and P. Magierski, Eigenstates for billiards of arbitrary shapes, preprint physics/9902057, 1999. [9] G. Casati and B.V. Chirikov, Eds., Quantum Chaos: Between Order and Disorder (Cambridge Univ. Press, 1995). [10] Y. Colin de Verdière, Ergodicité et fonctions propres du laplacien, Comm. Math. phys. 102 (1985), 497-502. [11] P. J. Davis, Circulant matrices, A Wiley-Interscience publication, Canada, 1979. [12] S. Deus, P.M. Koch, and L. Sirko, Statistical properties of the eigenfre-quency distribution of three-dimensional microwave cavities, Phys. Rev. E 52, 1146 (1995). [13] E. Doron and U. Smilansky, Semiclassical quantization of chaotic billiards- -a scattering theory approach. Nonlinearity, 5:1055-1084, 1992. [14] H. Eisen and W. Heinrichs and K. Witsch, Spectral collocation meth-ods and polar coordinate singularities. J. Comput. phys., 96(2):241-257, 1991. [15] G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., The John Hopkins University Press, Baltimore, London, 1996. [16] M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, Berlin, 1991). [17] F. Haake, Quantum Signatures of Chaos (Springer, Berlin, 1991). [18] E. J. Heller, Bound state eigenfunctions of classically chaotic hamil-tonian systems: Scars of periodic orbits, Phys. Rev. Lett., 53:1515, 1984. [19] E. J. Heller, Semiclassical wave packet dynamics and chaos in quantum mechanics, In M. J. Giannoni, A. Voros, and J. Zinn-Justin, editors, Proceedings of the 1989 Les Houches Summer School on “Chaos and Quantum Physics”, pages 547-663, North-Holland, 1991. Elsevier Sci-ence Publishers B.V. [20] W. Huang and D. M. Sloa, Pole condition for singular problems: the pseudospectral approximation. J. Comput. Phys., 107(2):254-261, 1993. [21] T. M. Hwang, W. Wang, Analyzing and Visualizing A Discretized Semi-linear Elliptic Problem with Neumann Boundary conditions. Numerical Methods in Partial Di¤erential Equations, NCTS 2001_4. [22] T. M. Hwang, W. W. Lin, J. L. Liu, and W. Wang, Numerical com-putation of cubic eigenvalue problems for a semiconductor quantum dot model with non-parabolic e¤ ective mass approximation, NCTS Preprints in Mathematics 2001_12. [23] I. Kosztin and K. Schulten, Intl. J. Mod. Phys., 8:293-325, 1997. preprint physics/9702022. [24] P. Kurlberg and Z. Rudnick, On quantum unique ergodicity for linear maps of the torus, Commun. Math. Phys. 222 (2001) 1, 201-227. [25] M. C. Lai, A note on …nite di¤erence discretizations for Poisson equa-tion on a disk. Numerical Methods for Partial Di¤erential Equations. 17(3):199-203, 2001. [26] B. Li, Phys. Rev. E, 55:5376-79, 1997. [27] B. Li and B. Hu, J. Phys. A, 31:483-504, 1998. [28] B. Li and M. Robnik, J. Phys. A, 28:2799, 1995. [29] B. Li, M. Robnik, and B. Hu, Phys. Rev. E, 57:4095-4105, 1998. [30] S. W. McDonald and A. N. Kaufman, Phys. Rev. Lett., 42:1189, 1979. [31] C. C. Paige, B. N. Parlett, and H. A. Van Der Vorst, Approximate solutions and eigenvalue bounds from Krylov subspaces, Numer. Linear Algebra Appl., 2 (1995), pp. 115-133. [32] H. Primack, Quantal and Semiclassical analysis of the three-dimensional Sinai billiard, PhD thesis, Weizmann Institute, Rehovot, Israel, Septem-ber 1997. [33] T. Prosen, Physica D, 91:244, 1996. [34] T. Prosen and M. Robnik, J. Phys. A, 27:8059, 1994. [35] Jr. R. J. Riddell, Comp. Phys., 31:21-41; 42-59, 1979. [36] M. Robnik, J. Phys. A, 17:1049, 1984. [37] A. Schnirelman, Ergodic properties of eigenfunctions, Usp. Math. Nauk 29 (1974), 1814-182. [38] G. L. G. Sleijpen, A. G. L. Botten, D. R. Fokkema, and H. A. van der Vorst, Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems. BIT, 36(3):595-633, 1996. [39] G. L. G. Sleijpen and H. A. van der Vorst, A Jacobi-Davidson iteration method for linear eigenvalue problems. SIAM J. Martix Anal. Appl., 17(2):401-425, April 1996. [40] P. N. Swarztrauber and R. A. Sweet, The direct solution of the discrete Poisson equation on a disk. SIAM J. Numer. Anal., 10:200, 1973. [41] E. Vergini and M. Saraceno, Calculation by scaling of highly excited states of billiards, Phys. Rev. E, 52:2204-2207, 1995. [42] S. Zelditch, Uniform distribution of eigenfunctions on compact hyper-bolic surfaces, Duke Math. J. 55 (1987), 919-941.
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