How chaotic is the stadium billiard? A semiclassical analysis
暂无分享,去创建一个
[1] J. Hannay,et al. Resonant periodic orbits and the semiclassical energy spectrum , 1987 .
[2] M. Berry,et al. Closed orbits and the regular bound spectrum , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.
[3] J. Hannay,et al. Periodic orbits and a correlation function for the semiclassical density of states , 1984 .
[4] G. Vattay,et al. Beyond the periodic orbit theory , 1997, chao-dyn/9712002.
[5] O. Bohigas,et al. Manifestations of classical phase space structures in quantum mechanics , 1993 .
[6] Eberhard R. Hilf,et al. Spectra of Finite Systems , 1980 .
[7] H. R. Dullin,et al. Symbolic Dynamics and Periodic Orbits for the Cardioid Billiard , 1995 .
[8] L. Bunimovich. On the ergodic properties of nowhere dispersing billiards , 1979 .
[9] Tomsovic,et al. Dynamical quasidegeneracies and separation of regular and irregular quantum levels. , 1990, Physical review letters.
[10] S. Berman,et al. Nuovo Cimento , 1983 .
[11] J. Keating,et al. Calculation of spectral determinants , 1994, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.
[12] Biham,et al. Unstable periodic orbits in the stadium billiard. , 1992, Physical review. A, Atomic, molecular, and optical physics.
[13] J. Keating,et al. A new asymptotic representation for ζ(½ + it) and quantum spectral determinants , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.
[14] Mark S. C. Reed,et al. Method of Modern Mathematical Physics , 1972 .
[15] Per Dahlqvist,et al. Determination of resonance spectra for bound chaotic systems , 1994 .
[16] Andreev,et al. Spectral statistics: From disordered to chaotic systems. , 1995, Physical review letters.
[17] Eric J. Heller,et al. Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits , 1984 .
[18] The semiclassical resonance spectrum of hydrogen in a constant magnetic field , 1996, chao-dyn/9601009.
[19] Scherer,et al. Quantum eigenvalues from classical periodic orbits. , 1991, Physical review letters.
[20] G. Casati,et al. On the connection between quantization of nonintegrable systems and statistical theory of spectra , 1980 .
[21] R. Lathe. Phd by thesis , 1988, Nature.
[22] J. Keating,et al. A rule for quantizing chaos , 1990 .
[23] J. H. Lefebvre,et al. Studies of Bogomolny's semiclassical quantization of integrable and nonintegrable systems , 1994 .
[24] Stephen C. Creagh,et al. Non-generic spectral statistics in the quantized stadium billiard , 1993 .
[25] M. Sieber. Uniform approximation for bifurcations of periodic orbits with high repetition numbers , 1996 .
[26] E. Bogomolny. Semiclassical quantization of multidimensional systems , 1992 .
[27] B. Lauritzen. Semiclassical Poincare map for integrable systems. , 1992, Chaos.
[28] P. Cvitanović,et al. Periodic orbit expansions for classical smooth flows , 1991 .
[29] A. Voros,et al. Spectral functions, special functions and the Selberg zeta function , 1987 .
[30] Kaufman,et al. Wave chaos in the stadium: Statistical properties of short-wave solutions of the Helmholtz equation. , 1988, Physical review. A, General physics.
[31] R. Balian,et al. Solution of the Schrodinger Equation in Terms of Classical Paths , 1974 .
[32] G. Tanner,et al. Quantization of chaotic systems. , 1992, Chaos.
[33] Cvitanovic,et al. Periodic-orbit quantization of chaotic systems. , 1989, Physical review letters.
[34] G. Tanner,et al. Classical and semiclassical zeta functions in terms of transition probabilities , 1995 .
[35] M. Berry,et al. Calculating the bound spectrum by path summation in action-angle variables , 1977 .
[36] U. Smilansky,et al. Penumbra diffraction in the semiclassical quantization of concave billiards , 1996, chao-dyn/9611009.
[37] Orbital magnetism in the ballistic regime: geometrical effects , 1996, cond-mat/9609201.
[38] R. Balian,et al. Distribution of eigenfrequencies for the wave equation in a finite domain: III. Eigenfrequency density oscillations , 1972 .
[39] M. Berry,et al. Semiclassical theory of spectral rigidity , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.
[40] J. Stein,et al. "Quantum" chaos in billiards studied by microwave absorption. , 1990, Physical review letters.
[41] E. Aurell,et al. Convergence of the Semi-Classical Periodic Orbit Expansion , 1989 .
[42] Allen S. Mandel. Comment … , 1978, British heart journal.
[43] Ikeda,et al. Complex Classical Trajectories and Chaotic Tunneling. , 1995, Physical review letters.
[44] S. Creagh. Trace Formula for Broken Symmetry , 1996 .
[45] J. Keating,et al. False singularities in partial sums over closed orbits , 1987 .
[46] Jorge V. José,et al. Chaos in classical and quantum mechanics , 1990 .
[47] Per Dahlqvist,et al. Approximate zeta functions for the Sinai billiard and related systems , 1994, chao-dyn/9402007.
[48] O. Bohigas,et al. Characterization of chaotic quantum spectra and universality of level fluctuation laws , 1984 .
[49] W. Hauschild,et al. Review of fundamentals , 1992 .
[50] Vattay,et al. Entire Fredholm determinants for evaluation of semiclassical and thermodynamical spectra. , 1993, Physical review letters.
[51] Prangé,et al. Exact and quasiclassical Fredholm solutions of quantum billiards. , 1995, Physical review letters.
[52] Weidenmüller,et al. Distribution of eigenmodes in a superconducting stadium billiard with chaotic dynamics. , 1992, Physical review letters.
[53] Stein,et al. Experimental determination of billiard wave functions. , 1992, Physical review letters.
[54] E. Bogomolny,et al. Gutzwiller's Trace Formula and Spectral Statistics: Beyond the Diagonal Approximation. , 1996, Physical review letters.
[55] Haggerty. Semiclassical quantization using Bogomolny's quantum surface of section. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[56] Giulio Casati,et al. Quantum chaos : between order and disorder , 1995 .
[57] Y. C. Verdière,et al. Ergodicité et fonctions propres du laplacien , 1985 .
[58] Semiclassical description of tunneling in mixed systems: Case of the annular billiard. , 1995, Physical review letters.
[59] Edge diffraction, trace formulae and the cardioid billiard , 1995, chao-dyn/9509005.
[60] Tomsovic,et al. Semiclassical trace formulas of near-integrable systems: Resonances. , 1995, Physical review letters.
[61] Steve Zelditch,et al. Uniform distribution of eigenfunctions on compact hyperbolic surfaces , 1987 .
[62] Allan N. Kaufman,et al. Spectrum and Eigenfunctions for a Hamiltonian with Stochastic Trajectories , 1979 .
[63] P. A. Boasman. Semiclassical accuracy for billiards , 1994 .
[64] Spectral statistics beyond random matrix theory. , 1995, Physical review letters.
[65] Tanner,et al. Semiclassical quantization of intermittency in helium. , 1995, Physical review letters.
[66] O'Connor,et al. Quantum localization for a strongly classically chaotic system. , 1988, Physical review letters.
[67] Steiner,et al. Quantization of chaos. , 1991, Physical review letters.
[68] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.
[69] L. Bunimovich,et al. Conditions of stochasticity of two-dimensional billiards. , 1991, Chaos.
[70] A. Voros. Unstable periodic orbits and semiclassical quantisation , 1988 .
[71] P. Gaspard,et al. Role of the edge orbits in the semiclassical quantization of the stadium billiard , 1994 .
[72] Cvitanovic,et al. Invariant measurement of strange sets in terms of cycles. , 1988, Physical review letters.
[73] Rafael I. Nepomechie,et al. Integrable open spin chains with nonsymmetric R-matrices , 1991 .