Asymptotic rate of quantum ergodicity in chaotic euclidean billiards
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[1] Y. C. Verdière,et al. Ergodicité et fonctions propres du laplacien , 1985 .
[2] Arnd Bäcker,et al. Numerical Aspects of Eigenvalue and Eigenfunction Computations for Chaotic Quantum Systems , 2002 .
[3] Steve Zelditch,et al. Quantum Ergodicity and Mixing of Eigenfunctions , 2006 .
[5] Steve Zelditch,et al. Uniform distribution of eigenfunctions on compact hyperbolic surfaces , 1987 .
[6] M. Berry,et al. Quantum scars of classical closed orbits in phase space , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.
[7] K. Vahala. Handbook of stochastic methods for physics, chemistry and the natural sciences , 1986, IEEE Journal of Quantum Electronics.
[8] Fishman,et al. Semiclassical criterion for scars in wave functions of chaotic systems. , 1994, Physical review letters.
[9] André Martinez,et al. An Introduction to Semiclassical and Microlocal Analysis , 2002 .
[10] S. Zelditch. Note on quantum unique ergodicity , 2003 .
[11] Alex H. Barnett,et al. Quasi-orthogonality on the boundary for Euclidean Laplace eigenfunctions , 2006, math-ph/0601006.
[12] Chaos and Energy Spreading for Time-Dependent Hamiltonians, and the Various Regimes in the Theory of Quantum Dissipation , 1999, cond-mat/9902168.
[13] J. Marklof. Arithmetic Quantum Chaos , 2006 .
[14] E. Bogomolny,et al. Chaotic billiards generated by arithmetic groups. , 1992, Physical review letters.
[15] T. Prosen,et al. Quantization of generic chaotic 3D billiard with smooth boundary II: structure of high-lying eigenstates , 1996, chao-dyn/9611016.
[16] Michael V Berry,et al. Regular and irregular semiclassical wavefunctions , 1977 .
[17] L. Hörmander. The Analysis of Linear Partial Differential Operators III , 2007 .
[18] Marko Robnik,et al. Study of Regular and Irregular States in Generic Systems , 1999, nlin/0003061.
[19] D. Robert,et al. Distribution of matrix elements and level spacings for classically chaotic systems , 1994 .
[20] E. Lindenstrauss. Invariant measures and arithmetic quantum unique ergodicity , 2006 .
[21] S. Zelditch. On the rate of Quantum Ergodicity, II: Lower bounds , 1994 .
[22] M. Srednicki,et al. Random matrix elements and eigenfunctions in chaotic systems , 1997, chao-dyn/9711020.
[23] E. Heller,et al. Rate of energy absorption for a driven chaotic cavity , 2000, nlin/0006041.
[24] S. Zelditch. Quantum ergodicity on the sphere , 1992 .
[25] Peter Sarnak,et al. Spectra and eigenfunctions of laplacians , 1997 .
[26] S. Zelditch,et al. Ergodicity of eigenfunctions for ergodic billiards , 1996 .
[27] P. Sarnak,et al. Quantum variance for Hecke eigenforms , 2004 .
[28] M. Wilkinson. A semiclassical sum rule for matrix elements of classically chaotic systems , 1987 .
[29] E. Heller,et al. Parametric evolution for a deformed cavity. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.
[30] Jorge V. José,et al. Chaos in classical and quantum mechanics , 1990 .
[31] P. Sarnak. Spectra of hyperbolic surfaces , 2003 .
[32] Z. Rudnick. Quantum Chaos? , 2007 .
[33] Pérès,et al. Distribution of matrix elements of chaotic systems. , 1986, Physical review. A, General physics.
[34] Vergini,et al. Calculation by scaling of highly excited states of billiards. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[35] T. Prosen. Statistical Properties of Matrix Elements in a Hamilton System Between Integrability and Chaos , 1994 .
[36] H. Donnelly,et al. Quantum unique ergodicity , 2002 .
[37] Gregor Tanner,et al. How chaotic is the stadium billiard? A semiclassical analysis , 1996, chao-dyn/9610013.
[38] Distributions of transition matrix elements in classically mixed quantum systems. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[39] Bambi Hu,et al. Statistical analysis of scars in stadium billiard , 1997, cond-mat/9712082.
[40] Fishman,et al. Approach to ergodicity in quantum wave functions. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[41] Scars on quantum networks ignore the Lyapunov exponent. , 2003, Physical review letters.
[42] E. Heller,et al. Measuring scars of periodic orbits. , 1998, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[43] S. Zelditch. Quantum transition amplitudes for ergodic and for completely integrable systems , 1990 .
[44] Eric J. Heller,et al. Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits , 1984 .
[45] Peter Sarnak,et al. The behaviour of eigenstates of arithmetic hyperbolic manifolds , 1994 .
[46] Giulio Casati,et al. The quantum mechanics of chaotic billiards , 1999 .
[47] R. Aurich,et al. On the rate of quantum ergodicity on hyperbolic surfaces and for billiards , 1997, chao-dyn/9707016.
[48] Tomaž Prosen,et al. Quantization of a generic chaotic 3D billiard with smooth boundary. I. Energy level statistics , 1996, chao-dyn/9611015.
[49] R. Schubertz,et al. On the Number of Bouncing Ball Modes in Billiards , 1997 .
[50] T. Tate. Some remarks on the off-diagonal asymptotics in quantum ergodicity , 1999 .
[51] S. Swain. Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences , 1984 .
[52] Ericka Stricklin-Parker,et al. Ann , 2005 .
[53] S. Zelditch. A Random Matrix Model for Quantum Mixing , 1996 .
[54] D. Robert,et al. Semiclassical sum rules and generalized coherent states , 1995 .
[55] Lev Kaplan,et al. Linear and Nonlinear Theory of Eigenfunction Scars , 1998, chao-dyn/9809011.
[56] S. Zelditch. On the rate of quantum ergodicity I: Upper bounds , 1994 .
[57] Lloyd N. Trefethen,et al. Reviving the Method of Particular Solutions , 2005, SIAM Rev..
[58] Stéphane Nonnenmacher,et al. Communications in Mathematical Physics Scarred Eigenstates for Quantum Cat Maps of Minimal Periods , 2003 .
[59] V. G. Sigillito,et al. Eigenvalues of the Laplacian in Two Dimensions , 1984 .
[60] E. Bogomolny. Smoothed wave functions of chaotic quantum systems , 1988 .
[61] E. Austin,et al. Distribution of matrix elements of a classically chaotic system , 1992 .
[62] R. Schubertz,et al. On the Rate of Quantum Ergodicity in Euclidean Billiards , 1998 .