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Volumn 129, Issue 1-2, 1999, Pages 1-14

Maximum norms of chaotic quantum eigenstates and random waves

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EID: 0038363064     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00287-5     Document Type: Article
Times cited : (30)

References (53)
  • 2
    • 0000450808 scopus 로고
    • Regular and irregular semiclassical wavefunctions
    • M.V. Berry, Regular and irregular semiclassical wavefunctions, J. Phys. A 10 (1977) 2083-2091.
    • (1977) J. Phys. A , vol.10 , pp. 2083-2091
    • Berry, M.V.1
  • 3
    • 26144456693 scopus 로고
    • Wave chaos in the stadium: Statistical properties of short-wave solutions of the Helmholtz equation
    • S.W. McDonald, A.N. Kaufmann, Wave chaos in the stadium: statistical properties of short-wave solutions of the Helmholtz equation, Phys. Rev. A 37 (1988) 3067-3086.
    • (1988) Phys. Rev. A , vol.37 , pp. 3067-3086
    • McDonald, S.W.1    Kaufmann, A.N.2
  • 4
    • 0001107629 scopus 로고
    • On the topography of Mass waveforms for PSL(2, ℤ): Experiments and heuristics
    • D.A. Hejhal, B.N. Rackner, On the topography of Mass waveforms for PSL(2, ℤ): experiments and heuristics, Exp. Math. 1 (1992) 275-305.
    • (1992) Exp. Math. , vol.1 , pp. 275-305
    • Hejhal, D.A.1    Rackner, B.N.2
  • 5
    • 0000956176 scopus 로고
    • Statistical properties of highly excited quantum eigenstates of a strongly chaotic system
    • R. Aurich, F. Steiner, Statistical properties of highly excited quantum eigenstates of a strongly chaotic system, PhysicaD 64 (1993) 185-214.
    • (1993) PhysicaD , vol.64 , pp. 185-214
    • Aurich, R.1    Steiner, F.2
  • 6
    • 36149033614 scopus 로고
    • Statistical properties of high-lying chaotic eigenstates
    • B. Li, M. Robnik, Statistical properties of high-lying chaotic eigenstates, J. Phys. A 27 (1994) 5509-5523.
    • (1994) J. Phys. A , vol.27 , pp. 5509-5523
    • Li, B.1    Robnik, M.2
  • 7
    • 0001022947 scopus 로고
    • Ergodic properties of eigenfunctions
    • (in Russian)
    • A.I. Shnirelman, Ergodic properties of eigenfunctions, Usp. Math. Nauk 29 (1974) 181-182 (in Russian).
    • (1974) Usp. Math. Nauk , vol.29 , pp. 181-182
    • Shnirelman, A.I.1
  • 8
    • 0008995315 scopus 로고
    • On the asymptotic properties of eigenfunctions in the regions of chaotic motion
    • V.F. Lazutkin (Ed.), Springer, Berlin
    • A.I. Shnirelman, On the asymptotic properties of eigenfunctions in the regions of chaotic motion, in V.F. Lazutkin (Ed.), KAM Theory and Semiclassical Approximations to Eigenfunctions, Springer, Berlin, 1993.
    • (1993) KAM Theory and Semiclassical Approximations to Eigenfunctions
    • Shnirelman, A.I.1
  • 9
    • 84972564374 scopus 로고
    • Uniform distribution of eigenfunctions on compact hyperbolic surfaces
    • S. Zelditch, Uniform distribution of eigenfunctions on compact hyperbolic surfaces, Duke. Math. J. 55 (1987) 919-941.
    • (1987) Duke. Math. J. , vol.55 , pp. 919-941
    • Zelditch, S.1
  • 10
    • 14944371344 scopus 로고
    • Ergodicité et fonctions propres du laplacien
    • Y. Colin de Verdière, Ergodicité et fonctions propres du laplacien, Commun. Math. Phys. 102 (1985) 111-134.
    • (1985) Commun. Math. Phys. , vol.102 , pp. 111-134
    • De Colin Verdière, Y.1
  • 11
    • 84973997812 scopus 로고
    • Ergodic properties of eigenfunctions for the Dirichlet problem
    • P. Gérard, E. Leichtnam, Ergodic properties of eigenfunctions for the Dirichlet problem, Duke Math. J. 71 (1993) 559-607.
    • (1993) Duke Math. J. , vol.71 , pp. 559-607
    • Gérard, P.1    Leichtnam, E.2
  • 12
    • 0030530411 scopus 로고    scopus 로고
    • Ergodicity of eigenfunctions for ergodic billiards
    • S. Zelditch, M. Zworski, Ergodicity of eigenfunctions for ergodic billiards, Commun. Math. Phys. 175 (1996) 673-682.
    • (1996) Commun. Math. Phys. , vol.175 , pp. 673-682
    • Zelditch, S.1    Zworski, M.2
  • 13
    • 18444380929 scopus 로고
    • Bound-state eigenfunctions of classically chaotic Hamiltonian systems: Scars of periodic orbits
    • E.J. Heller, Bound-state eigenfunctions of classically chaotic Hamiltonian systems: scars of periodic orbits, Phys. Rev. Lett. 53 (1984) 1515-1518.
    • (1984) Phys. Rev. Lett. , vol.53 , pp. 1515-1518
    • Heller, E.J.1
  • 14
    • 0031582148 scopus 로고    scopus 로고
    • How chaotic is the stadium billiard? a semiclassical analysis
    • G. Tanner, How chaotic is the stadium billiard? a semiclassical analysis, J. Phys. A 30 (1997) 2863-2888.
    • (1997) J. Phys. A , vol.30 , pp. 2863-2888
    • Tanner, G.1
  • 15
    • 0031558524 scopus 로고    scopus 로고
    • On the number of bouncing-ball modes in billiards
    • A. Bäcker, R. Schubert, P. Stifter, On the number of bouncing-ball modes in billiards, J. Phys. A 30 (1997) 6783-6795.
    • (1997) J. Phys. A , vol.30 , pp. 6783-6795
    • Bäcker, A.1    Schubert, R.2    Stifter, P.3
  • 16
    • 0000662003 scopus 로고
    • Arithmetic quantum chaos
    • P. Sarnak, Arithmetic quantum chaos, Israel Math. Conf. Proc. 8 (1995) 183-236.
    • (1995) Israel Math. Conf. Proc. , vol.8 , pp. 183-236
    • Sarnak, P.1
  • 18
    • 0346831238 scopus 로고
    • Quantum eigenstates of a strongly chaotic system and the scar phenomenon
    • R. Aurich, F. Steiner, Quantum eigenstates of a strongly chaotic system and the scar phenomenon, Chaos Solitons Fractals 5 (1995) 229-255.
    • (1995) Chaos Solitons Fractals , vol.5 , pp. 229-255
    • Aurich, R.1    Steiner, F.2
  • 20
    • 0001743035 scopus 로고
    • Bounds for eigenfunctions of differential operators
    • A. Seeger, C.D. Sogge, Bounds for eigenfunctions of differential operators, Indiana Univ. Math. J. 38 (1989) 669-682.
    • (1989) Indiana Univ. Math. J. , vol.38 , pp. 669-682
    • Seeger, A.1    Sogge, C.D.2
  • 21
    • 33646945324 scopus 로고
    • The spectral function for an elliptic operator
    • L. Hörmander, The spectral function for an elliptic operator, Acta Math. 127 (1968) 193-218.
    • (1968) Acta Math. , vol.127 , pp. 193-218
    • Hörmander, L.1
  • 23
    • 0001656782 scopus 로고
    • L∞ norms of eigenfunctions of arithmetic surfaces
    • H. Iwaniec, P. Sarnak, L∞ norms of eigenfunctions of arithmetic surfaces, Ann. Math. 141 (1995) 301-320.
    • (1995) Ann. Math. , vol.141 , pp. 301-320
    • Iwaniec, H.1    Sarnak, P.2
  • 24
    • 21344499327 scopus 로고
    • The behaviour of eigenstates of arithmetic hyperbolic manifolds
    • Z. Rudnick, P. Sarnak, The behaviour of eigenstates of arithmetic hyperbolic manifolds, Commun. Math. Phys. 161 (1994) 195-213.
    • (1994) Commun. Math. Phys. , vol.161 , pp. 195-213
    • Rudnick, Z.1    Sarnak, P.2
  • 25
    • 84974003809 scopus 로고
    • L∞-norms of eigenfunctions for arithmetic hyperbolic three-manifolds
    • S.Y. Koyama, L∞-norms of eigenfunctions for arithmetic hyperbolic three-manifolds, Duke Math. J. 77 (1995) 799-817.
    • (1995) Duke Math. J. , vol.77 , pp. 799-817
    • Koyama, S.Y.1
  • 26
    • 0000553312 scopus 로고
    • On the periodic orbits of a strongly chaotic system
    • R. Aurich, F. Steiner, On the periodic orbits of a strongly chaotic system, Physica D 32 (1988) 451-460.
    • (1988) Physica D , vol.32 , pp. 451-460
    • Aurich, R.1    Steiner, F.2
  • 28
    • 2442581340 scopus 로고
    • Arithmetical chaos and violation of universality in energy level statistics
    • J. Bolte, G. Steil, F. Steiner, Arithmetical chaos and violation of universality in energy level statistics, Phys. Rev. Lett. 69 (1992) 2188-2191.
    • (1992) Phys. Rev. Lett. , vol.69 , pp. 2188-2191
    • Bolte, J.1    Steil, G.2    Steiner, F.3
  • 29
    • 0039443227 scopus 로고
    • Some studies on arithmetical chaos in classical and quantum mechanics
    • J. Bolte, Some studies on arithmetical chaos in classical and quantum mechanics, Int. J. Mod. Phys B 7 (1993) 4451-4553.
    • (1993) Int. J. Mod. Phys B , vol.7 , pp. 4451-4553
    • Bolte, J.1
  • 30
    • 0001172372 scopus 로고
    • On the subtleties of arithmetical quantum chaos
    • R. Aurich, F. Scheffler, F. Steiner, On the subtleties of arithmetical quantum chaos, Phys. Rev. E 51 (1995) 4173-4189.
    • (1995) Phys. Rev. E , vol.51 , pp. 4173-4189
    • Aurich, R.1    Scheffler, F.2    Steiner, F.3
  • 32
    • 0001264939 scopus 로고    scopus 로고
    • L∞ norms and quantum ergodicity on the sphere
    • J.M. VanderKam, L∞ norms and quantum ergodicity on the sphere, Int. Math. Res. Notices 7 (1997) 329-347.
    • (1997) Int. Math. Res. Notices , vol.7 , pp. 329-347
    • Vanderkam, J.M.1
  • 35
    • 0001358945 scopus 로고
    • Some properties of trigonometric series whose terms have random signs
    • R. Salem, A. Zygmund, Some properties of trigonometric series whose terms have random signs, Acta Math. 91 (1954) 245-301.
    • (1954) Acta Math. , vol.91 , pp. 245-301
    • Salem, R.1    Zygmund, A.2
  • 36
    • 24144467398 scopus 로고
    • Growth and geometry of eigenfunctions of the Laplacian, in Analysis and partial differential equations: A collection of papers dedicated to Mischa Cotlar
    • H. Donnelly, C. Fefferman, Growth and geometry of eigenfunctions of the Laplacian, in Analysis and partial differential equations: a collection of papers dedicated to Mischa Cotlar, Lecture Notes Pure Appl. Math. 122 (1990) 635-655.
    • (1990) Lecture Notes Pure Appl. Math. , vol.122 , pp. 635-655
    • Donnelly, H.1    Fefferman, C.2
  • 37
    • 0009074255 scopus 로고    scopus 로고
    • A random matrix model for quantum mixing
    • S. Zelditch, A random matrix model for quantum mixing, Int. Math. Res. Notices 3 (1996) 115-137.
    • (1996) Int. Math. Res. Notices , vol.3 , pp. 115-137
    • Zelditch, S.1
  • 39
    • 0242353287 scopus 로고    scopus 로고
    • On the rate of quantum ergodicity on hyperbolic surfaces and billiards
    • R. Aurich, M. Taglieber, On the rate of quantum ergodicity on hyperbolic surfaces and billiards, Physica D 118 (1998) 84-102.
    • (1998) Physica D , vol.118 , pp. 84-102
    • Aurich, R.1    Taglieber, M.2
  • 40
    • 4243649192 scopus 로고    scopus 로고
    • Rate of quantum ergodicity in Euclidean billiards
    • A. Bäcker, R. Schubert, P. Stifter, Rate of quantum ergodicity in Euclidean billiards, Phys. Rev. E 57 (1998) 5425-5447.
    • (1998) Phys. Rev. E , vol.57 , pp. 5425-5447
    • Bäcker, A.1    Schubert, R.2    Stifter, P.3
  • 41
    • 29444443343 scopus 로고
    • On the ergodic properties of nowhere dispersing billiards
    • L.A. Bunimovich, On the ergodic properties of nowhere dispersing billiards, Commun. Math. Phys. 65 (1979) 295-312.
    • (1979) Commun. Math. Phys. , vol.65 , pp. 295-312
    • Bunimovich, L.A.1
  • 42
    • 0001454859 scopus 로고
    • Classical dynamics of a family of billiards with analytic boundaries
    • M. Robnik, Classical dynamics of a family of billiards with analytic boundaries, J. Phys. A 16 (1983) 3971-3986.
    • (1983) J. Phys. A , vol.16 , pp. 3971-3986
    • Robnik, M.1
  • 43
    • 0001043657 scopus 로고
    • Ergodicity in Hamiltonian systems
    • C.K.R.T. Jones, U. Kirchgraber, H.O. Walther (Eds.), Springer, Berlin
    • C. Liverani, M.P. Wojtkowski, Ergodicity in Hamiltonian systems, in: C.K.R.T. Jones, U. Kirchgraber, H.O. Walther (Eds.), Dynamics Reported. Expositions in Dynamical Systems. New series. Vol. 4, Springer, Berlin, 1995, pp. 130-202.
    • (1995) Dynamics Reported. Expositions in Dynamical Systems. New Series , vol.4 , pp. 130-202
    • Liverani, C.1    Wojtkowski, M.P.2
  • 44
    • 0030541582 scopus 로고    scopus 로고
    • Nonuniformly hyperbolic K-systems are Bernoulli
    • N.I. Chernov, C.Haskell, Nonuniformly hyperbolic K-systems are Bernoulli, Ergod. Th. Dynam. Sys. 16 (1996) 19-44.
    • (1996) Ergod. Th. Dynam. Sys. , vol.16 , pp. 19-44
    • Chernov, N.I.1    Haskell, C.2
  • 46
    • 36149039923 scopus 로고
    • Quantising a generic family of billiards with analytic boundaries
    • M. Robnik, Quantising a generic family of billiards with analytic boundaries, J. Phys. A 17 (1984) 1049-1074.
    • (1984) J. Phys. A , vol.17 , pp. 1049-1074
    • Robnik, M.1
  • 47
    • 21144475698 scopus 로고
    • Energy level statistics in the transition region between integrability and chaos
    • T. Prosen, M. Robnik, Energy level statistics in the transition region between integrability and chaos, J. Phys. A 26 (1993) 2371-2387.
    • (1993) J. Phys. A , vol.26 , pp. 2371-2387
    • Prosen, T.1    Robnik, M.2
  • 48
    • 0003009280 scopus 로고
    • Boundary-distribution solution of the Helmholtz equation for a region with corners
    • R.J. Riddel Jr., Boundary-distribution solution of the Helmholtz equation for a region with corners, J. Comp. Phys. 31 (1979) 21-41.
    • (1979) J. Comp. Phys. , vol.31 , pp. 21-41
    • Riddel R.J., Jr.1
  • 49
  • 51
    • 0009290263 scopus 로고    scopus 로고
    • On value distribution properties of automorphic functions along closed horocycles
    • I. Laine et al. (Eds.), Finland, 1-5 August 1995, Walter de Gruyter, Berlin
    • D.A. Hejhal, On value distribution properties of automorphic functions along closed horocycles, in: I. Laine et al. (Eds.), 16th Rolf Nevanlinna colloquium, Proc. Int. Conference held in Joensuu, Finland, 1-5 August 1995, Walter de Gruyter, Berlin, 1996, pp. 39-52.
    • (1996) 16th Rolf Nevanlinna Colloquium, Proc. Int. Conference Held in Joensuu , pp. 39-52
    • Hejhal, D.A.1
  • 52
    • 0010115710 scopus 로고
    • Born-Oppenheimer adiabatic mechanism for regularity of states in the quantum stadium billiard
    • Y.Y. Bai, G. Hose, K. Stefański, H.S. Taylor, Born-Oppenheimer adiabatic mechanism for regularity of states in the quantum stadium billiard, Phys. Rev. A 31 (1985) 2821-2826.
    • (1985) Phys. Rev. A , vol.31 , pp. 2821-2826
    • Bai, Y.Y.1    Hose, G.2    Stefański, K.3    Taylor, H.S.4
  • 53
    • 45549120661 scopus 로고
    • Smoothed wave functions of chaotic quantum systems
    • E.B. Bogomolny, Smoothed wave functions of chaotic quantum systems, Physica D 31 (1988) 169-189.
    • (1988) Physica D , vol.31 , pp. 169-189
    • Bogomolny, E.B.1


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