메뉴 건너뛰기




Volumn 35, Issue 3, 2002, Pages 539-564

Autocorrelation function of eigenstates in chaotic and mixed systems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0037169447     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/35/3/307     Document Type: Article
Times cited : (43)

References (59)
  • 1
    • 0000450808 scopus 로고
    • Regular and irregular semiclassical wavefunctions
    • Berry M V 1977 Regular and irregular semiclassical wavefunctions J. Phys. A: Math. Gen. 10 2083
    • (1977) J. Phys. A: Math. Gen. , vol.10 , pp. 2083
    • Berry, M.V.1
  • 2
    • 26144456693 scopus 로고
    • Wave chaos in the stadium: Statistical properties of short-wave solutions of the Helmholtz equation
    • McDonald S W and Kaufmann A N 1988 Wave chaos in the stadium: statistical properties of short-wave solutions of the Helmholtz equation Phys. Rev. A 37 3067
    • (1988) Phys. Rev. A , vol.37 , pp. 3067
    • McDonald, S.W.1    Kaufmann, A.N.2
  • 3
    • 0000956176 scopus 로고
    • Statistical properties of highly excited quantum eigenstates of a strongly chaotic system
    • Aurich R and Steiner F 1993 Statistical properties of highly excited quantum eigenstates of a strongly chaotic system Physica D 64 185
    • (1993) Physica D , vol.64 , pp. 185
    • Aurich, R.1    Steiner, F.2
  • 4
    • 36149033614 scopus 로고
    • Statistical properties of high-lying chaotic eigenstates
    • Li B and Robnik M 1994 Statistical properties of high-lying chaotic eigenstates J. Phys. A: Math. Gen. 27 5509
    • (1994) J. Phys. A: Math. Gen. , vol.27 , pp. 5509
    • Li, B.1    Robnik, M.2
  • 5
    • 35348855615 scopus 로고    scopus 로고
    • Semi-classical approximation in quantum mechanics. A survey of old and recent mathematical results
    • Robert D 1998 Semi-classical approximation in quantum mechanics. A survey of old and recent mathematical results Helv. Phys. Acta 71 44
    • (1998) Helv. Phys. Acta , vol.71 , pp. 44
    • Robert, D.1
  • 6
    • 0001022947 scopus 로고
    • Ergodic properties of eigenfunctions
    • in Russian
    • Shnirelman A I 1974 Ergodic properties of eigenfunctions Usp, Math. Nauk 29 181 (in Russian)
    • (1974) Usp. Math. Nauk , vol.29 , pp. 181
    • Shnirelman, A.I.1
  • 7
    • 84972564374 scopus 로고
    • Uniform distribution of eigenfunctions on compact hyperbolic surfaces
    • Zelditch S 1987 Uniform distribution of eigenfunctions on compact hyperbolic surfaces Duke. Math. J. 55 919
    • (1987) Duke. Math. J. , vol.55 , pp. 919
    • Zelditch, S.1
  • 8
    • 14944371344 scopus 로고
    • Ergodicité et fonctions propres du laplacien
    • in French
    • Colin de Verdiére Y 1985 Ergodicité et fonctions propres du laplacien Commun. Math. Phys. 102 497 (in French)
    • (1985) Commun. Math. Phys. , vol.102 , pp. 497
    • Colin de Verdiére, Y.1
  • 10
    • 84973997812 scopus 로고
    • Ergodic properties of eigenfunctions for the Dirichlet problem
    • Gérard P and Leichtnam E 1993 Ergodic properties of eigenfunctions for the Dirichlet problem Duke Math. J. 71 559
    • (1993) Duke Math. J. , vol.71 , pp. 559
    • Gérard, P.1    Leichtnam, E.2
  • 11
    • 0030530411 scopus 로고    scopus 로고
    • Ergodicity of eigenfunctions for ergodic billiards
    • Zelditch S and Zworski M 1996 Ergodicity of eigenfunctions for ergodic billiards Commun. Math. Phys. 175 673
    • (1996) Commun. Math. Phys. , vol.175 , pp. 673
    • Zelditch, S.1    Zworski, M.2
  • 12
    • 4243649192 scopus 로고    scopus 로고
    • Rate of quantum ergodicity in Euclidean billiards
    • Bäcker A, Schubert R and Stifter P 1998 Rate of quantum ergodicity in Euclidean billiards Phys. Rev. E 57 5425
    • (1998) Phys. Rev. E , vol.57 , pp. 5425
    • Bäcker, A.1    Schubert, R.2    Stifter, P.3
  • 14
    • 0002527909 scopus 로고
    • Semi-classical approximations
    • Voros A 1976 Semi-classical approximations Ann. Inst. H Poincaré A 24 31
    • (1976) Ann. Inst. H Poincaré A , vol.24 , pp. 31
    • Voros, A.1
  • 15
    • 0009446345 scopus 로고
    • Asymptotic ℏ-expansions of stationary quantum states
    • Voros A 1977 Asymptotic ℏ-expansions of stationary quantum states Ann. Inst. H Poincaré A 26 343
    • (1977) Ann. Inst. H Poincaré A , vol.26 , pp. 343
    • Voros, A.1
  • 18
    • 0001387597 scopus 로고    scopus 로고
    • Gaussian random eigenfunctions and spatial correlations in quantum dots
    • Srednicki M 1996 Gaussian random eigenfunctions and spatial correlations in quantum dots Phys. Rev. E 54 954
    • (1996) Phys. Rev. E , vol.54 , pp. 954
    • Srednicki, M.1
  • 19
    • 0000218306 scopus 로고    scopus 로고
    • Correlations in chaotic eigenfunctions at large separation
    • Hortikar S and Srednicki M 1998 Correlations in chaotic eigenfunctions at large separation Phys. Rev. Lett. 80 1646
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 1646
    • Hortikar, S.1    Srednicki, M.2
  • 20
    • 0032084156 scopus 로고    scopus 로고
    • Random matrix elements and eigenfunctions in chaotic systems
    • Hortikar S and Srednicki M 1998 Random matrix elements and eigenfunctions in chaotic systems Phys. Rev. E 57 7313
    • (1998) Phys. Rev. E , vol.57 , pp. 7313
    • Hortikar, S.1    Srednicki, M.2
  • 22
    • 0035860671 scopus 로고    scopus 로고
    • Correlations of chaotic eigenfunctions: A semiclassical analysis
    • Li B and Rouben D C 2001 Correlations of chaotic eigenfunctions: a semiclassical analysis J. Phys. A: Math. Gen. 34 7381
    • (2001) J. Phys. A: Math. Gen. , vol.34 , pp. 7381
    • Li, B.1    Rouben, D.C.2
  • 24
    • 3743125628 scopus 로고
    • Onset of chaos in an isolated energy eigenstate
    • Shapiro M and Goelman G 1984 Onset of chaos in an isolated energy eigenstate Phys. Rev. Lett. 53 1714
    • (1984) Phys. Rev. Lett. , vol.53 , pp. 1714
    • Shapiro, M.1    Goelman, G.2
  • 25
    • 0010045640 scopus 로고
    • Scaling laws and correlation length of quantum and classical ergodic states
    • Shapiro M, Ronkin J and Brumer P 1988 Scaling laws and correlation length of quantum and classical ergodic states Chem. Phys. Lett. 148 177
    • (1988) Chem. Phys. Lett. , vol.148 , pp. 177
    • Shapiro, M.1    Ronkin, J.2    Brumer, P.3
  • 26
    • 0033543389 scopus 로고    scopus 로고
    • Study of regular and irregular states in generic systems
    • Veble G, Robnik M and Liu J 1999 Study of regular and irregular states in generic systems J. Phys. A: Math. Gen. 32 6423
    • (1999) J. Phys. A: Math. Gen. , vol.32 , pp. 6423
    • Veble, G.1    Robnik, M.2    Liu, J.3
  • 28
    • 34250395980 scopus 로고
    • On ergodic properties of certain billiards
    • Bunimovich L A 1974 On ergodic properties of certain billiards Funct. Anal. Appl. 8 254
    • (1974) Funct. Anal. Appl. , vol.8 , pp. 254
    • Bunimovich, L.A.1
  • 29
    • 29444443343 scopus 로고
    • On the ergodic properties of nowhere dispersing billiards
    • Bunimovich LA 1979 On the ergodic properties of nowhere dispersing billiards Commun. Math. Phys. 65 295
    • (1979) Commun. Math. Phys. , vol.65 , pp. 295
    • Bunimovich, L.A.1
  • 30
    • 0001454859 scopus 로고
    • Classical dynamics of a family of billiards with analytic boundaries
    • Robnik M 1983 Classical dynamics of a family of billiards with analytic boundaries J. Phys. A: Math. Gen. 16 3971
    • (1983) J. Phys. A: Math. Gen. , vol.16 , pp. 3971
    • Robnik, M.1
  • 31
    • 36149039923 scopus 로고
    • Quantising a generic family of billiards with analytic boundaries
    • Robnik M 1984 Quantising a generic family of billiards with analytic boundaries J. Phys. A: Math. Gen. 17 1049
    • (1984) J. Phys. A: Math. Gen. , vol.17 , pp. 1049
    • Robnik, M.1
  • 32
    • 0000928980 scopus 로고
    • Principles for the design of billiards with nonvanishing Lyapunov exponents
    • Wojtkowski M 1986 Principles for the design of billiards with nonvanishing Lyapunov exponents Commun. Math. Phys. 105 391
    • (1986) Commun. Math. Phys. , vol.105 , pp. 391
    • Wojtkowski, M.1
  • 33
    • 0000232377 scopus 로고
    • On the K-property of some planar hyperbolic billiards
    • Szász D 1992 On the K-property of some planar hyperbolic billiards Commun. Math. Phys. 145 595
    • (1992) Commun. Math. Phys. , vol.145 , pp. 595
    • Szász, D.1
  • 34
    • 0001385478 scopus 로고
    • New ergodic billiards: Exact results
    • Markarian R 1993 New ergodic billiards: exact results Nonlinearity 6 819
    • (1993) Nonlinearity , vol.6 , pp. 819
    • Markarian, R.1
  • 36
    • 21144475698 scopus 로고
    • Energy level statistics in the transition region between integrability and chaos
    • Prosen T and Robnik M 1993 Energy level statistics in the transition region between integrability and chaos J. Phys. A: Math. Gen. 26 2371
    • (1993) J. Phys. A: Math. Gen. , vol.26 , pp. 2371
    • Prosen, T.1    Robnik, M.2
  • 37
    • 0003009280 scopus 로고
    • Boundary-distribution solution of the Helmholtz equation for a region with corners
    • Riddel R J Jr 1979 Boundary-distribution solution of the Helmholtz equation for a region with corners J. Comput. Phys. 31 21
    • (1979) J. Comput. Phys. , vol.31 , pp. 21
    • Riddel R.J., Jr.1
  • 38
    • 0000933445 scopus 로고
    • Diabolical points in the spectra of triangles
    • Berry M V and Wilkinson M 1984 Diabolical points in the spectra of triangles Proc. R. Soc. A 392 15
    • (1984) Proc. R. Soc. A , vol.392 , pp. 15
    • Berry, M.V.1    Wilkinson, M.2
  • 40
    • 0001744338 scopus 로고
    • Calculation of highly excited states of billiards
    • Vergini E and Saraceno M 1995 Calculation of highly excited states of billiards Phys. Rev. E 52 2204
    • (1995) Phys. Rev. E , vol.52 , pp. 2204
    • Vergini, E.1    Saraceno, M.2
  • 41
    • 18444380929 scopus 로고
    • Bound-state eigenfunctions of classically chaotic Hamiltonian systems: Scars of periodic orbits
    • Heller E J 1984 Bound-state eigenfunctions of classically chaotic Hamiltonian systems: scars of periodic orbits Phys. Rev. Lett. 53 1515
    • (1984) Phys. Rev. Lett. , vol.53 , pp. 1515
    • Heller, E.J.1
  • 42
    • 0010115710 scopus 로고
    • Born-oppenheimer adiabatic mechanism for regularity of states in the quantum stadium billiard
    • Bai Y Y, Hose G, Stefański K and Taylor H S 1985 Born-Oppenheimer adiabatic mechanism for regularity of states in the quantum stadium billiard Phys. Rev. A 31 2821
    • (1985) Phys. Rev. A , vol.31 , pp. 2821
    • Bai, Y.Y.1    Hose, G.2    Stefański, K.3    Taylor, H.S.4
  • 43
    • 4243704927 scopus 로고
    • Quantum localization for a strongly classically chaotic system
    • O'Connor P W and Heller E J 1988 Quantum localization for a strongly classically chaotic system Phys. Rev. Lett. 61 2288
    • (1988) Phys. Rev. Lett. , vol.61 , pp. 2288
    • O'Connor, P.W.1    Heller, E.J.2
  • 44
    • 0031582148 scopus 로고    scopus 로고
    • How chaotic is the stadium billiard? A semiclassical analysis
    • Tanner G 1997 How chaotic is the stadium billiard? A semiclassical analysis J. Phys. A: Math. Gen. 30 2863
    • (1997) J. Phys. A: Math. Gen. , vol.30 , pp. 2863
    • Tanner, G.1
  • 48
    • 0040634667 scopus 로고
    • Classical and quantum billiards, integrable, nonintegrable, and pseudo-integrable
    • Zyczkowski K 1992 Classical and quantum billiards, integrable, nonintegrable, and pseudo-integrable Acta Phys. Pol. B 23 245
    • (1992) Acta Phys. Pol. B , vol.23 , pp. 245
    • Zyczkowski, K.1
  • 49
  • 50
    • 0000518407 scopus 로고
    • Normal modes of billiards portrayed in the stellar (or nodal) representation
    • Tualle J M and Voros A 1995 Normal modes of billiards portrayed in the stellar (or nodal) representation, Chaos, Solitons Fractals 5 1085
    • (1995) Chaos, Solitons Fractals , vol.5 , pp. 1085
    • Tualle, J.M.1    Voros, A.2
  • 51
    • 0031249998 scopus 로고    scopus 로고
    • Quantitative study of scars in the boundary section of the stadium billiard
    • Simonotti F P, Vergini E and Saraceno M 1997 Quantitative study of scars in the boundary section of the stadium billiard Phys. Rev. E 56 3859
    • (1997) Phys. Rev. E , vol.56 , pp. 3859
    • Simonotti, F.P.1    Vergini, E.2    Saraceno, M.3
  • 52
    • 0037169436 scopus 로고    scopus 로고
    • Amplitude distribution of eigenfunctions in mixed systems
    • (preceding paper) (nlin.CD/0106017)
    • Bäcker A and Schubert R 2002 Amplitude distribution of eigenfunctions in mixed systems J. Phys. A: Math, Gen. 35 527 (preceding paper) (nlin.CD/0106017)
    • (2002) J. Phys. A: Math, Gen. , vol.35 , pp. 527
    • Bäcker, A.1    Schubert, R.2
  • 54
    • 0001222812 scopus 로고
    • Dynamical quasidegeneracies and separation of regular and irregular quantum levels
    • Bohigas O, Tomsovic S and Ullmo D 1990 Dynamical quasidegeneracies and separation of regular and irregular quantum levels Phys. Rev. Lett. 64 1479
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 1479
    • Bohigas, O.1    Tomsovic, S.2    Ullmo, D.3
  • 55
    • 21344479635 scopus 로고
    • Survey of the eigenfunctions of a billiard system between integrability and chaos
    • Prosen T and Robnik M 1993 Survey of the eigenfunctions of a billiard system between integrability and chaos J. Phys. A: Math. Gen. 26 5365
    • (1993) J. Phys. A: Math. Gen. , vol.26 , pp. 5365
    • Prosen, T.1    Robnik, M.2
  • 56
    • 21844481610 scopus 로고
    • Separating the regular and irregular energy levels and their statistics in a Hamiltonian system with mixed classical dynamics
    • Li B and Robnik M 1995 Separating the regular and irregular energy levels and their statistics in a Hamiltonian system with mixed classical dynamics J. Phys.-A: Math. Gen. 28 4843
    • (1995) J. Phys.-A: Math. Gen. , vol.28 , pp. 4843
    • Li, B.1    Robnik, M.2
  • 57
    • 21844504280 scopus 로고
    • Geometry of high-lying eigenfunctions in a plane billiard system having mixed-type classical dynamics
    • Li B and Robnik M 1995 Geometry of high-lying eigenfunctions in a plane billiard system having mixed-type classical dynamics J. Phys. A: Math. Gen. 28 2799
    • (1995) J. Phys. A: Math. Gen. , vol.28 , pp. 2799
    • Li, B.1    Robnik, M.2
  • 58
    • 0040644489 scopus 로고    scopus 로고
    • Numerical verification of Percival's conjecture in a quantum billiard
    • chao-dyn/9804016
    • Carlo G, Vergini E and Fendrik A 1998 Numerical verification of Percival's conjecture in a quantum billiard Phys. Rev. E 57 5397 (chao-dyn/9804016)
    • (1998) Phys. Rev. E , vol.57 , pp. 5397
    • Carlo, G.1    Vergini, E.2    Fendrik, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.