메뉴 건너뛰기




Volumn 690, Issue , 2006, Pages 367-381

Recent results on quantum map eigenstates

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33749026652     PISSN: 00758450     EISSN: None     Source Type: Book Series    
DOI: 10.1007/3-540-34273-7_27     Document Type: Article
Times cited : (2)

References (26)
  • 1
    • 26844555937 scopus 로고    scopus 로고
    • The eigenfunctions of the Laplacian do not concentrate on sets of small topological entropy
    • preprint june
    • N. Anantharaman, The eigenfunctions of the Laplacian do not concentrate on sets of small topological entropy, preprint june 2004.
    • (2004)
    • Anantharaman, N.1
  • 2
    • 33749006401 scopus 로고    scopus 로고
    • private communication, march
    • N. Anantharaman, private communication, march 2005.
    • (2005)
    • Anantharaman, N.1
  • 3
    • 0041972697 scopus 로고    scopus 로고
    • Ruelle-Perron-Frobenius spectrum for Anosov maps
    • M. Blank, G. Keller, C. Liverani, Ruelle-Perron-Frobenius spectrum for Anosov maps, Nonlinearity 15, no. 6, 1905-1973 (2002).
    • (2002) Nonlinearity , vol.15 , Issue.6 , pp. 1905-1973
    • Blank, M.1    Keller, G.2    Liverani, C.3
  • 4
    • 33749024836 scopus 로고    scopus 로고
    • Long time propagation and control on scarring for perturbed quantized hyperbolic toral automorphisms
    • mp_arc 04-305 to appear
    • J. M. Bouclet, S. De Bièvre, Long time propagation and control on scarring for perturbed quantized hyperbolic toral automorphisms, mp_arc 04-305, Annales H. Poincaré, to appear.
    • Annales H. Poincaré
    • Bouclet, J.M.1    De Bièvre, S.2
  • 5
    • 0001920949 scopus 로고    scopus 로고
    • Equipartition of the eigenfunctions of quantized ergodic maps on the torus
    • A. Bouzouina, S De Biévre, Equipartition of the eigenfunctions of quantized ergodic maps on the torus, Comm. Math. Phys. 178, 83-105 (1996).
    • (1996) Comm. Math. Phys. , vol.178 , pp. 83-105
    • Bouzouina, A.1    De Bièvre, S.2
  • 6
    • 0032039822 scopus 로고    scopus 로고
    • Equidistribution des valeurs propres et ergodicité semi-classique de symplectomorphismes du tore quantifiés
    • A. Bouzouina, S. De Bièvre, Equidistribution des valeurs propres et ergodicité semi-classique de symplectomorphismes du tore quantifiés, C. R. Acad. Sci. Paris, Série I t.326, 1021-1024 (1998).
    • (1998) C. R. Acad. Sci. Paris, Série I , vol.326 , pp. 1021-1024
    • Bouzouina, A.1    De Bièvre, S.2
  • 7
    • 11244271621 scopus 로고    scopus 로고
    • A lower bound for periods of matrices
    • P. Corvaja, Z. Rudnick, U. Zannier, A lower bound for periods of matrices, Comm. Math. Phys. 252, 1-3, 535-541 (2004).
    • (2004) Comm. Math. Phys. , vol.252 , Issue.1-3 , pp. 535-541
    • Corvaja, P.1    Rudnick, Z.2    Zannier, U.3
  • 8
    • 0034178794 scopus 로고    scopus 로고
    • Exponential mixing and lnh time scales in quantized hyperbolic maps on the torus
    • F. Bonecchi, S. De Bièvre, Exponential mixing and lnh time scales in quantized hyperbolic maps on the torus, Comm. Math. Phys. 211, 659-686 (2000).
    • (2000) Comm. Math. Phys. , vol.211 , pp. 659-686
    • Bonecchi, F.1    De Bièvre, S.2
  • 9
    • 0037534326 scopus 로고    scopus 로고
    • Controlling strong scarring for quantized ergodic toral automorphisms
    • F. Bonecchi, S. De Bièvre, Controlling strong scarring for quantized ergodic toral automorphisms, Duke Math. J, Vol. 117, No. 3, 571-587 (2003).
    • (2003) Duke Math. J , vol.117 , Issue.3 , pp. 571-587
    • Bonecchi, F.1    De Bièvre, S.2
  • 10
    • 26844483650 scopus 로고    scopus 로고
    • Controlling strong scarring for quantized ergodic toral automorphisms
    • Section 5, mp arc 02-81
    • F. Bonecchi, S. De Bi èvre, Controlling strong scarring for quantized ergodic toral automorphisms, Section 5, mp arc 02-81 (2002).
    • (2002)
    • Bonecchi, F.1    De Bièvre, S.2
  • 11
    • 0038741639 scopus 로고    scopus 로고
    • Quantum chaos: A brief first visit
    • mp_arc 01-207
    • S. De Bièvre, Quantum chaos: A brief first visit, mp_arc 01-207, Contemporary Mathematics 289, 161-218 (2001).
    • (2001) Contemporary Mathematics , vol.289 , pp. 161-218
    • De Bièvre, S.1
  • 12
    • 0002218395 scopus 로고    scopus 로고
    • Egorov Theorems and equipartition of eigenfunctions for quantized sawtooth and Baker maps on the torus
    • mp_arc 96-210
    • S. De Bièvre, M. Degli Esposti, Egorov Theorems and equipartition of eigenfunctions for quantized sawtooth and Baker maps on the torus, mp_arc 96-210, Ann. Inst. H. Poincaré 69, 1, 1-30 (1998).
    • (1998) Ann. Inst. H. Poincaré , vol.69 , Issue.1 , pp. 1-30
    • De Bièvre, S.1    Degli Esposti, M.2
  • 13
    • 0000390289 scopus 로고
    • Stochastic properties of the quantum Arnold cat in the classical limit
    • M. Degli Esposti, S. Graffi, S. Isola, Stochastic properties of the quantum Arnold cat in the classical limit, Commun. Math. Phys. 167, 471-509 (1995).
    • (1995) Commun. Math. Phys. , vol.167 , pp. 471-509
    • Degli Esposti, M.1    Graffi, S.2    Isola, S.3
  • 15
    • 0042417242 scopus 로고    scopus 로고
    • Scarred eigenstates for quantum cats of minimal periods
    • F. Faure, S. Nonnenmacher, S. De Bièvre, Scarred eigenstates for quantum cats of minimal periods, Commun. Math. Phys. 239, 449-492 (2003).
    • (2003) Commun. Math. Phys. , vol.239 , pp. 449-492
    • Faure, F.1    Nonnenmacher, S.2    De Bièvre, S.3
  • 16
    • 1542718367 scopus 로고    scopus 로고
    • On the maximal scarring for quantum cat map eigenstates
    • F. Faure, S. Nonnenmacher, On the maximal scarring for quantum cat map eigenstates, Commun. Math. Phys. 245, 201-214 (2004).
    • (2004) Commun. Math. Phys. , vol.245 , pp. 201-214
    • Faure, F.1    Nonnenmacher, S.2
  • 18
    • 84956071876 scopus 로고
    • Quantization of linear maps-Fresnel diffraction by a periodic grating
    • J.H. Hannay, M.V. Berry, Quantization of linear maps-Fresnel diffraction by a periodic grating, Physica D 1, 267-290 (1980).
    • (1980) Physica D , vol.1 , pp. 267-290
    • Hannay, J.H.1    Berry, M.V.2
  • 19
    • 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, 16, 1515-1518 (1984).
    • (1984) Phys. Rev. Lett. , vol.53 , Issue.16 , pp. 1515-1518
    • Heller, E.J.1
  • 20
    • 0000370409 scopus 로고
    • Asymptotic properties of the periodic orbits of the cat maps
    • J.P. Keating, Asymptotic properties of the periodic orbits of the cat maps, Nonlinearity 4, 277-307 (1990).
    • (1990) Nonlinearity , vol.4 , pp. 277-307
    • Keating, J.P.1
  • 21
    • 0034179090 scopus 로고    scopus 로고
    • Pseudo-symmetries of Anosov maps and Spectral statistics
    • J.P. Keating, F. Mezzadri, Pseudo-symmetries of Anosov maps and Spectral statistics, Nonlinearity 13, 747-775 (2000).
    • (2000) Nonlinearity , vol.13 , pp. 747-775
    • Keating, J.P.1    Mezzadri, F.2
  • 22
    • 0002273985 scopus 로고    scopus 로고
    • Hecke theory and equidistribution for the quantization of linear maps of the torus
    • P. Kurlberg, Z. Rudnick, Hecke theory and equidistribution for the quantization of linear maps of the torus, Duke Math. J. 103, 1, 47-77 (2000).
    • (2000) Duke Math. J. , vol.103 , Issue.1 , pp. 47-77
    • Kurlberg, P.1    Rudnick, Z.2
  • 23
    • 0035536274 scopus 로고    scopus 로고
    • On quantum ergodicity for linear maps of the torus
    • P. Kurlberg, Z. Rudnick, On quantum ergodicity for linear maps of the torus, Comm. Math. Phys. 222, 1, 201-227 (2001).
    • (2001) Comm. Math. Phys. , vol.222 , Issue.1 , pp. 201-227
    • Kurlberg, P.1    Rudnick, Z.2
  • 24
    • 84871173223 scopus 로고    scopus 로고
    • Invariant measures and arithmetic quantum unique ergodicity
    • to appear
    • E. Lindenstrauss, Invariant measures and arithmetic quantum unique ergodicity, Annals of Math., to appear.
    • Annals of Math.
    • Lindenstrauss, E.1
  • 25
    • 11844298351 scopus 로고    scopus 로고
    • Weyl's law and quantum ergodicity for maps with divided phase space
    • mp_arc 04-122
    • J. Marklof, S. O'Keefe, Weyl's law and quantum ergodicity for maps with divided phase space, mp_arc 04-122, Nonlinearity 18, 277-304 (2005).
    • (2005) Nonlinearity , vol.18 , pp. 277-304
    • Marklof, J.1    O'Keefe, S.2
  • 26
    • 79951804475 scopus 로고    scopus 로고
    • Quantum ergodicity and mixing of eigenfunctions
    • math-ph/0503026, preprint to appear
    • S. Zelditch, Quantum ergodicity and mixing of eigenfunctions, math-ph/ 0503026, preprint (2005), Elsevier Encyclopedia of Mathematical Physics, to appear.
    • (2005) Elsevier Encyclopedia of Mathematical Physics
    • Zelditch, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.