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Volumn 109, Issue 3-4, 2002, Pages 777-801

Algebraic decay in hierarchical graphs

Author keywords

Algebraic decay; Pollicott Ruelle resonances; Quantum scattering resonances; Survival probability

Indexed keywords


EID: 0036388160     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020427018179     Document Type: Article
Times cited : (4)

References (47)
  • 1
    • 48549109899 scopus 로고
    • Correlation properties of dynamical chaos in Hamiltonian systems
    • B. V. Chirikov and D. L. Shepelyansky, Correlation properties of dynamical chaos in Hamiltonian systems, Phys. D 13:395 (1984).
    • (1984) Phys. D , vol.13 , pp. 395
    • Chirikov, B.V.1    Shepelyansky, D.L.2
  • 3
    • 34250119129 scopus 로고
    • Algebraic decay in self-similar Markov chains
    • J. D. Hanson, J. R. Cary, and J. D. Meiss, Algebraic decay in self-similar Markov chains, J. Statist. Phys. 39:327 (1985).
    • (1985) J. Statist. Phys. , vol.39 , pp. 327
    • Hanson, J.D.1    Cary, J.R.2    Meiss, J.D.3
  • 4
    • 0000844752 scopus 로고
    • Markov tree model of intrinsic transport in Hamiltonian systems
    • J. D. Meiss and E. Ott, Markov tree model of intrinsic transport in Hamiltonian systems, Phys. Rev Lett. 55:2741 (1985).
    • (1985) Phys. Rev Lett. , vol.55 , pp. 2741
    • Meiss, J.D.1    Ott, E.2
  • 5
    • 46149130013 scopus 로고
    • Markov tree model of transport in area-preserving maps
    • J. D. Meiss and E. Ott, Markov tree model of transport in area-preserving maps, Phys. D 20:387 (1986).
    • (1986) Phys. D , vol.20 , pp. 387
    • Meiss, J.D.1    Ott, E.2
  • 7
    • 0010890055 scopus 로고
    • Symplectic maps, variational principles, and transport
    • J. D. Meiss, Symplectic maps, variational principles, and transport, Rev. Mod. Phys. 64:795 (1992).
    • (1992) Rev. Mod. Phys. , vol.64 , pp. 795
    • Meiss, J.D.1
  • 8
    • 17044374336 scopus 로고
    • On the rate of mixing of axiom a flows
    • M. Pollicott, On the rate of mixing of axiom a flows, Invent. Math. 81:413 (1985). D. Ruelle, Resonances of chaotic dynamical systems, Phys. Rev. Lett. 56:405 (1986); Locating resonances for Axiom A dynamical systems, J. Statist. Phys. 44:281 (1986); Resonances for Axiom A flows, J. Differential Geom. 25:99 (1987); One-dimensional Gibbs states and Axiom A diffeomorphisms, J. Differential Geom. 25:117 (1987).
    • (1985) Invent. Math. , vol.81 , pp. 413
    • Pollicott, M.1
  • 9
    • 0001337517 scopus 로고
    • Resonances of chaotic dynamical systems
    • M. Pollicott, On the rate of mixing of axiom a flows, Invent. Math. 81:413 (1985). D. Ruelle, Resonances of chaotic dynamical systems, Phys. Rev. Lett. 56:405 (1986); Locating resonances for Axiom A dynamical systems, J. Statist. Phys. 44:281 (1986); Resonances for Axiom A flows, J. Differential Geom. 25:99 (1987); One-dimensional Gibbs states and Axiom A diffeomorphisms, J. Differential Geom. 25:117 (1987).
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 405
    • Ruelle, D.1
  • 10
    • 0000792565 scopus 로고
    • M. Pollicott, On the rate of mixing of axiom a flows, Invent. Math. 81:413 (1985). D. Ruelle, Resonances of chaotic dynamical systems, Phys. Rev. Lett. 56:405 (1986); Locating resonances for Axiom A dynamical systems, J. Statist. Phys. 44:281 (1986); Resonances for Axiom A flows, J. Differential Geom. 25:99 (1987); One-dimensional Gibbs states and Axiom A diffeomorphisms, J. Differential Geom. 25:117 (1987).
    • (1986) J. Statist. Phys. , vol.44 , pp. 281
  • 11
    • 6144269308 scopus 로고
    • M. Pollicott, On the rate of mixing of axiom a flows, Invent. Math. 81:413 (1985). D. Ruelle, Resonances of chaotic dynamical systems, Phys. Rev. Lett. 56:405 (1986); Locating resonances for Axiom A dynamical systems, J. Statist. Phys. 44:281 (1986); Resonances for Axiom A flows, J. Differential Geom. 25:99 (1987); One-dimensional Gibbs states and Axiom A diffeomorphisms, J. Differential Geom. 25:117 (1987).
    • (1987) J. Differential Geom. , vol.25 , pp. 99
  • 12
    • 84972533601 scopus 로고
    • M. Pollicott, On the rate of mixing of axiom a flows, Invent. Math. 81:413 (1985). D. Ruelle, Resonances of chaotic dynamical systems, Phys. Rev. Lett. 56:405 (1986); Locating resonances for Axiom A dynamical systems, J. Statist. Phys. 44:281 (1986); Resonances for Axiom A flows, J. Differential Geom. 25:99 (1987); One-dimensional Gibbs states and Axiom A diffeomorphisms, J. Differential Geom. 25:117 (1987).
    • (1987) J. Differential Geom. , vol.25 , pp. 117
  • 15
    • 6144292336 scopus 로고
    • Chaotic scattering theory, thermodynamic formalism, and transport coefficients
    • P. Gaspard and J. R. Dorfman, Chaotic scattering theory, thermodynamic formalism, and transport coefficients, Phys. Rev. E 52:3525 (1995).
    • (1995) Phys. Rev. E , vol.52 , pp. 3525
    • Gaspard, P.1    Dorfman, J.R.2
  • 16
    • 35949007775 scopus 로고
    • Chaotic scattering theory of transport reaction-rate coefficients
    • J. R. Dorfman and P. Gaspard, Chaotic scattering theory of transport and reaction-rate coefficients, Phys. Rev. E51, 28 (1995).
    • (1995) Phys. Rev. E , vol.51 , pp. 28
    • Dorfman, J.R.1    Gaspard, P.2
  • 17
    • 0001437632 scopus 로고
    • Transport properties, Lyapunov exponents, and entropy per unit time
    • P. Gaspard and G. Nicolis, Transport properties, Lyapunov exponents, and entropy per unit time, Phys. Rev. Lett. 65:1693 (1990).
    • (1990) Phys. Rev. Lett. , vol.65 , pp. 1693
    • Gaspard, P.1    Nicolis, G.2
  • 18
    • 0034297708 scopus 로고    scopus 로고
    • Frobenius-Perron resonances for maps with a mixed phase space
    • J. Weber, F. Haake, and P. Šeba, Frobenius-Perron resonances for maps with a mixed phase space, Phys. Rev. Lett. 85:3620 (2000).
    • (2000) Phys. Rev. Lett. , vol.85 , pp. 3620
    • Weber, J.1    Haake, F.2    Šeba, P.3
  • 19
    • 0034293773 scopus 로고    scopus 로고
    • Relaxation to the invariant density for the kicked rotor
    • M. Khodas, S. Fishman, and O. Agam, Relaxation to the invariant density for the kicked rotor, Phys. Rev. E 62:4769 (2000).
    • (2000) Phys. Rev. E , vol.62 , pp. 4769
    • Khodas, M.1    Fishman, S.2    Agam, O.3
  • 20
    • 0035795879 scopus 로고    scopus 로고
    • Conductance fluctuations of generic billiards: Fractal or isolated?
    • L. Hufnagel, R. Ketzmerick, and M. Weiss, Conductance fluctuations of generic billiards: Fractal or isolated?, Europhys Lett. 54:703 (2001).
    • (2001) Europhys Lett. , vol.54 , pp. 703
    • Hufnagel, L.1    Ketzmerick, R.2    Weiss, M.3
  • 21
    • 0039248446 scopus 로고
    • Ph.D. thesis (University of Utrecht, Utrecht)
    • G. A. van Velzen, Lorentz Lattice Gases, Ph.D. thesis (University of Utrecht, Utrecht, 1990).
    • (1990) Lorentz Lattice Gases
    • Van Velzen, G.A.1
  • 23
    • 0000640914 scopus 로고    scopus 로고
    • Hydrodynamic modes as singular eigenstates of the Liouvillian dynamics: Deterministic diffusion
    • P. Gaspard, Hydrodynamic modes as singular eigenstates of the Liouvillian dynamics: Deterministic diffusion, Phys. Rev. E 53:4379 (1996).
    • (1996) Phys. Rev. E , vol.53 , pp. 4379
    • Gaspard, P.1
  • 25
    • 0345982349 scopus 로고    scopus 로고
    • Chaotic dynamics and the origin of statistical laws
    • August
    • G. M. Zaslavsky, Chaotic dynamics and the origin of statistical laws, Physics Today 39 (August 1999).
    • (1999) Physics Today , vol.39
    • Zaslavsky, G.M.1
  • 26
    • 0001318852 scopus 로고    scopus 로고
    • Fractal conductance fluctuations in generic chaotic cavities
    • R. Ketzmerick, Fractal conductance fluctuations in generic chaotic cavities, Phys. Rev. B 54:10841 (1996).
    • (1996) Phys. Rev. B , vol.54 , pp. 10841
    • Ketzmerick, R.1
  • 27
    • 0001257553 scopus 로고    scopus 로고
    • Quantum chaos on graphs
    • T. Kottos and U. Smilansky, Quantum chaos on graphs, Phys. Rev. Lett. 79:4794 (1997); Periodic orbit theory and spectral statistics for quantum graphs, Ann. Physics 274:76 (1999).
    • (1997) Phys. Rev. Lett. , vol.79 , pp. 4794
    • Kottos, T.1    Smilansky, U.2
  • 28
    • 0347963946 scopus 로고    scopus 로고
    • Periodic orbit theory and spectral statistics for quantum graphs
    • T. Kottos and U. Smilansky, Quantum chaos on graphs, Phys. Rev. Lett. 79:4794 (1997); Periodic orbit theory and spectral statistics for quantum graphs, Ann. Physics 274:76 (1999).
    • (1999) Ann. Physics , vol.274 , pp. 76
  • 29
    • 0034588698 scopus 로고    scopus 로고
    • Spectral statistics for quantum graphs: Periodic orbits and combinatorics
    • H. Schanz and U. Smilansky, Spectral statistics for quantum graphs: Periodic orbits and combinatorics, Philos. Mag. B 80:1999 (2000).
    • (2000) Philos. Mag. B , vol.80 , pp. 1999
    • Schanz, H.1    Smilansky, U.2
  • 30
    • 0033550128 scopus 로고    scopus 로고
    • Two-point spectral correlations for star graphs
    • G. Berkolaiko and J. P. Keating, Two-point spectral correlations for star graphs, J. Phys. A: Math. & Gen. 32:7827 (1999).
    • (1999) J. Phys. A: Math. & Gen. , vol.32 , pp. 7827
    • Berkolaiko, G.1    Keating, J.P.2
  • 31
    • 0034288234 scopus 로고    scopus 로고
    • On the level spacing distribution in quantum graphs
    • F. Barra and P. Gaspard, On the level spacing distribution in quantum graphs, J. Statist. Phys. 101:283 (2000).
    • (2000) J. Statist. Phys. , vol.101 , pp. 283
    • Barra, F.1    Gaspard, P.2
  • 32
    • 41349114577 scopus 로고    scopus 로고
    • Transport and dynamics on open quantum graphs
    • F. Barra and P. Gaspard, Transport and dynamics on open quantum graphs, Phys. Rev. E 65:016205 (2002).
    • (2002) Phys. Rev. E , vol.65 , pp. 016205
    • Barra, F.1    Gaspard, P.2
  • 33
  • 34
    • 0346688180 scopus 로고    scopus 로고
    • Periodic-orbit theory of Anderson localization on graphs
    • H. Schanz and U. Smilansky, Periodic-orbit theory of Anderson localization on graphs, Phys. Rev. Lett. 84:1427 (2000).
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 1427
    • Schanz, H.1    Smilansky, U.2
  • 35
    • 4244085880 scopus 로고    scopus 로고
    • Classical dynamics on graphs
    • F. Barra and P. Gaspard, Classical dynamics on graphs, Phys. Rev. E 63:66215 (2001).
    • (2001) Phys. Rev. E , vol.63 , pp. 66215
    • Barra, F.1    Gaspard, P.2
  • 36
    • 0001569076 scopus 로고
    • Quantum conduction on a Cayley tree
    • B. Shapiro, Quantum conduction on a Cayley tree, Phys. Rev. Lett. 50:747 (1983).
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 747
    • Shapiro, B.1
  • 40
    • 4243980743 scopus 로고
    • Chaotic scattering and diffusion in the Lorentz gas
    • P. Gaspard and F. Baras, Chaotic scattering and diffusion in the Lorentz gas, Phys. Rev. E 51:5332 (1995).
    • (1995) Phys. Rev. E , vol.51 , pp. 5332
    • Gaspard, P.1    Baras, F.2
  • 42
    • 36549101751 scopus 로고
    • Scattering from a classically chaotic repeller
    • P. Gaspard and S. A. Rice, Scattering from a classically chaotic repeller, J. Chem. Phys. 90:2225 (1989); Semi-classical quantization of the scattering from a classically chaotic repeller, 90:2242 (1989); Exact quantization of the scattering from a classically chaotic repeller, 90:2255 (1989); Erratum: "Scattering from a classically chaotic repeller," 91:3279 (1989); Erratum: "Semi-classical quantization of the scattering from a classically chaotic repeller," 91:3279 (1989) Erratum: "Exact quantization of the scattering from a classically chaotic repeller," 91:3280 (1989).
    • (1989) J. Chem. Phys. , vol.90 , pp. 2225
    • Gaspard, P.1    Rice, S.A.2
  • 43
    • 85204099211 scopus 로고
    • P. Gaspard and S. A. Rice, Scattering from a classically chaotic repeller, J. Chem. Phys. 90:2225 (1989); Semi-classical quantization of the scattering from a classically chaotic repeller, 90:2242 (1989); Exact quantization of the scattering from a classically chaotic repeller, 90:2255 (1989); Erratum: "Scattering from a classically chaotic repeller," 91:3279 (1989); Erratum: "Semi-classical quantization of the scattering from a classically chaotic repeller," 91:3279 (1989) Erratum: "Exact quantization of the scattering from a classically chaotic repeller," 91:3280 (1989).
    • (1989) Semi-classical Quantization of the Scattering from a Classically Chaotic Repeller , vol.90 , pp. 2242
  • 44
    • 85204067096 scopus 로고
    • P. Gaspard and S. A. Rice, Scattering from a classically chaotic repeller, J. Chem. Phys. 90:2225 (1989); Semi-classical quantization of the scattering from a classically chaotic repeller, 90:2242 (1989); Exact quantization of the scattering from a classically chaotic repeller, 90:2255 (1989); Erratum: "Scattering from a classically chaotic repeller," 91:3279 (1989); Erratum: "Semi-classical quantization of the scattering from a classically chaotic repeller," 91:3279 (1989) Erratum: "Exact quantization of the scattering from a classically chaotic repeller," 91:3280 (1989).
    • (1989) Exact Quantization of the Scattering from a Classically Chaotic Repeller , vol.90 , pp. 2255
  • 45
    • 85204071232 scopus 로고    scopus 로고
    • Erratum: "Scattering from a classically chaotic repeller," 91:3279 (1989);
    • P. Gaspard and S. A. Rice, Scattering from a classically chaotic repeller, J. Chem. Phys. 90:2225 (1989); Semi-classical quantization of the scattering from a classically chaotic repeller, 90:2242 (1989); Exact quantization of the scattering from a classically chaotic repeller, 90:2255 (1989); Erratum: "Scattering from a classically chaotic repeller," 91:3279 (1989); Erratum: "Semi-classical quantization of the scattering from a classically chaotic repeller," 91:3279 (1989) Erratum: "Exact quantization of the scattering from a classically chaotic repeller," 91:3280 (1989).
  • 46
    • 85204079755 scopus 로고    scopus 로고
    • Erratum: "Semi-classical quantization of the scattering from a classically chaotic repeller," 91:3279 (1989)
    • P. Gaspard and S. A. Rice, Scattering from a classically chaotic repeller, J. Chem. Phys. 90:2225 (1989); Semi-classical quantization of the scattering from a classically chaotic repeller, 90:2242 (1989); Exact quantization of the scattering from a classically chaotic repeller, 90:2255 (1989); Erratum: "Scattering from a classically chaotic repeller," 91:3279 (1989); Erratum: "Semi-classical quantization of the scattering from a classically chaotic repeller," 91:3279 (1989) Erratum: "Exact quantization of the scattering from a classically chaotic repeller," 91:3280 (1989).
  • 47
    • 85204082954 scopus 로고    scopus 로고
    • Erratum: "Exact quantization of the scattering from a classically chaotic repeller," 91:3280 (1989).
    • P. Gaspard and S. A. Rice, Scattering from a classically chaotic repeller, J. Chem. Phys. 90:2225 (1989); Semi-classical quantization of the scattering from a classically chaotic repeller, 90:2242 (1989); Exact quantization of the scattering from a classically chaotic repeller, 90:2255 (1989); Erratum: "Scattering from a classically chaotic repeller," 91:3279 (1989); Erratum: "Semi-classical quantization of the scattering from a classically chaotic repeller," 91:3279 (1989) Erratum: "Exact quantization of the scattering from a classically chaotic repeller," 91:3280 (1989).


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