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Volumn 64, Issue 4, 2009, Pages 651-699

Anomalous current in periodic Lorentz gases with infinite horizon

Author keywords

Billiards; Diffusion; Electric current; Lorentz gas; Ohm's law

Indexed keywords


EID: 77951526945     PISSN: 00360279     EISSN: None     Source Type: Journal    
DOI: 10.1070/RM2009v064n04ABEH004630     Document Type: Article
Times cited : (51)

References (34)
  • 1
    • 6144222097 scopus 로고
    • Steady-state electrical conduction in the periodic Lorentz gas
    • N. I. Chernov, G.L. Eyink, J. L. Lebowitz, and Ya. G. Sinai, "Steady-state electrical conduction in the periodic Lorentz gas", Comm. Math. Phys. 154:3 (1993), 569-601.
    • (1993) Comm. Math. Phys , vol.154 , Issue.3 , pp. 569-601
    • Chernov, N.I.1    Eyink, G.L.2    Lebowitz, J.L.3    Sinai Ya., G.4
  • 2
    • 34548648549 scopus 로고    scopus 로고
    • Limit laws and recurrence for the planar Lorentz process with infinite horizon
    • D. Szász and T. Varjú, "Limit laws and recurrence for the planar Lorentz process with infinite horizon", J. Statist. Phys. 129:1 (2007), 59-80.
    • (2007) J. Statist. Phys , vol.129 , pp. 59-80
    • Szász, D.1    Varjú, T.2
  • 3
    • 0001457843 scopus 로고
    • The motion of electrons in metallic bodies
    • H. A. Lorentz, "The motion of electrons in metallic bodies", Proc. Amst. Acad. 7 (1904), 438-453.
    • (1904) Proc. Amst. Acad , vol.7 , pp. 438-453
    • Lorentz, H.A.1
  • 4
    • 77951589038 scopus 로고    scopus 로고
    • Russian source
  • 5
    • 84927896522 scopus 로고
    • Dynamical systems with elastic reflections
    • English transl
    • English transl., Ya. G. Sinai, "Dynamical systems with elastic reflections", Russian Math. Surveys 25:2 (1970), 137-189.
    • (1970) Russian Math. Surveys , vol.25 , Issue.2 , pp. 137-189
    • Sinai, Ya.G.1
  • 6
    • 0001822139 scopus 로고
    • Billiards and Bernoulli schemes
    • G. Gallavotti and D. S. Ornstein, "Billiards and Bernoulli schemes", Comm. Math. Phys. 38:2 (1974), 83-101.
    • (1974) Comm. Math. Phys , vol.38 , Issue.2 , pp. 83-101
    • Gallavotti, G.1    Ornstein, D.S.2
  • 7
    • 77951556136 scopus 로고    scopus 로고
    • Russian source
  • 8
    • 84956084246 scopus 로고
    • Statistical properties of two-dimensional hyperbolic billiards
    • English transl.
    • English transl., L.A. Bunimovich, Ya. G. Sinai, and N.I. Chernov, "Statistical properties of two-dimensional hyperbolic billiards", Russian Math. Surveys 46:4 (1991), 47-106.
    • (1991) Russian Math. Surveys , vol.46 , Issue.4 , pp. 47-106
    • Bunimovich, L.A.1    Sinai Ya., G.2    Chernov, N.I.3
  • 10
    • 11744373241 scopus 로고
    • Statistical properties of Lorentz gas with periodic configuration of scatterers
    • L.A. Bunimovich and Ya. G. Sinai, "Statistical properties of Lorentz gas with periodic configuration of scatterers", Coram. Math. Phys. 78:4 (1981), 479-497.
    • (1981) Coram. Math. Phys , vol.78 , Issue.4 , pp. 479-497
    • Bunimovich, L.A.1    Sinai Ya., G.2
  • 11
    • 0032348050 scopus 로고    scopus 로고
    • Statistical properties of dynamical systems with some hyperbolicity
    • 2
    • Lai-Sang Young, "Statistical properties of dynamical systems with some hyperbolicity", Ann. of Math. (2) 147:3 (1998), 585-650.
    • (1998) Ann. of Math. , vol.147 , Issue.3 , pp. 585-650
    • Young, L.-S.1
  • 12
    • 0001688902 scopus 로고
    • Derivation of Ohm's law in a deterministic mechanical model
    • N. I. Chernov, G.L. Eyink, J. L. Lebowitz, and Ya. G. Sinai, "Derivation of Ohm's law in a deterministic mechanical model", Phys. Rev. Lett. 70:15 (1993), 2209-2212.
    • (1993) Phys. Rev. Lett. , vol.70 , Issue.15 , pp. 2209-2212
    • Chernov, N.I.1    Eyink, G.L.2    Lebowitz, J.L.3    Sinai Ya., G.4
  • 13
    • 0001568349 scopus 로고
    • Diffusion in a periodic Lorentz gas
    • B. Moran, W. G. Hoover, and S. Bestiale, "Diffusion in a periodic Lorentz gas", J. Statist. Phys. 48:3-4 (1987), 709-726.
    • (1987) J. Statist. Phys. , vol.48 , Issue.3-4 , pp. 709-726
    • Moran, B.1    Hoover, W.G.2    Bestiale, S.3
  • 14
    • 0035532207 scopus 로고    scopus 로고
    • Sinai billiards under small external forces
    • N. Chernov, "Sinai billiards under small external forces", Ann. Henri Poincaré 2:2 (2001), 197-236.
    • (2001) Ann. Henri Poincaré , vol.2 , Issue.2 , pp. 197-236
    • Chernov, N.1
  • 15
    • 40949132133 scopus 로고    scopus 로고
    • Sinai billiards under small external forces. II
    • N. Chernov, "Sinai billiards under small external forces. II", Ann. Henri Poincaré 9:1 (2008), 91-107.
    • (2008) Ann. Henri Poincaré , vol.9 , Issue.1 , pp. 91-107
    • Chernov, N.1
  • 16
    • 34547223398 scopus 로고    scopus 로고
    • Diffusive motion and recurrence on an idealized Galton board
    • paper 030601
    • N. Chernov and D. Dolgopyat, "Diffusive motion and recurrence on an idealized Galton board", Phys. Rev. Lett. 99:3 (2007), paper 030601 (4 pages).
    • (2007) Phys. Rev. Lett. , vol.99 , Issue.3 , pp. 4
    • Chernov, N.1    Dolgopyat, D.2
  • 17
    • 70349264465 scopus 로고    scopus 로고
    • The Galton board: Limit theorems and recurrence
    • N. Chernov and D. Dolgopyat, "The Galton board: limit theorems and recurrence", J. Amer. Math. Soc. 22 (2009), 821-858.
    • (2009) J. Amer. Math. Soc. , vol.22 , pp. 821-858
    • Chernov, N.1    Dolgopyat, D.2
  • 20
    • 0000313327 scopus 로고
    • Statistical properties of two-dimensional periodic Lorentz gas with infinite horizon
    • P. M. Bleher, "Statistical properties of two-dimensional periodic Lorentz gas with infinite horizon", J. Statist. Phys. 66:1-2 (1992), 315-373.
    • (1992) J. Statist. Phys. , vol.66 , Issue.1-2 , pp. 315-373
    • Bleher, P.M.1
  • 21
    • 44949104085 scopus 로고    scopus 로고
    • Kinetic transport in the two-dimensional periodic lorentz gas
    • J. Marklof and A. Strömbergsson, "Kinetic transport in the two-dimensional periodic Lorentz gas", Nonlinearity 21:7 (2008), 1413-1422.
    • (2008) Nonlinearity , vol.21 , Issue.7 , pp. 1413-1422
    • Marklof, J.1    Strömbergsson, A.2
  • 22
    • 44949088428 scopus 로고    scopus 로고
    • The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems
    • to appear arxiv.org: 0706.4395
    • J. Marklof and A. Strömbergsson, "The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems", Ann. of Math. (to appear); arxiv.org: 0706.4395, 2007.
    • (2007) Ann. of Math.
    • Marklof, J.1    Strömbergsson, A.2
  • 23
    • 0033074305 scopus 로고    scopus 로고
    • Decay of correlations and dispersing billiards
    • N. Chernov, "Decay of correlations and dispersing billiards", J. Statist. Phys. 94:3-4 (1999), 513-556.
    • (1999) J. Statist. Phys. , vol.94 , Issue.3-4 , pp. 513-556
    • Chernov, N.1
  • 24
    • 84956256298 scopus 로고
    • Dimension, entropy and Lyapunov exponents
    • Lai-Sang Young, "Dimension, entropy and Lyapunov exponents", Ergodic Theory Dynam. Systems 2:1 (1982), 109-124.
    • (1982) Ergodic Theory Dynam. Systems , vol.2 , Issue.1 , pp. 109-124
    • Young, L.-S.1
  • 25
    • 14644396555 scopus 로고    scopus 로고
    • Statistical limit theorems for suspension flows
    • I. Melbourne and A. Török, "Statistical limit theorems for suspension flows", Israel J. Math. 144:2 (2004), 191-209.
    • (2004) Israel J. Math. , vol.144 , Issue.2 , pp. 191-209
    • Melbourne, I.1    Török, A.2
  • 26
    • 0034360484 scopus 로고    scopus 로고
    • W-flows on Weyl manifolds and Gaussian thermostats
    • 9
    • M. P. Wojtkowski, "W-flows on Weyl manifolds and Gaussian thermostats", J. Math. Pures Appl. (9) 79:10 (2000), 953-974.
    • (2000) J. Math. Pures Appl. , vol.79 , Issue.10 , pp. 953-974
    • Wojtkowski, M.P.1
  • 27
    • 21244475162 scopus 로고    scopus 로고
    • Billiards with polynomial mixing rates
    • N. Chernov and H.-K. Zhang, "Billiards with polynomial mixing rates", Nonlinearity 18:4 (2005), 1527-1553.
    • (2005) Nonlinearity , vol.18 , Issue.4 , pp. 1527-1553
    • Chernov, N.1    Zhang, H.-K.2
  • 28
    • 84971972535 scopus 로고
    • Dynamical systems with generalized hyperbolic attractors: Hyperbolic, ergodic and topological properties
    • Ya. B. Pesin, "Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties", Ergodic Theory Dynam. Systems 12:1 (1992), 123-151.
    • (1992) Ergodic Theory Dynam. Systems , vol.12 , Issue.1 , pp. 123-151
    • Pesin Ya., B.1
  • 29
    • 77951559524 scopus 로고
    • E.A.
    • E.A. YMH 47:1 (1992), 147-202;
    • (1992) YMH , vol.47 , Issue.1 , pp. 147-202
  • 30
    • 0001282015 scopus 로고
    • Invariant measures for hyperbolic maps with singularities
    • English transl
    • English transl., E.A. Sataev, "Invariant measures for hyperbolic maps with singularities", Russian Math. Surveys 47:1 (1992), 191-251.
    • (1992) Russian Math. Surveys , vol.47 , Issue.1 , pp. 191-251
    • Sataev, E.A.1
  • 32
    • 36448967888 scopus 로고    scopus 로고
    • Improved estimates for correlations in billiards
    • N. Chernov and H.-K. Zhang, "Improved estimates for correlations in billiards", Comm. Math. Phys. 277:2 (2008), 305-321.
    • (2008) Comm. Math. Phys. , vol.277 , Issue.2 , pp. 305-321
    • Chernov, N.1    Zhang, H.-K.2
  • 34
    • 1642331620 scopus 로고    scopus 로고
    • Limit theorems for partially hyperbolic systems
    • D. Dolgopyat, "Limit theorems for partially hyperbolic systems", Trans. Amer. Math. Soc. 356:4 (2004), 1637-1689.
    • (2004) Trans. Amer. Math. Soc , vol.356 , Issue.4 , pp. 1637-1689
    • Dolgopyat, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.