메뉴 건너뛰기




Volumn 269, Issue 2, 2007, Pages 425-471

The distribution of the free path lengths in the periodic two-dimensional Lorentz gas in the small-scatterer limit

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33845755341     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0137-7     Document Type: Article
Times cited : (44)

References (36)
  • 2
    • 0037805841 scopus 로고
    • Thom's problem on irrational flows
    • Blank, S., Krikorian, N.: Thom's problem on irrational flows. Internat. J. Math. 4, 721-726 (1993)
    • (1993) Internat. J. Math. , vol.4 , pp. 721-726
    • Blank, S.1    Krikorian, N.2
  • 3
    • 0000313327 scopus 로고
    • Statistical properties of two-dimensional periodic Lorentz with infinite horizon
    • Bleher, P.: Statistical properties of two-dimensional periodic Lorentz with infinite horizon. J. Stat. Phys. 66, 315-373 (1992)
    • (1992) J. Stat. Phys. , vol.66 , pp. 315-373
    • Bleher, P.1
  • 4
    • 0034349969 scopus 로고    scopus 로고
    • Distribution of lattice points visible from the origin
    • Boca, F.P., Cobeli, C., Zaharescu, A.: Distribution of lattice points visible from the origin. Commun. Math. Phys. 213, 433-470 (2000)
    • (2000) Commun. Math. Phys. , vol.213 , pp. 433-470
    • Boca, F.P.1    Cobeli, C.2    Zaharescu, A.3
  • 6
    • 3042590463 scopus 로고    scopus 로고
    • The average length of a trajectory in a certain billiard in a flat two-torus
    • Boca, F.P., Gologan, R.N., Zaharescu, A.: The average length of a trajectory in a certain billiard in a flat two-torus. New York J. Math. 9, 303-330 (2003)
    • (2003) New York J. Math. , vol.9 , pp. 303-330
    • Boca, F.P.1    Gologan, R.N.2    Zaharescu, A.3
  • 7
    • 0242473182 scopus 로고    scopus 로고
    • The statistics of the trajectory of a billiard in a flat two-torus
    • Boca, F.P., Gologan, R.N., Zaharescu, A.: The statistics of the trajectory of a billiard in a flat two-torus. Commun. Math. Phys. 240, 53-73 (2003)
    • (2003) Commun. Math. Phys. , vol.240 , pp. 53-73
    • Boca, F.P.1    Gologan, R.N.2    Zaharescu, A.3
  • 8
    • 0002673989 scopus 로고
    • Numerical study of a D-dimensional periodic Lorentz gas with universal properties
    • Bouchaud, J.-P., Le Doussal, P.: Numerical study of a D-dimensional periodic Lorentz gas with universal properties. J. Stat. Phys. 41, 225-248 (1985)
    • (1985) J. Stat. Phys. , vol.41 , pp. 225-248
    • Bouchaud, J.-P.1    Le Doussal, P.2
  • 9
    • 0032326766 scopus 로고    scopus 로고
    • On the distribution of free path lengths for the periodic Lorentz gas
    • Bourgain, J., Golse, F., Wennberg, B.: On the distribution of free path lengths for the periodic Lorentz gas. Commun. Math. Phys. 190, 491-508 (1998)
    • (1998) Commun. Math. Phys. , vol.190 , pp. 491-508
    • Bourgain, J.1    Golse, F.2    Wennberg, B.3
  • 10
    • 0037805840 scopus 로고    scopus 로고
    • Billiards and other hyperbolic systems
    • Dynamical systems, ergodic theory and applications, edited by Ya.G. Sinai, Berlin: Springer-Verlag
    • Bunimovich, L.: Billiards and other hyperbolic systems. In: Dynamical systems, ergodic theory and applications, edited by Ya.G. Sinai, Encyclopaedia Math. Sci. Vol. 100, Berlin: Springer-Verlag, 2000, pp. 192-233
    • (2000) Encyclopaedia Math. Sci. , vol.100 , pp. 192-233
    • Bunimovich, L.1
  • 11
    • 0038648793 scopus 로고    scopus 로고
    • On the distribution of free path lengths for the periodic Lorentz gas. III
    • Caglioti, E., Golse, F.: On the distribution of free path lengths for the periodic Lorentz gas. III. Commun. Math. Phys. 236, 199-221 (2003)
    • (2003) Commun. Math. Phys. , vol.236 , pp. 199-221
    • Caglioti, E.1    Golse, F.2
  • 12
    • 0038157138 scopus 로고
    • New proof of Sinai's formula for the entropy of hyperbolic billiard systems. Application to Lorentz gases and Bunimovich stadium
    • Chernov, N.: New proof of Sinai's formula for the entropy of hyperbolic billiard systems. Application to Lorentz gases and Bunimovich stadium. Funct. Anal. and Appl. 25(3), 204-219 (1991)
    • (1991) Funct. Anal. and Appl. , vol.25 , Issue.3 , pp. 204-219
    • Chernov, N.1
  • 13
    • 0038820177 scopus 로고    scopus 로고
    • Entropy values and entropy bounds
    • Hard ball systems and the Lorentz gas, edited by D. Szász, Berlin: Springer-Verlag
    • Chernov, N.: Entropy values and entropy bounds. In: Hard ball systems and the Lorentz gas, edited by D. Szász, Encyclopaedia Math. Sci., Vol. 101, Berlin: Springer-Verlag, 2000, pp. 121-143
    • (2000) Encyclopaedia Math. Sci. , vol.101 , pp. 121-143
    • Chernov, N.1
  • 14
    • 0041040101 scopus 로고    scopus 로고
    • The Lyapunov exponent in the Sinai billiard in the small scatterer limit
    • Dahlqvist, P.: The Lyapunov exponent in the Sinai billiard in the small scatterer limit. Nonlinearity 10, 159-173 (1997)
    • (1997) Nonlinearity , vol.10 , pp. 159-173
    • Dahlqvist, P.1
  • 15
    • 0000102459 scopus 로고
    • Kloosterman sums and Fourier coefficients of cusp forms
    • Deshouillers, J.-M., Iwaniec, H.: Kloosterman sums and Fourier coefficients of cusp forms. Invent. Math. 70, 219-288 (1982/1983)
    • (1982) Invent. Math. , vol.70 , pp. 219-288
    • Deshouillers, J.-M.1    Iwaniec, H.2
  • 16
    • 0031138747 scopus 로고    scopus 로고
    • Remarks on the notion of mean free path for a periodic array of spherical obstacles
    • Dumas, H.S., Dumas, L., Golse, F.: Remarks on the notion of mean free path for a periodic array of spherical obstacles. J. Stat. Phys. 87(3/4), 943-950 (1997)
    • (1997) J. Stat. Phys. , vol.87 , Issue.3-4 , pp. 943-950
    • Dumas, H.S.1    Dumas, L.2    Golse, F.3
  • 17
    • 0013286070 scopus 로고
    • Some results on diophantine approximation
    • Erdös, P.: Some results on diophantine approximation. Acta Arith. 5, 359-369 (1959)
    • (1959) Acta Arith. , vol.5 , pp. 359-369
    • Erdös, P.1
  • 18
    • 33845572254 scopus 로고
    • Remarks on the theory of diophantine approximation
    • Erdös, P., Szüsz, P., Turán, P.: Remarks on the theory of diophantine approximation. Colloq. Math. 6, 119-126 (1958)
    • (1958) Colloq. Math. , vol.6 , pp. 119-126
    • Erdös, P.1    Szüsz, P.2    Turán, P.3
  • 19
    • 84971114237 scopus 로고
    • On Kloosterman's sum
    • Estermann, T.: On Kloosterman's sum. Mathematika 8, 83-86 (1961)
    • (1961) Mathematika , vol.8 , pp. 83-86
    • Estermann, T.1
  • 21
    • 0041081046 scopus 로고
    • Universal behaviour of Sinai billiard systems in the small-scatterer limit
    • Friedman, B., Oono, Y., Kubo, I.: Universal behaviour of Sinai billiard systems in the small-scatterer limit. Phys. Rev. Lett. 52, 709-712 (1984)
    • (1984) Phys. Rev. Lett. , vol.52 , pp. 709-712
    • Friedman, B.1    Oono, Y.2    Kubo, I.3
  • 22
    • 0012945855 scopus 로고
    • Lectures on the billiard
    • Dynamical systems, theory and applications (Rencontres, Battelle Res. Inst., Seattle, Wash., 1974), edited by J. Moser, Berlin-Heidelberg-Newyork: Springer-Verlag
    • Gallavotti, G.: Lectures on the billiard. In: Dynamical systems, theory and applications (Rencontres, Battelle Res. Inst., Seattle, Wash., 1974), edited by J. Moser, Lecture Notes in Phys. Vol. 38, Berlin-Heidelberg-Newyork: Springer-Verlag, 1975, pp. 236-295
    • (1975) Lecture Notes in Phys. , vol.38 , pp. 236-295
    • Gallavotti, G.1
  • 23
    • 0000894344 scopus 로고
    • Sums of Kloosterman sums
    • Goldfeld, D., Sarnak, P.: Sums of Kloosterman sums. Invent. Math. 71, 243-250 (1983)
    • (1983) Invent. Math. , vol.71 , pp. 243-250
    • Goldfeld, D.1    Sarnak, P.2
  • 24
    • 84967430756 scopus 로고    scopus 로고
    • On the statistics of free-path lengths for the periodic Lorentz gas
    • (Lisbon, 2003), edited by J.-C. Zambrini, River Edge, NJ: World Sci. Publ.
    • Golse, F.: On the statistics of free-path lengths for the periodic Lorentz gas. In: XIV International Congress on Mathematical Physics (Lisbon, 2003), edited by J.-C. Zambrini, River Edge, NJ: World Sci. Publ., 2006, pp. 439-446
    • (2006) XIV International Congress on Mathematical Physics , pp. 439-446
    • Golse, F.1
  • 25
    • 0034550165 scopus 로고    scopus 로고
    • On the distribution of free path lengths for the periodic Lorentz gas. II
    • Golse, F., Wennberg, B.: On the distribution of free path lengths for the periodic Lorentz gas. II. M2AN Math. Model. Numer. Anal. 34, 1151-1163 (2000)
    • (2000) M2AN Math. Model. Numer. Anal. , vol.34 , pp. 1151-1163
    • Golse, F.1    Wennberg, B.2
  • 26
    • 0343706593 scopus 로고    scopus 로고
    • Physics and arithmetic chaos in the Fourier transform
    • The mathematical beauty of physics (Saclay, 1996). edited by J.M. Drouffe, J.B. Zuber, River Edge, NJ: World Sci. Publ.
    • Gutzwiller, M.: Physics and arithmetic chaos in the Fourier transform. In: The mathematical beauty of physics (Saclay, 1996). edited by J.M. Drouffe, J.B. Zuber, Adv. Series in Math. Phys. Vol. 24, River Edge, NJ: World Sci. Publ., 1997, pp. 258-280
    • (1997) Adv. Series in Math. Phys. , vol.24 , pp. 258-280
    • Gutzwiller, M.1
  • 27
    • 0002420896 scopus 로고
    • An asymptotic formula in the theory of numbers
    • Hooley, C.: An asymptotic formula in the theory of numbers. Proc. London Math. Soc. 7, 396-413 (1957)
    • (1957) Proc. London Math. Soc. , vol.7 , pp. 396-413
    • Hooley, C.1
  • 28
    • 0040998839 scopus 로고
    • Some probabilistic theorems on diophantine approximations
    • Kesten, H.: Some probabilistic theorems on diophantine approximations. Trans. Amer. Math. Soc. 103, 189-217 (1962)
    • (1962) Trans. Amer. Math. Soc. , vol.103 , pp. 189-217
    • Kesten, H.1
  • 29
    • 0001265239 scopus 로고
    • The Petterson conjecture for forms of weight zero and Linnik's conjecture
    • (N.S.) 479
    • Kuznetsov, N.V.: The Petterson conjecture for forms of weight zero and Linnik's conjecture. Math. Sb. (N.S.) 111(153), 334-383, 479 (1980)
    • (1980) Math. Sb. , vol.111 , Issue.153 , pp. 334-383
    • Kuznetsov, N.V.1
  • 31
    • 0001660135 scopus 로고
    • Le mouvement des électrons dans les métaux
    • Lorentz, H.A.: Le mouvement des électrons dans les métaux. Arch. Néerl. 10, 336 (1905).
    • (1905) Arch. Néerl. , vol.10 , pp. 336
    • Lorentz, H.A.1
  • 32
    • 0003946758 scopus 로고
    • Reprinted in The Hague: Martinus Nijhoff
    • Reprinted in Collected papers. Vol. 3. The Hague: Martinus Nijhoff, 1936
    • (1936) Collected Papers , vol.3
  • 33
    • 33845810342 scopus 로고
    • Zahlentheoretisches und wahrscheinlichkeitstheoretisches über die sichtweite im walde
    • Pólya, G.: Zahlentheoretisches und wahrscheinlichkeitstheoretisches über die sichtweite im walde. Arch. Math. Phys. 27, 135-142 (1918)
    • (1918) Arch. Math. Phys. , vol.27 , pp. 135-142
    • Pólya, G.1
  • 34
    • 14044271129 scopus 로고
    • Sobre la distribucion probable de corpusculos en un cuerpo. Deducida de la distribucion en sus secciones y problemas analogos
    • Santaló, L.A.: Sobre la distribucion probable de corpusculos en un cuerpo. Deducida de la distribucion en sus secciones y problemas analogos. Rev. Un. Mat. Argentina 9, 145-164 (1943)
    • (1943) Rev. Un. Mat. Argentina , vol.9 , pp. 145-164
    • Santaló, L.A.1
  • 35
    • 84927896522 scopus 로고
    • Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards
    • Sinai, Y.G.: Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards. Russ. Math. Surveys 25, 137-189 (1970)
    • (1970) Russ. Math. Surveys , vol.25 , pp. 137-189
    • Sinai, Y.G.1
  • 36
    • 0001303344 scopus 로고
    • On some exponential sums
    • Weil, A.: On some exponential sums. Proc. Nat. Acad. Sci. USA 34, 204-207 (1948)
    • (1948) Proc. Nat. Acad. Sci. USA , vol.34 , pp. 204-207
    • Weil, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.