Abstract:
We introduce a Mittag-Leffler correlated random force leading to anomalous diffusion. Starting from a generalized Langevin equation, and using Laplace analysis we derive exact expressions for the mean values, variances and diffusion coefficient for a free particle in terms of generalized Mittag-Leffler functions and its derivatives. The asymptotic behavior of these quantities are obtained, from which the anomalous diffusion behavior of the particle is displayed. © 2007 The American Physical Society.
Registro:
Documento: |
Artículo
|
Título: | Anomalous diffusion induced by a Mittag-Leffler correlated noise |
Autor: | Viñales, A.D.; Despósito, M.A. |
Filiación: | Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina Consejo Nacional de Investigaciones Científicas y Técnicas, CONICET, Buenos Aires, Argentina
|
Palabras clave: | Diffusion; Elementary particles; Laplace equation; Nonlinear equations; Anomalous diffusion; Langevin equations; Laplace analysis; Mean values; Random processes |
Año: | 2007
|
Volumen: | 75
|
Número: | 4
|
DOI: |
http://dx.doi.org/10.1103/PhysRevE.75.042102 |
Título revista: | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
|
Título revista abreviado: | Phys. Rev. E Stat. Nonlinear Soft Matter Phys.
|
ISSN: | 15393755
|
CODEN: | PLEEE
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v75_n4_p_Vinales |
Referencias:
- Metzler, R., Klafter, J., (2000) Phys. Rep., 339, p. 1. , For a review, see PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3
- Metzler, R., Barkai, E., Klafter, J., (1999) Phys. Rev. Lett., 82, p. 3563. , PRLTAO 0031-9007 10.1103/PhysRevLett.82.3563
- Wang, K.G., Tokuyama, M., (1999) Physica A, 265, p. 341. , PHYADX 0378-4371 10.1016/S0378-4371(98)00644-X
- Porra, J.M., Wang, K.G., Masoliver, J., (1996) Phys. Rev. e, 53, p. 5872. , PLEEE8 1063-651X 10.1103/PhysRevE.53.5872
- Pottier, N., (2003) Physica A, 317, p. 371. , PHYADX 0378-4371 10.1016/S0378-4371(02)01361-4
- Viñales, A.D., Despósito, M.A., (2006) Phys. Rev. e, 73, p. 016111. , PLEEE8 1063-651X 10.1103/PhysRevE.73.016111
- Kou, S.C., Xie, X.S., (2004) Phys. Rev. Lett., 93, p. 180603. , PRLTAO 0031-9007 10.1103/PhysRevLett.93.180603
- Min, W., Luo, G., Cherayil, B.J., Kou, S.C., Xie, X.S., (2005) Phys. Rev. Lett., 94, p. 198302. , PRLTAO 0031-9007 10.1103/PhysRevLett.94.198302
- Chaudhury, S., Cherayil, B.J., (2006) J. Chem. Phys., 125, p. 024904. , JCPSA6 0021-9606 10.1063/1.2209231
- Bao, J.D., Zhuo, Y.Z., (2003) Phys. Rev. C, 67, p. 064606. , PRVCAN 0556-2813 10.1103/PhysRevC.67.064606
- Risken, H., (1989) The Fokker-Plank Equation, , Springer-Verlag, Berlin
- Wang, K.G., (1992) Phys. Rev. A, 45, p. 833. , PLRAAN 1050-2947 10.1103/PhysRevA.45.833
- Kupferman, R., (2004) J. Stat. Phys., 114, p. 291. , JSTPBS 0022-4715 10.1023/B:JOSS.0000003113.22621.f0
- Lutz, E., (2001) Phys. Rev. e, 64, p. 051106. , PLEEE8 1063-651X 10.1103/PhysRevE.64.051106
- Erdelyi, A., (1981) Higher Transcendental Functions, 3. , Krieger, Malabar
- Mainardi, F., Gorenflo, R., (2000) J. Comput. Appl. Math., 118, p. 283. , JCAMDI 0377-0427 10.1016/S0377-0427(00)00294-6
- Mainardi, F., (2000) Physica A, 287, p. 468. , PHYADX 0378-4371 10.1016/S0378-4371(00)00386-1
- Podlubny, I., (1999) Fractional Differential Equations, , Academic, London
- Fa, K.S., (2006) Phys. Rev. e, 73, p. 061104. , PLEEE8 1063-651X 10.1103/PhysRevE.73.061104
- Morgado, R., Oliveira, F.A., Batrouni, G.G., Hansen, A., (2002) Phys. Rev. Lett., 89, p. 100601. , PRLTAO 0031-9007 10.1103/PhysRevLett.89.100601
- Weiss, U., (1993) Quantum Dissipative Systems, , World Scientific, Singapore
- Berberan-Santos, M.N., (2005) J. Math. Chem., 38, p. 629. , JMCHEG 0259-9791
Citas:
---------- APA ----------
Viñales, A.D. & Despósito, M.A.
(2007)
. Anomalous diffusion induced by a Mittag-Leffler correlated noise. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 75(4).
http://dx.doi.org/10.1103/PhysRevE.75.042102---------- CHICAGO ----------
Viñales, A.D., Despósito, M.A.
"Anomalous diffusion induced by a Mittag-Leffler correlated noise"
. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 75, no. 4
(2007).
http://dx.doi.org/10.1103/PhysRevE.75.042102---------- MLA ----------
Viñales, A.D., Despósito, M.A.
"Anomalous diffusion induced by a Mittag-Leffler correlated noise"
. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 75, no. 4, 2007.
http://dx.doi.org/10.1103/PhysRevE.75.042102---------- VANCOUVER ----------
Viñales, A.D., Despósito, M.A. Anomalous diffusion induced by a Mittag-Leffler correlated noise. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 2007;75(4).
http://dx.doi.org/10.1103/PhysRevE.75.042102