Two-point correlation functions of the diffusion-limited annihilation in one dimension

Su-Chan Park; Jeong-Man Park; Doochul Kim

doi:10.1103/PhysRevE.63.057102

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Two-point correlation functions of the diffusion-limited annihilation in one dimension

Su-Chan Park¹, Jeong-Man Park², and Doochul Kim¹

¹School of Physics, Seoul National University, Seoul 151-747, Korea
²Department of Physics, The Catholic University of Korea, Puchon 420-743, Korea

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Phys. Rev. E 63, 057102 – Published 18 April, 2001

DOI: https://doi.org/10.1103/PhysRevE.63.057102

Abstract

Two-point density-density correlation functions for the diffusive binary reaction system $A + \vec{A} \emptyset$ are obtained in one dimension via Monte Carlo simulation. The long-time behavior of these correlation functions clearly deviates from that of a recent analytical prediction of Bares and Mobilia [Phys. Rev. Lett. 83, 5214 (1999)]. An alternative expression for the asymptotic behavior is conjectured from numerical data.

References (16)

Nonequilibrium Statistical Mechanics in One Dimension, edited by V. Privman (Cambridge University Press, Cambridge, England, 1997).
J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, England, 1999).
L.P. Kadanoff and J. Swift, Phys. Rev. 165, 310 (1968); M. Doi, J. Phys. A 9, 1465 (1976).
S. Redner and K. Kang, Phys. Rev. Lett. 51, 1729 (1983); K. Kang and S. Redner, Phys. Rev. A 32, 435 (1985).
B.P. Lee, J. Phys. A 27, 2633 (1994).
S.-C. Park, D. Kim, and J.-M. Park, Phys. Rev. E 62, 7642 (2000).
A.A. Lushnikov, Phys. Lett. A 120, 135 (1987).
M.D. Grynberg and R.B. Stinchcombe, Phys. Rev. Lett. 74, 1242 (1995).
G.M. Schütz, Phys. Rev. E 53, 1475 (1996).
J.L. Spouge, Phys. Rev. Lett. 60, 871 (1988).
P.-A. Bares and M. Mobilia, Phys. Rev. Lett. 83, 5214 (1999); ibid.85, 893 (2000).
S.-C. Park, J.-M. Park, and D. Kim, Phys. Rev. Lett. 85, 892 (2000).
E. Carlon, M. Henkel, and U. Schollwöck, Phys. Rev. E 63, 036101 (2001); ibid.H. Hinrichsen, 63, 036102 (2001).
M. Henkel and U. Schollwöck, e-print, cond-mat/0010061.
J.R.G. de Mendoça and M.J. de Oliveira, J. Stat. Phys. 92, 651 (1998).
J.E. Santos, G.M. Schütz, and R.B. Stinchcombe, J. Chem. Phys. 105, 2399 (1996).

[c1] Nonequilibrium Statistical Mechanics in One Dimension, edited by V. Privman (Cambridge University Press, Cambridge, England, 1997).

[c2] J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, England, 1999).

[c3] L.P. Kadanoff and J. Swift, Phys. Rev. 165, 310 (1968); M. Doi, J. Phys. A 9, 1465 (1976).

[c4] S. Redner and K. Kang, Phys. Rev. Lett. 51, 1729 (1983); K. Kang and S. Redner, Phys. Rev. A 32, 435 (1985).

[c5] B.P. Lee, J. Phys. A 27, 2633 (1994).

[c6] S.-C. Park, D. Kim, and J.-M. Park, Phys. Rev. E 62, 7642 (2000).

[c7] A.A. Lushnikov, Phys. Lett. A 120, 135 (1987).

[c8] M.D. Grynberg and R.B. Stinchcombe, Phys. Rev. Lett. 74, 1242 (1995).

[c9] G.M. Schütz, Phys. Rev. E 53, 1475 (1996).

[c10] J.L. Spouge, Phys. Rev. Lett. 60, 871 (1988).

[c11] P.-A. Bares and M. Mobilia, Phys. Rev. Lett. 83, 5214 (1999); ibid.85, 893 (2000).

[c12] S.-C. Park, J.-M. Park, and D. Kim, Phys. Rev. Lett. 85, 892 (2000).

[c13] E. Carlon, M. Henkel, and U. Schollwöck, Phys. Rev. E 63, 036101 (2001); ibid.H. Hinrichsen, 63, 036102 (2001).

[c14] M. Henkel and U. Schollwöck, e-print, cond-mat/0010061.

[c15] J.R.G. de Mendoça and M.J. de Oliveira, J. Stat. Phys. 92, 651 (1998).

[c16] J.E. Santos, G.M. Schütz, and R.B. Stinchcombe, J. Chem. Phys. 105, 2399 (1996).

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Two-point correlation functions of the diffusion-limited annihilation in one dimension

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