Application of Bogolyubov’s theory of weakly nonideal Bose gases to the [Formula presented] reaction-diffusion system

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 69, Issue 1, 2004, Pages 16-

  Konkoli, Zoran ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85036354684     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.69.011106     Document Type: Article

References (29)

1. A.S. Mikhailov, Phys. Rep. 184, 307 (1989).
2. V. Privman, Nonequilibrium Statistical Mechanics in One Dimension (Cambridge University Press, Cambridge, England, 1997).
3. Comprehensive Chemical Kinetics, edited by C.H. Bamford, C.F.H. Tipper, and R.G. Compton, Diffusion-limited Reactions Vol. 25 (Elsevier, New York, 1985).
4. E. Kotomin and V. Kuzovkov, in Comprehensive Chemical Kinetics, edited by R.G. Compton and G. Hancock, Modern Aspects of Diffusion-Controlled Reactions Vol. 34 (Elsevier, New York, 1996).
5. E. Kotomin and V. Kuzovkov, Rep. Prog. Phys. 55, 2079 (1992).
6. D.C. Mattis and M.L. Glasser, Rev. Mod. Phys. 70, 979 (1998).
7. J. Cardy, e-print cond-mat/9607163.
8. A.S. Mikhailov and V.V. Yashin, J. Stat. Phys. 38, 347 (1985).
9. For a very concise review of Smoluchowskii approach and WBGA, please see A.A. Ovchinnikov, S.F. Timashev, and A. A. Belyy, Kinetics of Diffusion Controlled Chemical Processes (Nova Science, New York, 1989).
10. For original work on weakly nonideal Bose gases please see N.N. Bogolybov, Izv. Akad. Nauk SSSR, Ser. Fiz. II, 77 (1974);Lectures on Quantum Statistics (Gordon and Breach, New York, 1967), pp. 107–119.
11. M. Doi, J. Phys. A 9, 1465 (1976).
12. Y.B. Zeldovich and A.A. Ovchinnikov, Zh. Eksp. Teor. Fiz. 74, 1588 (1978).
13. S.F. Burlatskii, A.A. Ovchinnikov, and K.A. Pronin, Zh. Eksp. Teor. Fiz. 92, 625 (1987).
14. A.M. Gutin, A.S. Mikhailov, and V.V. Yashin, Zh. Eksp. Teor. Fiz. 92, 941 (1987).
15. The initial state of the system was prepared by allowing for birth and annihilation of particles and waiting long enough to establish the stationary state. Once this stationary state was reached, particle birth ceased and the system continued to evolve by annihilation process solely.
16. For example, one way to prepare the system initially is to take a given number of particles and distribute them randomly one by one on the lattice. This way of preparation leads to a Poisson distribution of the particle number at each lattice site. Also, it is clear that preparing the system in this way does not lead to correlation among particles. Thus, saying that particles are distributed according to Poisson distribution amounts to saying that there are no correlations among them.
17. A.M.R. Cadilhe, M.L. Glasser, and V. Privman, Int. J. Mod. Phys. B 11, 109 (1997).
18. Z. Konkoli, H. Johannesson, and B.P. Lee, Phys. Rev. E 59, R3787 (1999).
19. Z. Konkoli and H. Johannesson, Phys. Rev. E 62, 3276 (2000).
20. B.P. Lee, J. Phys. A 27, 2633 (1994).
21. In Ref. 20 Eq. (43) of this work is listed as Eq. (54), and appears in a slightly different form. Also, there is a typographical error in the original equation.
22. The inverse Fourier transform of (Formula presented) is defined as (Formula presented)
23. The Fourier transform of Eq. (55) is calculated by using (Formula presented) Thus, translational invariance is ensured in the form of (Formula presented) The term (Formula presented) appears in Eq. (56) as an artifact of that.
24. M. Howard, J. Phys. A 29, 3437 (1996).
25. The density decay amplitude for (Formula presented) model is independent of (Formula presented) and (Formula presented) while the one for (Formula presented) model depends only on (Formula presented) (given that systems are observed below critical dimension, naturally).
26. S.A. Janowsky and J.L. Lebowitz, J. Stat. Phys. 77, 35 (1994);
27. S. Kwon, J. Lee, and H. Park, Phys. Rev. Lett. 85, 1682 (2000).
28. F.C. Alcaraz, M. Droz, M. Henkel, and V. Rittenberg, Ann. Phys. (N.Y.) 230, 250 (1994).
29. L.M. Delves and J.L. Mohamed, Computational Methods for Integral Equations (Cambridge University Press, Cambridge, England, 1985).