Universal large-deviation function of the Kardar-Parisi-Zhang equation in one dimension

Journal of Statistical Physics

Volumn 94, Issue 1-2, 1999, Pages 1-30

  Derrida, B ^a   Appert, C ^a  

^a LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

Author keywords

ASEP; Bethe ansatz; Burgers equation; Directed polymers; Growth models; KPZ equation; Large deviation function

Indexed keywords

EID: 0032589530     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004519626804     Document Type: Article

References (23)

1. 1. T. Halpin-Healy and Y. C. Zhang, Kinetic roughening phenomena, stochastic growth, directed polymers and all that, Phys. Rep. 254:216 (1995).
2. 2. M. Kardar, G. Parisi, and Y.-C. Zhang, Dynamic scaling of growing interfaces, Phys. Rev. Lett. 56:889 (1986).
3. 3. A. L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, 1995).
4. 4. F. Family and T. Vicsek, Dynamics of Fractal Surfaces (World Scientific, Singapore, 1991).
5. 5. B. Derrida and J. L. Lebowitz, Exact large deviation function in the asymmetric exclusion process, Phys. Rev. Lett. 80:209 (1998).
6. 6. P. Meakin, P. Ramanlal, L. M. Sander, and R. C. Ball, Ballistic deposition on surfaces, Phys. Rev. A 34:5091 (1986).
7. 7. L. H. Tang, Waiting time formulation of surface growth and mapping to directed polymers in a random medium, in Growth Patterns in Physical Sciences and Biology, E. Louis, S. M. Sander, P. Meakin, and J. M. Garcia-Ruiz, eds. (Plenum, New York, 1992).
8. 8. B. Derrida and M. R. Evans, The asymmetric exclusion model: exact results through a matrix approach, in Nonequilibrium Statistical Mechanics in One Dimension, V. Privman, ed. (Cambridge University Press, 1997), p. 277.
9. 9. F. R. Gantmacher, The Theory of Matrices, Vol.2 (New York, Chelsea Pub. Co., 1959).
10. 10. J. Krug, Origins of scale invariance in growth processes, Adv. Phys. 46:139 (1997).
11. 11. L.-H. Gwa and H. Spohn, Six-vertex model, roughened surfaces, and an asymmetric spin Hamiltonian, Phys. Rev. Lett. 68:725 (1992).
12. 12. L.-H. Gwa and H. Spohn, Bethe solution for the dynamical-scaling exponent of the noisy Burgers equation, Phys. Rev. A 46:844 (1992).
13. 13. J. M. Kim and J. M. Kosterlitz, Growth in a restricted solid-on-solid model, Phys. Rev. Lett. 62:2289 (1989).
14. 14. J. Kertész and D. E. Wolf, Noise reduction in Eden models: II. Surface structure and intrinsic width, J. Phys. A 21:747 (1988).
15. 15. J. Krug and H. Spohn, Anomalous fluctuations in the driven and damped Sine-Gordon chain, Europhys. Lett. 8:219 (1989).
16. 16. E. Ben-Naim, A. R. Bishop, I. Daruka, and P. L. Krapivsky, Mean-field theory of polynuclear surface growth, J. Phys. A. Math. Gen. 31:5001 (1998).
17. 17. J. M. Kim, M. A. Moore, and A. J. Bray, Zero-temperature directed polymers in a random potential, Phys. Rev. A 44:2345 (1991).
18. 18. T. Halpin-Healy, Directed polymers in random media: Probability distributions, Phys. Rev. A 44:R3415 (1991).
19. 19. J. Krug, P. Meakin and T. Halpin-Healy, Amplitude universality for driven interfaces and directed polymers in random media, Phys. Rev. A 45:638 (1992).
20. 20. Y. C. Zhang, Directed polymers in Hartree-Fock approximation, J. Stat. Phys. 57:1123 (1989).
21. 21. C. N. Yang and C. P. Yang, Thermodynamics of a one-dimensional system of Bosons with repulsive Delta-function interaction, J. Mach. Phys. 10:1115 (1969).
22. 22. D. Kim, Bethe ansatz solution for crossover scaling functions of the asymmetric XYZ chain and the Kardar-Parisi-Zhang-type growth model, Phys. Rev. E 52:3512 (1995).
23. 23. D. Kim, Asymmetrix XYZ chain at the antiferromagnetic transition: Spectra and partition functions, J. Phys. A 30:3817 (1997).