Stretched exponential in non-linear stochastic field theories

• Published in: Physica A Vol. 312; no. 3; pp. 363 - 368
• Main Authors: Schwartz, Moshe, Edwards, S.F.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.09.2002
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/S0378-4371(02)00608-8

We consider the time dependent two point function 〈 φ q ( t) φ − q (0)〉 in non-linear stochastic field theories, for which the KPZ equation serves as a prototype, in particular we consider small q's and long times such that ω q t⪢1 ( ω q being the corresponding decay rate). We find that, since the generic case has ω q ∝ q μ for small q where μ>1, the decay of the two point function is given by a stretched exponential in ω q t multiplied by a power of t, 〈φ −q(0)φ q(t)〉∝t β d exp [−γ(ω qt) 1/μ] , where β d =( d−1)/2 μ, d is the dimensionality of space and γ a dimensionless constant.