Stretched exponential in non-linear stochastic field theories

Moshe Schwartz and S.F. Edwards

Physica A: Statistical Mechanics and its Applications, 2002, vol. 312, issue 3, 363-368

Abstract: We consider the time dependent two point function 〈φq(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 ωqt⪢1 (ωq being the corresponding decay rate). We find that, since the generic case has ωq∝qμ for small q where μ>1, the decay of the two point function is given by a stretched exponential in ωqt multiplied by a power of t, 〈φ−q(0)φq(t)〉∝tβdexp[−γ(ωqt)1/μ], where βd=(d−1)/2μ, d is the dimensionality of space and γ a dimensionless constant.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:312:y:2002:i:3:p:363-368

DOI: 10.1016/S0378-4371(02)00608-8

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