Streched exponential in non-linear stochastic filed theories

Details Streched exponential in non-linear stochastic filed theories Streched exponential in non-linear stochastic filed theories

2000-12-07

arxiv.org/abs/cond-mat/0012107v1

Physica A312 (2002) 363-368

Physics

Condensed Matter

Statistical Mechanics

10 pages

Scientific paper

We consider the time dependent two point function, <\phi_q (t) \phi_-q (0)> in non-linear stochastic field theories, for which the KPZ equation serves as a prototype. In particular we consider the small q's and long times such that \omega_q t>>1 (\omega_q being the corresponding decay rate). We find that, since the generic case has \omega_q \propto q^\mu for small q where \mu>1, the decay of the two point function is given by a streched exponential in \omega_qt multiplied by a factor of t, <\phi_q (t) \phi_-q (0)> \propto t^{\beta_d}exp[-\gamma(\omega_qt)^{1/\mu}], where \beta_d=(d-1)/2\mu, d is the dimensionality of space and \gamma a dimensionless constant.

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