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arxiv: cond-mat/0012107 · v1 · pith:HVFWOTWVnew · submitted 2000-12-07 · ❄️ cond-mat.stat-mech

Streched exponential in non-linear stochastic filed theories

classification ❄️ cond-mat.stat-mech
keywords omegabetaconsiderdecayexponentialfunctiongammanon-linear
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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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