Stretched exponential in non-linear stochastic field theories
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...
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Published in | Physica A Vol. 312; no. 3; pp. 363 - 368 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
15.09.2002
|
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 0378-4371 1873-2119 |
DOI: | 10.1016/S0378-4371(02)00608-8 |