How do
marginal modes transmit energy, momentum
from V. Vitelli et al
PRE 2009
Excite modes of
frequency È w in a finite region
How does the energy
spread out in time?
distance2 È d(w)
(time)
as with particle
diffusion, we can infer d(w) from a correlation function
particles: d(w) =
(const) ˜0 ‡v(0) v(t)– dt
´
energy: d(w) =
(const) ˜0 ‡Je(0) Je(t)– dt
´
particle current
energy current
What is the energy
current for our system?
eg: independent steps
of length b every time t: ˜
‡v(0) v(t)– ¨ b2/t