energy current around a particle
energy E of central node m: 1/2 vm2  + 1/2 Œn U(rmn)
n
m
dE/dt = vm dv/dt  +  1/2 Œn UÕ(rmn) (vm - vn) ármn
vm  dv/dt = -vm F = Œn UÕ(rmn) (-vm) ármn 
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Combining, dE/dt  = -1/2 Œn UÕ(rmn) (vm +vn) ármn 
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Je
... change of E at    is the sum of Je from neighbors
Je for vibrational modes:
Single mode: energy just oscillates, no net current
–––V. Vitelli et al  PRE 2009
Mixture of two modes a and b at frequency w  have current Je(m)
Je(m) µ a | m m | (rm - rn)M | b
how is Je(m) correlated in space?
energy U