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
ö
ö
Combining, dE/dt = -1/2 Œn UÕ(rmn)
(vm +vn) ármn
ö
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