The static dielectric function for an interacting electron system is
where 
is the interaction potential, V is the volume and
is the Fermi function.
Consider a one-dimensional
system, where the energy depends on 
, but is independent of 
and
. The energy is given by 
, and
the Fermi surface is at 
.
Investigate the properties of the 
function at low temperature. Show that 
becomes zero at
for an arbitrarily small repulsive interaction,
.
Laszlo Mihaly
Thu Oct 31 13:23:11 EST 1996
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.