Equilibration of integer quantum Hall edge states
ArXiv 1009.4555 (2010)
Authors:
DL Kovrizhin, JT Chalker
Abstract:
We study equilibration of quantum Hall edge states at integer filling
factors, motivated by experiments involving point contacts at finite bias.
Idealising the experimental situation and extending the notion of a quantum
quench, we consider time evolution from an initial non-equilibrium state in a
translationally invariant system. We show that electron interactions bring the
system into a steady state at long times. Strikingly, this state is not a
thermal one: its properties depend on the full functional form of the initial
electron distribution, and not simply on the initial energy density. Further,
we demonstrate that measurements of the tunneling density of states at long
times can yield either an over-estimate or an under-estimate of the energy
density, depending on details of the analysis, and discuss this finding in
connection with an apparent energy loss observed experimentally. More
specifically, we treat several separate cases: for filling factor \nu=1 we
discuss relaxation due to finite-range or Coulomb interactions between
electrons in the same channel, and for filling factor \nu=2 we examine
relaxation due to contact interactions between electrons in different channels.
In both instances we calculate analytically the long-time asymptotics of the
single-particle correlation function. These results are supported by an exact
solution at arbitrary time for the problem of relaxation at \nu=2 from an
initial state in which the two channels have electron distributions that are
both thermal but with unequal temperatures, for which we also examine the
tunneling density of states.
