1202.2458 (Sumit R. Das et al.)

Non-equilibrium Dynamics of O(N) Nonlinear Sigma models: a Large-N
approach    [PDF]

Sumit R. Das, K. Sengupta

We study the time evolution of the mass gap of the O(N) non-linear sigma
model in 2+1 dimensions due to a time-dependent coupling in the large-N limit.
We start from a thermal equilibrium state of the model deep in the disordered
phase at initial time, let the coupling g change with time towards the
equilibrium critical point g_c according to a fixed protocol, and study the
behavior of the mass gap under such a dynamics. Using the Schwinger-Keldysh
approach, we derive a set of equations at large N which determine the time
dependent gap in terms of the coupling. These equations lead to a criterion for
the breakdown of adiabaticity for slow variation of the coupling, which differs
from the standard Landau criterion, but results in a Kibble-Zurek scaling law
appropriate for mean field transitions with z=2. We provide explicit numerical
solutions of these large-N equations, and demonstrate (for a protocol which has
a linear ramp in the vicinity of the equilibrium critical point g_c) that there
is a value of the coupling g= g_c^{dyn}> g_c where the gap function vanishes,
possibly indicating a dynamical instability. We study the dependence of
g_c^{\rm dyn} on both the rate of change of the coupling and the initial
temperature. We also show, by studying the evolution of the mass gap subsequent
to a sudden change in g, that the model does not display thermalization within
a finite time interval t_0 and discuss the implications of this observation for
its conjectured gravitational dual as a higher spin theory in AdS_4.

View original: http://arxiv.org/abs/1202.2458