Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2012-02-11
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, 9 figures. Typos corrected, references rearranged and added
Scientific paper
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.
Das Sumit R.
Sengupta Kausik
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