Sebastian Gemsheim, Ipsita Mandal, K. Sengupta, Zhiqiang Wang
Published 2019-06-12Version 1
We study non-equilibrium order parameter dynamics of the non-linear sigma model in the large $N$ limit, using Keldysh formalism. We provide a scheme for obtaining stable numerical solution of the Keldysh saddle point equations and use them to study order parameter dynamics of the model either following a ramp, or in the presence of a periodic drive. We find that the transient dynamics of the order parameter in the presence of a periodic drive is controlled by the drive frequency displaying the phenomenon of synchronization. We also study the approach of the order parameter to its steady state value following a ramp and find out the effective temperature of the steady state. We chart out the steady state temperature of the ordered phase as a function of ramp time and amplitude, and discuss the relation of our results to experimentally realizable spin models.
Comments: 13 pages, 5 figures
The $J_1$-$J_2$ spin chain and the $O(3)$ non-linear sigma model at $θ= π$
Dimensional Crossover in the Non-Linear Sigma Model
Semi-classical theory for quantum quenches in the O(3) non-linear sigma model
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