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arXiv · 1906.05306

Order parameter dynamics of the non-linear sigma model in the large $N$ limit

Sebastian Gemsheim·Ipsita Mandal·Krishnendu Sengupta·Zhiqiang Wang
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Abstract

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 solutions of the Keldysh saddle point equations, and use them to study the 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.

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Sebastian Gemsheim, Ipsita Mandal, Krishnendu Sengupta, Zhiqiang Wang. 2020-03-05. Order parameter dynamics of the non-linear sigma model in the large $N$ limit. https://doi.org/10.1140/epjb%2Fe2020-100445-1

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