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Non-equilibrium dynamics of O(N) nonlinear sigma models: a large-N approach

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Abstract

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. 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 leading to a Kibble-Zurek scaling law. We describe a self-consistent numerical procedure to solve these large-N equations and provide explicit numerical solutions for a coupling which asymptotes to constant values in the gapped phase and approaches the zero temperature equilibrium critical point in a linear fashion. We demonstrate that for such a protocol 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 \( g_c^{{dyn}} \) on both the rate of change of the coupling and the initial temperature. We also verify, 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.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Kentucky, 600 Rose Street, Lexington, KY, 40506, USA

    Sumit R. Das

  2. Theoretical Physics Department, Indian Association for the Cultivation of Science, 2A&2B Raja S C Mullick Road, Kolkata, 700032, India

    Krishnendu Sengupta

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  1. Sumit R. Das
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  2. Krishnendu Sengupta
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Correspondence to Sumit R. Das.

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Das, S.R., Sengupta, K. Non-equilibrium dynamics of O(N) nonlinear sigma models: a large-N approach. J. High Energ. Phys. 2012, 72 (2012). https://doi.org/10.1007/JHEP09(2012)072

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