2012

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

Das, Sumit R., Sengupta, K.

Understand

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 starts deep in the gapped phase at early times and approaches the zero temperature equilibrium critical point $g_c$ in a linear fashion.

Built on

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Then

R. A. Janik and R. B. Peschanski, “Gauge / gravity duality and thermalization of a boost-invariant perfect fluid,” Phys. Rev. D 74
Original
2010
Later among the works it cites.
S. R. Das, T. Nishioka, T. Takayanagi, “Probe Branes, Time-dependent Couplings and Thermalization in AdS/CFT,” JHEP 1007
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2010
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S. Giombi, X. Yin, “Higher Spin Gauge Theory and Holography: The Three-Point Functions,” JHEP 1009
Original
2010
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For a review see S. Mondal, D. Sen and K. Sengupta, “Non-equilibrium dynamics of quantum systems: order parameter evolution, defect generation, and qubit transfer,” Chap 2 in ”Quantum Quenching, Annealing and Computation”, Eds. A. Das, A. Chandra and B. K. Chakrabarti, Springer Lect. Notes Phys., 802
Original
2011
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S. R. Das, A. Jevicki, “Large N collective fields and holography,” Phys. Rev. D68
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2011
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N. Bao, X. Dong, E. Silverstein and G. Torroba, “Stimulated superconductivity at strong coupling,” JHEP 1110
Original
2011
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P. Basu and S. R. Das, JHEP 1201
Original
2012
Closest in time.
A. Polkovnikov, “Universal adiabatic dynamics in the vicinity of a quantum critical point,” Phys. Rev. B72
Original
2081
Closest in time.

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