Abstract
We study the critical exponents in the universal scaling laws of a holographic non-equilibrium steady state nearby its critical point of phase transition, which is driven by an AC electric field sitting in the boundary of the bulk. The applied electric filed drives the initial superconducting state into a non-equilibrium steady state with vanishing condensate as its amplitude is greater than a critical value. In the vicinity of the non-equilibrium critical point, we numerically calculate the six static and one dynamical critical exponents, and find that they have similar values to those in equilibrium systems within numerical errors.
Highlights
One of the most intriguing features in equilibrium continuous phase transition is the universal scaling behavior near the critical point, which groups various critical phenomena into universality classes; i.e., systems that lie in one universality class share the same scaling behavior [1]
We study the critical exponents in the universal scaling laws of a holographic nonequilibrium steady state near its critical point of phase transition, which is driven by an ac electric field sitting in the boundary of the bulk
In the Appendix, we briefly review the critical exponents in equilibrium dynamics
Summary
One of the most intriguing features in equilibrium continuous phase transition is the universal scaling behavior near the critical point, which groups various critical phenomena into universality classes; i.e., systems that lie in one universality class share the same scaling behavior [1]. AdS=CFT correspondence has been adopted in the study of hot QCD and strongly coupled quark-gluon plasma [14]; the nonequilibrium dynamics of superconducting order parameter after quench [15,16]; topological defects formation in Kibble-Zurek mechanism [17,18]; time evolution of nonlocal entanglement observables [19,20]; energy flows between two heat baths [21], etc. We are going to investigate the scaling laws near the critical point of holographic nonequilibrium steady states, which are driven by a sinusoidal applied ac electric field. It is found that there exists a critical value of the amplitude Ec, beyond which the system will become a normal state Based on this nonequilibrium phase transition, we investigate the scaling laws near the critical point Ec. We numerically explore the six static critical exponents, i.e., (α, β, γ, δ, η, ν) and one dynamical critical exponent z. In the Appendix we briefly review the critical exponents we considered in mean-field theory
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