Abstract
Typically, an interactive system evolves towards thermal equilibrium, with hydrodynamics representing a universal framework for its late-time dynamics. Classification of the dynamical fixed points (DFPs) of a driven Quantum Field Theory (with time dependent coupling constants, masses, external background fields, etc.) is unknown. We use holographic framework to analyze such fixed points in one example of strongly coupled gauge theory, driven by homogeneous and isotropic expansion of the background metric — equivalently, a late-time dynamics of the corresponding QFT in Friedmann-LemaitreRobertson-Walker Universe. We identify DFPs that are perturbatively stable, and those that are perturbatively unstable, computing the spectrum of the quasinormal modes in the corresponding holographic dual. We further demonstrate that a stable DFP can be unstable non-perturbatively, and explain the role of the entanglement entropy density as a litmus test for a non-perturbative stability. Finally, we demonstrated that a driven evolution might not have a fixed point at all: the entanglement entropy density of a system can grow without bounds.
Highlights
Introduction and summaryThermodynamic equilibrium is an internal state of a system without the net macroscopic flow of matter or energy
We further demonstrate that a stable dynamical fixed points (DFPs) can be unstable non-perturbatively, and explain the role of the entanglement entropy density as a litmus test for a non-perturbative stability
We can provide a formal definition of a dynamical fixed point (DFP): A Dynamical Fixed Point is an internal state of a quantum field theory with spatially homogeneous and time-independent one-point correlation functions of its stress energy tensor T μν, and set of gauge-invariant local operators {Oi}, and strictly positive divergence of the entropy current at late-times: lim ∇ · S > 0 τ →∞
Summary
Thermodynamic equilibrium is an internal state of a system without the net macroscopic flow of matter or energy. A Dynamical Fixed Point is an internal state of a quantum field theory with spatially homogeneous and time-independent one-point correlation functions of its stress energy tensor T μν, and (possibly additional) set of gauge-invariant local operators {Oi}, and strictly positive divergence of the entropy current at late-times: lim ∇ · S > 0 τ →∞. There is an excellent agreement between the growth rate of unstable (small amplitude) fluctuations in a simulation, with the corresponding frequency of the unstable QNM of the DFP Another nontrivial consistency check on numerics is the high accuracy agreement between the two different expressions for the vacuum entanglement entropy densities of various DFPs, see appendix D.2
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