Theory of driven nonequilibrium critical phenomena

Abstract

A system driven in the vicinity of its critical point by varying a relevant field in an arbitrary function of time is a generic system that possesses a long relaxation time compared with the driving time scale and thus represents a large class of nonequilibrium systems. For such a manifestly nonlinear nonequilibrium strongly fluctuating system, we show that there exists universal nonequilibrium critical behavior that is well described incredibly by its equilibrium critical properties. A dynamic renormalization-group theory is developed to account for the behavior. The weak driving may give rise to several time scales depending on its form and thus rich nonequilibrium phenomena of various regimes and their crossovers, negative susceptibilities, as well as violation of fluctuation-dissipation theorem. An initial condition that can be in either equilibrium or nonequilibrium but has longer correlations than the driving scales also results in a unique regime and complicates the situation. Implication of the results on measurement is also discussed. The theory may shed light on study of other nonequilibrium systems and even nonlinear science.

Effects Induced by the Initial Condition in the Quantum Kibble–Zurek Scaling for Changing the Symmetry-Breaking Field

“…Besides the case of changing g, it has been shown that the dynamics of changing the symmetry-breaking field h as h = R h t + h 0 for a large h 0 also shows a scaling behavior [22,23,28,29,34]. In this case, h 0 is irrelevant.…”

“…In this case, h 0 is irrelevant. According to the FTS theory [28,29,34], the effective time scale induced by the external driving is ζ e ∼ R h −z/r h , in which r h = z + βδ/ν, with δ being defined as M ∼ h 1/δ at g = 0.…”

“…As a result, the initial condition will affect the driven dynamics. This inspires many studies on how to generalize the Kibble-Zurek mechanism to take the effects induced by the initial conditions into account in both classical and quantum phase transitions [33][34][35][36][37][38].…”

Scaling in driven dynamics starting in the vicinity of a quantum critical point

“…To go beyond KZM, it is important to investigate, both theoretically and experimentally, to what extent the scaling theory should be modified when the initial adiabaticity breaks down. For classical phase transitions, effects induced by a non-equilibrium initial state near the critical point have been studied 26,27 . However, the conclusion cannot be directly generalized to the real-time quantum critical dynamics, because the dynamical properties are The dash-dotted line (blue), which is exactly at the critical point and parallel with the vertical axis, is the starting state in the driven dynamics studied in Ref.…”

Driving driven lattice gases to identify their universality classes

“…A candidate is finite-time scaling (FTS) through manipulating dynamics [52,53]. This is to change the parameter of a system through its critical point at a finite rate R. Similar to the instantaneous change of parameters in DLG, such kinds of driving can also lead to a series of driven nonequilibrium critical phenomena such as negative susceptibility and competition of various regimes and their crossovers, as well as violation of fluctuation-dissipation theorem and hysteresis [15]. FTS is the temporal correspondence to FSS.…”