Noise-Driven Universal Dynamics towards an Infinite Temperature State

Dynamical universality is the observation that the dynamical properties of different systems might exhibit universal behavior that are independent of the system details. In this Letter, we study the longtime dynamics of a one-dimensional noisy quantum magnetic model, and find that even though the system is inevitably driven to an infinite temperature state, the relaxation dynamics towards such a featureless state can be highly nontrivial and universal. The effect of various mode-coupling mechanisms (external potential, disorder, interaction, and the interplay between them) as well as the conservation law on the longtime dynamics of the systems have been studied, and their relevance with current ultracold atomic experiments has been discussed.

Figure 1

Dynamics of $M(t)$ in (a) small systems with open boundary condition (OBC); the inset is the decay rate as a function of $1/L^2$. (b) Large systems with a staggered external potential $h_i=V_0(-1{)}^i$, and (c) interacting systems with various $J_z$. $J_z=0$ for (a) and (b) and $\mathrm{\Delta }=\delta =0$ for (a)–(c). The system size $L=320$ for (b) and $L=96$ for (c).

Figure 2

(a) Dynamics of $M(t)$ with various disorder strength $\mathrm{\Delta }$ in a noninteracting ($J_z=0$) model with lattice length $L=320$). Dynamics of $C(t)$ (upper) and $M(t)$ (lower panels) with various $\mathrm{\Delta }$ but fixed interaction ($J_z=J$) in cases of (b) weak and (d) strong disorder; (c) different $J_z$ but fixed $\mathrm{\Delta }=J$; (e) $U(1)$ symmetry breaking $\delta =J_z=J$. (f) The equal-time correlation function $C(r,t)$ at different time with $\mathrm{\Delta }=J_z=J$. $L=96$ for (b)–(f), and the anisotropy $\delta =0$ except for (e).