Driven Quantum Coarsening

We study the driven dynamics of quantum coarsening. We analyze models of $M$-component rotors coupled to two electronic reservoirs at different chemical potential that generate a current threading through the system. In the large $M$ limit, we derive the dynamical phase diagram as a function of temperature, strength of quantum fluctuations, voltage, and coupling to the leads. We show that the slow relaxation in the ordering phase is universal. On large time and length scales, the dynamics are analogous to stochastic classical ones, even for the quantum system driven out of equilibrium at zero temperature. We argue that our results apply to generic driven quantum coarsening.

Figure 1

Nonequilibrium phase diagram for reservoirs with a much larger variation scale at the Fermi level than all other energy scales ($\hslash {\omega }_F\gg J$). Close to the critical point ${\overline{V}}_c=V_c(T=\Gamma =0)$, the critical lines are nonanalytical ($\mathrm{NA}$). Close to ${\overline{T}}_c$ and ${\overline{\Gamma }}_c$, they are power laws with exponents given in the right. The arrow above ${\overline{\Gamma }}_c$ indicates that the critical surface is pulled up by increasing the coupling to the leads.

Figure 2

Dynamics in the driven coarsening regime: numerical solution to Eqs. (2) after a quench to $T=0.2J$, $V=0.2J$, $\Gamma =1$, $g=1$ with $\hslash {\omega }_F=10J$. (a) The symmetric correlation $C(t,t_w)$. (b) The integrated linear response, $\chi (t,t_w)={\int }_{t_w}^t\mathrm{d}{t}^{\prime }R(t,t^{\prime })$ against $C$, for $t_w=1024$ and using $t$ as a parameter. The curved part corresponds to the stationary and oscillatory regime with $(t-t_w)/t_w\to 0$ while the straight line is for times in the monotonic aging decay of $C$.