Average diagonal entropy in nonequilibrium isolated quantum systems

The diagonal entropy was introduced as a good entropy candidate especially for isolated quantum systems out of equilibrium. Here we present an analytical calculation of the average diagonal entropy for systems undergoing unitary evolution and an external perturbation in the form of a cyclic quench. We compare our analytical findings with numerical simulations of various quantum systems. Our calculations elucidate various heuristic relations proposed recently in the literature.

Figure 1

$\mathrm{\Delta }S$ (solid black line) as a function of the coupling strength $\lambda$ for the DM with $j=20, N_t=250, \tau ={10}^7, \mathrm{\Delta }\tau =250$, and quench strength $\delta \lambda =0.1$. The initial state is $|n_0\rangle =|10\rangle$ (top) and $|100\rangle$ (bottom). Dashed horizontal line corresponds to $1-\gamma$; symbols are orders $O_1$ (squares), $O_2$ (triangles), and $O_3$ (circles). Inset: Examples of $S_{\mathrm{D}}\left(\tau \right)$ as a function of $\tau$, with $\lambda =0.65, \delta \lambda =0.1$, for three different initial states: (bottom) $|10\rangle$; (middle) $|100\rangle$; (top) $|250\rangle$. The dashed horizontal lines mark the corresponding values of $S_{{}_{\overline{\rho \left(\tau \right)}}}$.

Figure 2

$\mathrm{\Delta }S$ (solid black line) for the SW model with $p=0.06, \delta W=0.3, N=2^9, \tau ={10}^6, \mathrm{\Delta }\tau =2500$ (top), and $\mathrm{\Delta }\tau =3500$ (bottom), for one realization of disorder and of the shortcut links. Initial states are $|n_0\rangle =|10\rangle$ (top) and $|200\rangle$ bottom. Dashed horizontal line corresponds to $1-\gamma$; symbols are orders $O_1$ (squares), $O_2$ (triangles), and $O_3$ (circles).