Evolutional entanglement production

Evolutional entanglement production is defined as the amount of entanglement produced by the evolution operator. This quantity is analyzed for systems whose Hamiltonians are characterized by spin operators. The evolutional entanglement production at the initial stage grows quadratically in time. For longer times, it oscillates, being quasiperiodic or periodic depending on the system parameters.

Figure 1

Entanglement-production measure, for the case of periodic evolution, as a function of time measured in units of $1/J$, for different fields: (a) $h/J=1$ (the period is $\pi )$, (b) $h/J=5/7$ (the period is $7\pi )$, (c) $h/J=7$ (the period is $\pi )$, and (d) $h/J=8$ (the period is $2\pi )$.

Figure 2

Measure of evolutional entanglement production, illustrating quasiperiodic behavior, for different fields: (a) $h/J=\sqrt{2}$, (b) $h/J=\sqrt{3}/2$, (c) $h/J=\sqrt{5}$, and (d) $h/J=\sqrt{7}$.