Nonequilibrium dynamics of a system with two kinds of fermions after a pulse

The nonequilibrium evolution of the system of two kinds of fermions under the action of a pulse of the external field has been studied. The number of fermions of each kind oscillates (with beats and decaying) as a function of the duration of the pulse about the value determined by the magnitude of the pulse, and as a function of the magnitude of the pulse. For low-dimensional systems those oscillations can serve as a non-zero-temperature manifestation of dynamical quantum phase transitions. The response of a Fermi gas or liquid in a tilted magnetic field, an edge state of a topological insulator, a quantum wire with spin-orbit coupling, and a dimerized spin-1/2 chain to the pulse can manifest such dynamical oscillations, which can be observed in experiments.

Figure 1

The dependence of the change of the magnetization of the edge states of the topological insulator on the duration of the pulse $\tau$. The used values are the velocity $v=0.2$, the chemical potential $\mu =0.1$, the temperature $T=0.01$, and the magnitude of the pulse $h=0.1$ (in arbitrary units).

Figure 2

The dependence of the change of the magnetization of the edge states of the topological insulator on the magnitude of the pulse $h$. The duration of the pulse is $\tau =5$. Other parameters are the same as in Fig. 1, but with $\mu =0.05$.

Figure 3

The time dependence of the density of the return probability (Loschmidt echo) $l\left(t\right)$ (blue solid line) and the $\tau$ dependence of the magnetization (with the opposite sign, red long-dashed line) after the quantum quench at $t=0$ of the edge states of the topological insulator for $h=10$. Other parameters are the same as in Fig. 1. Nonanalyticities in $l\left(t\right)$ are DQPTs.

Figure 4

The $\tau$ dependence of the (normalized by $L$) change of the magnetization of the dimerized spin-1/2 chain. The used parameters are $J_1=1.2, J_2=0.8, {\mu }_1=1.05, {\mu }_2=0.95, T=0.01, H=0.1$, and $h=1.5$ (in arbitrary units).

Figure 5

The dependence of the (normalized by $L$) change of the magnetization of the dimerized spin-1/2 chain on the magnitude of the pulse $h$. The parameters are the same as in Fig. 4 but for $T=0$ and with $\tau =20$ (in arbitrary units).