Random phase approximation study of one-dimensional fermions after a quantum quench

The effect of interactions on a system of fermions that are in a nonequilibrium steady state due to a quantum quench is studied employing the random phase approximation. As a result of the quench, the distribution function of the fermions is greatly broadened. This gives rise to an enhanced particle-hole spectrum and overdamped collective modes for attractive interactions between fermions. On the other hand, for repulsive interactions, an undamped mode above the particle-hole continuum survives. The sensitivity of the result to the nature of the nonequilibrium steady state is explored by also considering a quench that produces a current-carrying steady state.

Figure 1

Initial $c$-fermion distributions for (a) no current ($k_0=0$), (b) nonzero current ($k_0=\pi /2$), and (c) maximum current ($k_0=\pi$). Note the sharp discontinuity for the case of nonzero current.

Figure 2

Undamped mode (dashed line) above the extended particle-hole continuum (shaded region). Inset: Equilibrium continuum and undamped mode.

Figure 3

Characteristic lines along which $\text{Re}\left[{\Pi }^R(q,\omega )\right]$ diverges, giving rise to damped modes for repulsive (solid lines) and attractive (dashed lines) interactions for $k_0=\frac{\pi }{4}$. Only the top line $\omega =2J\sin \frac{q}{2}$ corresponds to an undamped mode existing above the particle-hole continuum.