Multiparticle correlations of an oscillating scatterer

Using multiparticle distribution functions, we calculate the correlations produced by a periodically driven scatterer in a system of noninteracting electrons at zero temperature. The multiparticle correlations due to a quantum exchange effect are expressed in terms of photon-assisted scattering amplitudes. The results we obtain are valid for slow but arbitrary in strength driving. We show that even for large amplitude pumps the zero-frequency noise power is related to two-particle correlations. In addition to two-particle correlations a large amplitude pump can generate multiparticle correlations.

Figure 1

The occupation of single particle states ${ϵ}_n=ϵ+n\hslash \Omega$ in incoming channels $\left(\alpha \right)$ and in outgoing channels $\left(\beta \right)$ of a working pump at zero temperature. The filled box area is proportional to the occupation probability. The case shown corresponds to $n_{max}=3$, i.e., $S_{\beta \alpha ,\pm \mid n\mid }\approx 0$, for $n⩾4$. $\mu$ is the Fermi energy; $\Omega$ is a driving frequency.

Figure 2

Three particle correlation function $\delta f_{L,L,R}^{\left(out\right)}({ϵ}_{n_0},{ϵ}_{n_1},{ϵ}_{n_{-1}})$ as a function of the phase lag $\phi$. The scattering potential is as follows: $V(x,t)=\delta (x+a∕2)[V_0+2V_1\cos (\Omega t\left)\right]+\delta (x-a∕2)[V_0+2V_1\cos (\Omega t+\phi \left)\right]$ The parameters are as follows: $a=100\pi$; $V_0=20$; $V_1=10$; and the Fermi energy $\mu =1.0197$. We use the units $2m_e=\hslash =e=1$, where $m_e$ is the mass of an electron.