Full Counting Statistics in Strongly Interacting Systems: Non-Markovian Effects

We present a theory of full counting statistics for electron transport through interacting electron systems with non-Markovian dynamics. We illustrate our approach for transport through a single-level quantum dot and a metallic single-electron transistor to second order in the tunnel coupling, and discuss under which circumstances non-Markovian effects appear in the transport properties.

Figure 1

The first (a), second (b), third (c), and fourth (d) cumulant for a single-level quantum dot with $U\to \infty$ as a function of the level position $ϵ/e{V}_{\mathrm{sd}}$ for first (dashed lines) and first- plus second-order (solid lines) in tunneling with $e{V}_{\mathrm{sd}}=({\mu }_R-{\mu }_L)$. Other parameters are $\gamma =1$, $\Gamma =3\times {10}^{-2}e{V}_{\mathrm{sd}}$, $k_{\mathrm{B}}T={10}^{-1}e{V}_{\mathrm{sd}}$, and the high-energy cutoff $E_{\mathrm{c}}=10e{V}_{\mathrm{sd}}$.

Figure 2

Relative contribution of the non-Markovian part $⟨⟨I⟩{⟩}_{\mathrm{n}}-⟨⟨I⟩{⟩}_{\mathrm{n}}^{\mathrm{Markov}}$ to the $n$th cumulant $⟨⟨I⟩{⟩}_{\mathrm{n}}$ in first- plus second-order in tunneling. The full, dashed, and dot-dashed lines correspond to the second, third, and fourth cumulant for the same parameters as in Fig. 1.