# Waiting Time Distributions of Transport through a Two-Channel Quantum System
###### Abstract  
In this work, the waiting time distribution (WTD) statistics of electron transport through a two-channel quantum system in a strong Coulomb blockade regime and non-interacting dots are investigated by employing a particle-number resolved master equation with the Born-Markov approximation. The results show that the phase difference between the two channels, the asymmetry of the dot-state couplings to the left and right electrodes, and Coulomb repulsion have obvious effects on the WTD statistics of the system. In a certain parameter range, the system manifests the coherent oscillatory behavior of WTDs in the strong Coulomb blockade regime, and the phase difference between the two channels is clearly reflected in the oscillation phase of the WTDs. The two-channel quantum dot (QD) system for non-interacting dots manifests nonrenewal characteristics, and the electron waiting time of the system is negatively correlated. The different phase differences between the two channels can clearly enhance the negative correlation. These results deepen our understanding of the WTD statistical properties of electron transport through a mesoscopic QD system and help pave a new path toward constructing nanostructured QD electronic devices. quantum dots; waiting time distribution; master equation; nonrenewal; multiple reset 202  
itself [6; 7; 8; 9; 10; 11; 12]. However, FCS evaluates the probability distribution function of the number of electrons transferred through a conductor within a given time period; it also captures time-integrated correlation effects that have a long time limit, so important information about short-time physics may be lost [13; 14; 15; 16]. In addition to FCS, another complementary method of characterizing electron transport is by studying the waiting time distributions (WTDs), which are the distributions of the time intervals between two successive electrons transmitted through a conductor [13; 14; 15; 16]. WTDs are a particularly useful tool to describe short-time physics and correlations in mesoscopic conductors. Moreover, real-time counting statistics have been carried out experimentally on electron transport through quantum dots [12], and the measurements of WTDs for a mesoscopic device could soon be within reach. In recent years, WTDs have been investigated theoretically for quantum transport in quantum dots [16; 17; 18; 19], mesoscopic conductors [15; 20], and superconducting devices [21; 22]. Notably, [PERSON] discussed the waiting times and noise in single particle transport through single reset (double QDs in a strong Coulomb blockade regime) and multiple reset (an Anderson single-impurity model without Coulomb repulsion) systems [23]. The difference between single and multiple reset QD systems is that in single reset systems, the dot is empty after an electron tunnels out, whereas in a multiple reset system, the dot is empty only after a certain number of electrons has tunneled out. In more complicated systems, like the Anderson-Holstein model, an electron tunneling out can leave the system in various vibrational states, and there are thus multiple possibilities for the state after the electron jumps, even if there are only one or zero electrons involved in the transport [24; 25]. Recently, [PERSON] et al. studied the effects of cotunneling on the WTDs of an Anderson single-impurity model in a Coulomb blockade regime and tunneling regime and discovered nonrenewal statistics, which are the short-time correlations between subsequent waiting times and are invisible in the current cumulants [26]. On the other hand, [PERSON] et al. studied the effects of quantum interference and phase accumulations on the FCS of the electronic transport through a Coulomb blockade system with two identical transport channels, which can be realized by transport through two adjacent levels in a single QD or through two QDs in parallel [27]. This is of particular interest because this system is an analog of an optical double-slit interferometer.