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We develop a method for calculation of charge transfer statistics of persistent current in nanostructures in terms of the cumulant generating function (CGF) of transferred charge. We consider a simply connected one-dimensional system (a wire) and develop a procedure for the calculation of the CGF of persistent currents when the wire is closed into a ring via a weak link. For the non-interacting system we derive a general formula in terms of the two-particle Greens functions. We show that, contrary to the conventional tunneling contacts, the resulting cumulant generating function has a doubled periodicity as a function of the counting field. We apply our general formula to short tight-binding chains and show that the resulting CGF perfectly reproduces the known evidence for the persistent current. Its second cumulant turns out to be maximal at the switching points and vanishes identically at zero temperature. Furthermore, we apply our formalism for a computation of the charge transfer statistics of genuinely interacting systems. First we consider a ring with an embedded Anderson impurity and employing a self-energy approximation find an overall suppression of persistent current as well as of its noise. Finally, we compute the charge transfer statistics of a double quantum dot system in the deep Kondo limit using an exact analytical solution of the model at the Toulouse point. We analyze the behaviour of the resulting cumulants and compare them with those of a noninteracting double quantum dot system and find several pronounced differences, which can be traced back to interaction effects.
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We develop a scheme for the computation of the full-counting statistics of transport described by Markovian master equations with an arbitrary time dependence. It is based on a hierarchy of generalized density operators, where the trace of each operator yields one cumulant. This direct relation offers a better numerical efficiency than the equivalent number-resolved master equation. The proposed method is particularly useful for conductors with an elaborate time-dependence stemming, e.g., from pulses or combinations of slow and fast parameter switching. As a test bench for the evaluation of the numerical stability, we consider time-independent problems for which the full-counting statistics can be computed by other means. As applications, we study cumulants of higher order for two time-dependent transport problems of recent interest, namely steady-state coherent transfer by adiabatic passage and Landau-Zener-Stuckelberg-Majorana interference in an open double quantum dot.
We calculate the distribution of current fluctuations in two simple exclusion models. Although these models are classical, we recover even for small systems such as a simple or a double barrier, the same distibution of current as given by traditionnal formalisms for quantum mesoscopic conductors. Due to their simplicity, the full counting statistics in exclusion models can be reduced to the calculation of the largest eigenvalue of a matrix, the size of which is the number of internal configurations of the system. As examples, we derive the shot noise power and higher order statistics of current fluctuations (skewness, full counting statistics, ....) of various conductors, including multiple barriers, diffusive islands between tunnel barriers and diffusive media. A special attention is dedicated to the third cumulant, which experimental measurability has been demonstrated lately.
The electronic energy levels and optical transitions of a semiconductor quantum dot are subject to dynamics within the solid-state environment. In particular, fluctuating electric fields due to nearby charge traps or other quantum dots shift the transition frequencies via the Stark effect. The environment dynamics are mapped directly onto the fluorescence under resonant excitation and diminish the prospects of quantum dots as sources of indistinguishable photons in optical quantum computing. Here, we present an analysis of resonance fluorescence fluctuations based on photon counting statistics which captures the underlying time-averaged electric field fluctuations of the local environment. The measurement protocol avoids dynamic feedback on the electric environment and the dynamics of the quantum dots nuclear spin bath by virtue of its resonant nature and by keeping experimental control parameters such as excitation frequency and external fields constant throughout. The method introduced here is experimentally undemanding.
We developed a theoretical framework which extends the method of textit{full counting statistics} (FCS) from conventional single channel Kondo screening schemes to multi-channel Kondo paradigm. The developed idea of FCS has been demonstrated considering an example of two-stage Kondo (2SK) model. We analyzed the charge transferred statistics in the strong-coupling regime of a 2SK model using non-equilibrium Keldysh formulation. A bounded value of Fano factor, $1leq Fleq 5/3$, confirmed the cross-over regimes of charge transfered statistics in 2SK effect, from Poissonian to super-Poissonian. An innovative way of measuring transport properties of 2SK effect, by the independent measurements of charge current and noise, has been proposed
The coherent potential approximation (CPA) within full counting statistics (FCS) formalism is shown to be a suitable method to investigate average electric conductance, shot noise as well as higher order cumulants in disordered systems. We develop a similar FCS-CPA formalism for phonon transport through disordered systems. As a byproduct, we derive relations among coefficients of different phonon current cumulants. We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders. For binary disorders as well as Anderson disorders, we calculate up to the $8$-th phonon transmission moments and demonstrate that the numerical results of the FCS-CPA method agree very well with that of the brute force method. The benchmark shows that the FCS-CPA method achieves $20$ times more speedup ratio. Collective features of phonon current cumulants are also revealed.
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