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Register a new userCycle decomposition of full counting statistics
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David Andrieux
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This paper has been withdrawn by the author due to an error in the derivation.
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We report the first measurement of high order cumulants of the current fluctuations in an avalanche diode run through by a stationary dc current. Such a system is archetypic of devices in which transport is governed by a collective mechanism, here charge multiplication by avalanche. We have measured the first 5 cumulants of the probability distribution of the current fluctuations. We show that the charge multiplication factor is distributed according to a power law that is different from that of the usual avalanche below breakdown, when avalanches are well separated.
We study charge transport and fluctuations of the (3+1)-dimensional massive free Dirac theory. In particular, we focus on the steady state that emerges following a local quench whereby two independently thermalized halves of the system are connected and let to evolve unitarily for a long time. Based on the two-time von Neumann measurement statistics and exact computations, the scaled cumulant generating function associated with the charge transport is derived. We find that it can be written as a generalization of Levitov-Lesovik formula to the case in three spatial dimensions. In the massless case, we note that only the first four scaled cumulants are nonzero. Our results provide also a direct confirmation for the validity of the extended fluctuation relation in higher dimensions. An application of our approach to Lifshitz fermions is also briefly discussed.
We develop and test a computational framework to study heat exchange in interacting, nonequilibrium open quantum systems. Our iterative full counting statistics path integral (iFCSPI) approach extends a previously well-established influence functional path integral method, by going beyond reduced system dynamics to provide the cumulant generating function of heat exchange. The method is straightforward; we implement it for the nonequilibrium spin boson model to calculate transient and long-time observables, focusing on the steady-state heat current flowing through the system under a temperature difference. Results are compared to perturbative treatments and demonstrate good agreement in the appropriate limits. The challenge of converging nonequilibrium quantities, currents and high order cumulants, is discussed in detail. The iFCSPI, a numerically exact technique, naturally captures strong system-bath coupling and non-Markovian effects of the environment. As such, it is a promising tool for probing fundamental questions in quantum transport and quantum thermodynamics.
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.
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.
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