Article

# Bidirectional Single-Electron Counting and the Fluctuation Theorem

Physical review. B, Condensed matter (Impact Factor: 3.66). 08/2009; DOI: 10.1103/PhysRevB.81.125331

Source: arXiv

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**ABSTRACT:**We study single-electron transport through a double quantum dot (DQD) monitored by a capacitively coupled quantum point-contact (QPC) electrometer. We derive the full counting statistics for the coupled DQD - QPC system and obtain the joint probability distribution of the charges transferred through the DQD and the QPC consistent with the fluctuation theorem for four terminal system. For the two-terminal DQD system, the FT is not necessarily satisfied. It is due to the back action caused by the shot noise of the QPC, and the FT for the DQD is modified with an “effective temperature”.Journal of Physics Conference Series 12/2012; 400(4):2012-. - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper is devoted to multivariate fluctuation relations for all the currents flowing across an open system in contact with several reservoirs at different temperatures and chemical potentials, or driven by time-independent external mechanical forces. After some transient behavior, the open system is supposed to reach a nonequilibrium steady state that is controlled by the thermodynamic and mechanical forces, called the affinities. The time-reversal symmetry of the underlying Hamiltonian dynamics implies symmetry relations among the statistical properties of the fluctuating currents, depending on the values of the affinities. These multivariate fluctuation relations are not only compatible with the second law of thermodynamics, but they also imply remarkable relations between the linear or nonlinear response coefficients and the cumulants of the fluctuating currents. These relations include the Onsager and Casimir reciprocity relations, as well as their generalizations beyond linear response. Methods to deduce multivariate fluctuation relations are presented for classical, stochastic and quantum systems. In this way, multivariate fluctuation relations are obtained for energy or particle transport in the effusion of an ideal gas, heat transport in Hamiltonian systems coupled by Langevin stochastic forces to heat reservoirs, driven Brownian motion of an electrically charged particle subjected to an external magnetic field, and quantum electron transport in multi-terminal mesoscopic circuits where the link to the scattering approach is established.New Journal of Physics 11/2013; 15(11):5014-. · 3.67 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Using time-resolved charge detection in a double quantum dot, we present an experimental test of the fluctuation theorem. The fluctuation theorem, a result from nonequilibrium statistical mechanics, quantifies the ratio of occurrence of fluctuations that drive a small system against the direction favored by the second law of thermodynamics. Here, these fluctuations take the form of single electrons flowing against the source–drain bias voltage across the double quantum dot. Our results, covering configurations close to as well as far from equilibrium, agree with the theoretical predictions, when the finite bandwidth of the charge detection is taken into account. In further measurements, we study a fluctuation relation that is a generalization of the Johnson–Nyquist formula and relates the second-order conductance to the voltage dependence of the noise. Current and noise can be determined with the time-resolved charge detection method. Our measurements confirm the fluctuation relation in the nonlinear transport regime of the double quantum dot.Journal of Applied Physics 03/2013; 113(13). · 2.19 Impact Factor

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