Article

# Bidirectional Single-Electron Counting and the Fluctuation Theorem

Physical review. B, Condensed matter (Impact Factor: 3.77). 08/2009; DOI: 10.1103/PhysRevB.81.125331

Source: arXiv

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**ABSTRACT:**We study full counting statistics for transferred heat and entropy production between multi-terminal systems in absence of a finite junction. The systems are modelled as collections of coupled harmonic oscillators which are kept at different equilibrium temperatures and are connected via arbitrary time dependent couplings. Following consistent quantum framework and two-time measurement concept we obtain analytical expressions for the generalized cumulant generating function. We discuss transient and steady-state fluctuation theorems for the transferred quantities. We also address the effect of coupling strength on the exchange fluctuation theorem.Physical Review E 05/2014; 89(052101). · 2.31 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We evaluate the exact energy current and scaled cumulant generating function (related to the large-deviation function) in non-equilibrium steady states with energy flow, in any integrable model of relativistic quantum field theory (IQFT) with diagonal scattering. Our derivations are based on various recent results of D. Bernard and B. Doyon. The steady states are built by connecting homogeneously two infinite halves of the system thermalized at different temperatures $T_l$, $T_r$, and waiting for a long time. We evaluate the current $J(T_l,T_r)$ using the exact QFT density matrix describing these non-equilibrium steady states and using Al.B. Zamolodchikov's method of the thermodynamic Bethe ansatz (TBA). The scaled cumulant generating function is obtained from the extended fluctuation relations which hold in integrable models. We verify our formula in particular by showing that the conformal field theory (CFT) result is obtained in the high-temperature limit. We analyze numerically our non-equilibrium steady-state TBA equations for three models: the sinh-Gordon model, the roaming trajectories model, and the sine-Gordon model at a particular reflectionless point. Based on the numerics, we conjecture that an infinite family of non-equilibrium $c$-functions, associated to the scaled cumulants, can be defined, which we interpret physically. We study the full scaled distribution function and find that it can be described by a set of independent Poisson processes. Finally, we show that the "additivity" property of the current, which is known to hold in CFT and was proposed to hold more generally, does not hold in general IQFT, that is $J(T_l,T_r)$ is not of the form $f(T_l)-f(T_r)$.10/2013; - [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-. · 4.06 Impact Factor

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