The study of quantum thermal machines, and more generally of open quantum systems, often relies on master equations. Two approaches are mainly followed. On the one hand, there is the widely used, but often criticized, local approach, where machine sub-systems locally couple to thermal baths. On the other hand, in the more established global approach, thermal baths couple to global degrees of freedom of the machine. There has been debate as to which of these two conceptually different approaches should be used in situations out of thermal equilibrium. Here we compare the local and global approaches against an exact solution for a particular class of thermal machines. We consider thermodynamically relevant observables, such as heat currents, as well as the quantum state of the machine. Our results show that the use of a local master equation is generally well justified. In particular, for weak inter-system coupling, the local approach agrees with the exact solution, whereas the global approach fails for non-equilibrium situations. For intermediate coupling, the local and the global approach both agree with the exact solution and for strong coupling, the global approach is preferable. These results are backed by detailed derivations of the regimes of validity for the respective approaches.or more concretely of an electrical current [34,[42][43][44], the refrigeration of a quantum degree of freedom [45][46][47][48][49][50], the creation of entanglement [51][52][53], the determination of low temperatures [54], or the design of thermal transistors [55] and autonomous quantum clocks [56].The standard description of these systems crucially relies on Markovian master equations to predict the relevant observables, such as heat currents and power. Two main approaches are followed in the literature. The first is a local approach, where the thermal baths couple locally to sub-systems of the machine. The second is a global approach, where thermal baths couple to the global eigenmodes of the machine. As the two approaches are conceptually different, there has been considerable debate about which one should be used in order to accurately describe thermal machines, and more generally out-of-equilibrium systems. Since the global approach describes equilibrium situations accurately (see below), while the local in some cases does not, there has been incentive to use the global approach out of equilibrium as well. Furthermore, the local approach is often believed to be more phenomenological in nature [13,14,19,28,57] and it was even argued that it is unphysical in certain regimes [27,58,59].The goal of the present work is to discuss these questions in depth. We will consider a system for which the full unitary dynamics of the machine and the thermal baths can be solved exactly. This allows us to evaluate the performance of local and global master equations for the machine against the exact dynamics. In addition, we give detailed derivations of the local and the global approaches and discuss the involved approximations. Specifically, ...

Electron transport in mesoscopic conductors has traditionally involved investigations of the mean current and the fluctuations of the current. A complementary view on charge transport is provided by the distribution of waiting times between charge carriers, but a proper theoretical framework for coherent electronic systems has so far been lacking. Here we develop a quantum theory of electron waiting times in mesoscopic conductors expressed by a compact determinant formula. We illustrate our methodology by calculating the waiting time distribution for a quantum point contact and find a crossover from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off. Even when the low-frequency transport is noiseless, the electrons are not equally spaced in time due to their inherent wave nature. We discuss the implications for renewal theory in mesoscopic systems and point out several analogies with level spacing statistics and random matrix theory.

Recently demonstrated solid-state single-electron sources generate different quantum states depending on their operation condition. For adiabatic and nonadiabatic sources, we determine the Glauber correlation function in terms of the Floquet scattering matrix of the source. The correlation function provides full information on the shape of the state and on its time-dependent amplitude and phase. The coherence properties of single-electron states are therefore essential for the production of quantum multiparticle states.

A new type of electron sources has emerged which permits to inject particles in a controllable manner, one at a time, into an electronic circuit. Such single electron sources make it possible to fully exploit the particles' quantum nature. We determine the single-particle coherence length from the decay of the Aharonov-Bohm oscillations as a function of the imbalance of a Mach-Zehnder interferometer connected to a single electron source. The single-particle coherence length is of particular importance as it is an intrinsic property of the source in contrast to the dephasing length.PACS numbers: 73.23. Ad, In low temperature electron physics, thus far most electronic transport measurements have used either metallic contacts or superconductors in thermodynamic equilibrium as injectors of electrons. Such sources are suitable to investigate coherent phenomena but are not useful for quantum information as there is no control on the injection time of the single electrons. To the contrary, the recent experimental achievement of single electron sources [1, 2] heralds a new field in solid-state electronics. These single electron sources are high-frequency sources that can emit at a GHz rate single particles with a Lorentzian density profile [3] of half duration Γ SES . In the integer Quantum Hall regime, the emitted single particles are injected through a quantum point contact (QPC) into edge states, which are chiral due to suppressed backscattering [4,5] and which take the role of wave guides for electrons. When subject to an appropriate time-periodic voltage, the single electron source (SES) of Fève et al.[2] can be tuned to inject an electron in the first half cycle and a hole in the second half cycle into the same channel [6]. Other turnstile like sources separate the two types of carriers into different channels [7] and can produce a stream of electrons only. Thanks to their injection tunability, such single-particle state emitters present a powerful potential for quantum information processing [8]: multiparticle exchange, two-particle interference effects and entanglement [3,9] have already been proposed. However, the appearance of such single-electron sources demands a characterization of their basic property, namely the coherence length Λ of the single-particle states they generate [10]. This length sets the distance over which a single-particle is able to interfere with itself at the output of an interferometer.In this letter we propose an Aharonov-Bohm (AB) oscillation experiment with an electronic Mach-Zehnder interferometer (MZI) as shown in Fig. 1 to determine directly this single-particle coherence length Λ which reflects the coherence property of the source. In mesoscop-T L T R 1 2 4 Single electron source SES T u L d L SES ∆L Magnetic flux µ 3 V(t) Outgoing pulses Incoming pulse 2Γ PSfrag replacements Φ FIG. 1: (Color online) Single electron source (SES) coupled to a Mach-Zehnder interferometer (MZI) through a quantum point contact (QPC) with transmission probability TSES. A periodic voltage V (t) = V (t +...