We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants of the current using a recursive scheme. The finite-frequency noise is expressed not only in terms of the resolvent, but also initial system-environment correlations. As an illustrative example we consider electron transport through a dissipative double quantum dot for which we study the effects of dissipation on the zero-frequency cumulants of high orders and the finite-frequency noise.

We present a systematic definition and analysis of the thermo-electric linear response in gauge/gravity systems focusing especially on models with massive gravity in the bulk and therefore momentum dissipation in the dual field theory. A precise treatment of finite counter-terms proves to be essential to yield a consistent physical picture whose hydrodynamic and beyond-hydrodynamics behaviors noticeably match with field theoretical expectations. The model furnishes a possible gauge/gravity description of the crossover from the quantum-critical to the disorder-dominated Fermi-liquid behaviors, as expected in graphene.

Recent experimental progress has made it possible to detect in real-time single electrons tunneling through Coulomb blockade nanostructures, thereby allowing for precise measurements of the statistical distribution of the number of transferred charges, the so-called full counting statistics. These experimental advances call for a solid theoretical platform for equally accurate calculations of distribution functions and their cumulants. Here we develop a general framework for calculating zero-frequency current cumulants of arbitrary orders for transport through nanostructures with strong Coulomb interactions. Our recursive method can treat systems with many states as well as non-Markovian dynamics. We illustrate our approach with three examples of current experimental relevance: bunching transport through a two-level quantum dot, transport through a nanoelectromechanical system with dynamical Franck-Condon blockade, and transport through coherently coupled quantum dots embedded in a dissipative environment. We discuss properties of high-order cumulants as well as possible subtleties associated with non-Markovian dynamics.

We present a theory of full counting statistics for electron transport through interacting electron systems with non-Markovian dynamics. We illustrate our approach for transport through a single-level quantum dot and a metallic single-electron transistor to second order in the tunnel coupling, and discuss under which circumstances non-Markovian effects appear in the transport properties.

We provide an analytical derivation of the thermoelectric transport coefficients of the simplest momentum-dissipating model in gauge/gravity where the lack of momentum conservation is realized by means of explicit graviton mass in the bulk. We rely on the procedure recently described by Donos and Gauntlett for holographic models where momentum dissipation is realized through nontrivial scalars. The analytical approach confirms and supports the results found previously by means of numerical computations and the associated holographic renormalization procedure. Importantly, it also provides a precise identification of the range of validity of the hydrodynamic approximation.

We present an exhaustive theoretical analysis of charge and thermoelectric transport in a normal-metal–ferromagnetic-insulator–superconductor junction and explore the possibility of its use as a sensitive thermometer. We investigate the transfer functions and the intrinsic noise performance for different measurement configurations. A common feature of all configurations is that the best temperature-noise performance is obtained in the nonlinear temperature regime for a structure based on an Europium chalcogenide ferromagnetic insulator in contact with a superconducting Al film structure. For an open-circuit configuration, although the maximal intrinsic temperature sensitivity can achieve $10\mathrm{nK}{\mathrm{Hz}}^{-1/2}$, a realistic amplifying chain will reduce the sensitivity up to $10\mu \mathrm{K}{\mathrm{Hz}}^{-1/2}$. To overcome this limitation, we propose a measurement scheme in a closed-circuit configuration based on state-of-the-art superconducting-quantum-interference-device detection technology in an inductive setup. In such a case, we show that temperature-noise can be as low as $35\mathrm{nK}{\mathrm{Hz}}^{-1/2}$. We also discuss a temperature-to-frequency converter where the obtained thermovoltage developed over a Josephson junction operated in the dissipative regime is converted into a high-frequency signal. We predict that the structure can generate frequencies up to approximately 120 GHz and transfer functions up to $200\mathrm{GHz}/\mathrm{K}$ at around 1 K. If operated as an electron thermometer, the device may provide temperature-noise lower than $35\mathrm{nK}{\mathrm{Hz}}^{-1/2}$ thereby being potentially attractive for radiation-sensing applications.