Stochastic path integral formulation of full counting statistics

Tricritical Behavior in Dynamical Phase Transitions

We identify a new scenario for dynamical phase transitions associated with time-integrated observables occurring in diffusive systems described by the macroscopic fluctuation theory. It is characterized by the pairwise meeting of first- and second-order bias-induced phase transition curves at two tricritical points. We formulate a simple, general criterion for its appearance and derive an exact Landau theory for the tricritical behavior. The scenario is demonstrated in three examples: the simple symmetric exclusion process biased by an activity-related structural observable; the Katz-Lebowitz-Spohn lattice gas model biased by its current; and in an active lattice gas biased by its entropy production.

Dynamical fluctuations in the Riesz gas

We consider an infinite system of particles on a line performing identical Brownian motions and interacting through the |x-y|^{-s} Riesz potential, causing the overdamped motion of particles. We investigate fluctuations of the integrated current and the position of a tagged particle. We show that for 0<s<1, the standard deviations of both quantities grow as t^{s/2(1+s)}. When s>1, the interactions are effectively short-ranged, and the universal subdiffusive t^{1/4} growth emerges with only amplitude depending on the exponent s. We also show that the two-time correlations of the tagged-particle position have the same form as for fractional Brownian motion.

Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space

We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of Markovian diffusion in equilibrium or nonequilibrium steady states on all timescales. We unravel a deep connection between current fluctuations and generalized time-reversal symmetry, providing new insight into time-averaged observables. We highlight the essential role of coarse graining in space from mathematical, thermodynamical, and experimental points of view. Spatial coarse graining is required to uncover salient features of currents that break detailed balance, and a thermodynamically "optimal" coarse graining ensures the most precise inference of dissipation. Defined without coarse graining, the fluctuations of empirical density and current are proven to diverge on all timescales in dimensions higher than one, which has far-reaching consequences for the central-limit regime in continuous space. We apply the results to examples of irreversible diffusion. Our findings provide new intuition about time-averaged observables and allow for a more efficient analysis of single-molecule experiments.

Evolution of Non-Gaussian Hydrodynamic Fluctuations

In the context of the search for the QCD critical point using non-Gaussian fluctuations, we obtain the evolution equations for non-Gaussian cumulants to the leading order of the systematic expansion in the magnitude of thermal fluctuations. We develop a diagrammatic technique in which the leading order contributions are given by tree diagrams. We introduce a Wigner transform for multipoint correlators and derive the evolution equations for three- and four-point Wigner functions for the problem of nonlinear stochastic diffusion with multiplicative noise.

Full counting statistics of the particle currents through a Kitaev chain and the exchange fluctuation theorem

Exchange fluctuation theorems (XFTs) describe a fundamental symmetry relation for particle and energy exchange between several systems. Here we study the XFTs of a Kitaev chain connected to two reservoirs at the same temperature but different bias. By varying the parameters in the Kitaev chain model, we calculate analytically the full counting statistics of the transport current and formulate the corresponding XFTs for multiple current components. We also demonstrate the XFTs with numerical results. We find that due to the presence of the U(1) symmetry breaking terms in the Hamiltonian of the Kitaev chain, various forms of the XFTs emerge, and they can be interpreted in terms of various well-known transport processes.

Large deviations and fluctuation theorem for the quantum heat current in the spin-boson model

We study the heat current flowing between two baths consisting of harmonic oscillators interacting with a qubit through a spin-boson coupling. An explicit expression for the generating function of the total heat flowing between the right and left baths is derived by evaluating the corresponding Feynman-Vernon path integral by performing the noninteracting blip approximation (NIBA). We recover the known expression, obtained by using the polaron transform. This generating function satisfies the Gallavotti-Cohen fluctuation theorem, both before and after performing the NIBA. We also verify that the heat conductance is proportional to the variance of the heat current, retrieving the well-known fluctuation dissipation relation. Finally, we present numerical results for the heat current.

Infinite family of universal profiles for heat current statistics in Fourier's law

Using tools from large deviation theory, we study fluctuations of the heat current in a model of d-dimensional incompressible fluid driven out of equilibrium by a temperature gradient. We find that the most probable temperature fields sustaining atypical values of the global current can be naturally classified in an infinite set of curves, allowing us to exhaustively analyze their topological properties and to define universal profiles onto which all optimal fields collapse. We also compute the statistics of empirical heat current, where we find remarkable logarithmic tails for large current fluctuations orthogonal to the thermal gradient. Finally, we determine explicitly a number of cumulants of the current distribution, finding interesting relations between them.

Heat transfer statistics in mixed quantum-classical systems

The modelling of quantum heat transfer processes at the nanoscale is crucial for the development of energy harvesting and molecular electronic devices. Herein, we adopt a mixed quantum-classical description of a device, in which the open subsystem of interest is treated quantum mechanically and the surrounding heat baths are treated in a classical-like fashion. By introducing such a mixed quantum-classical description of the composite system, one is able to study the heat transfer between the subsystem and bath from a closed system point of view, thereby avoiding simplifying assumptions related to the bath time scale and subsystem-bath coupling strength. In particular, we adopt the full counting statistics approach to derive a general expression for the moment generating function of heat in systems whose dynamics are described by the quantum-classical Liouville equation (QCLE). From this expression, one can deduce expressions for the dynamics of the average heat and heat current, which may be evaluated using numerical simulations. Due to the approximate nature of the QCLE, we also find that the steady state fluctuation symmetry holds up to order ℏ for systems whose subsystem-bath couplings and baths go beyond bilinear and harmonic, respectively. To demonstrate the approach, we consider the nonequilibrium spin boson model and simulate its time-dependent average heat and heat current under various conditions.

Structure of the optimal path to a fluctuation

Macroscopic fluctuations have become an essential tool to understand physics far from equilibrium due to the link between their statistics and nonequilibrium ensembles. The optimal path leading to a fluctuation encodes key information on this problem, shedding light on, e.g., the physics behind the enhanced probability of rare events out of equilibrium, the possibility of dynamic phase transitions, and new symmetries. This makes the understanding of the properties of these optimal paths a central issue. Here we derive a fundamental relation which strongly constrains the architecture of these optimal paths for general d-dimensional nonequilibrium diffusive systems, and implies a nontrivial structure for the dominant current vector fields. Interestingly, this general relation (which encompasses and explains previous results) makes manifest the spatiotemporal nonlocality of the current statistics and the associated optimal trajectories.

Numerical study of continuous and discontinuous dynamical phase transitions for boundary-driven systems

The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary-driven systems with a constrained integrated current. It is shown that certain models exhibit a discontinuous transition between two different density profiles and a continuous transition between a time-independent and a time-dependent profile. We also verified that the Kipnis-Marchioro-Presutti model exhibits no phase transitions in a range much larger than previously explored.

Dynamical Symmetry Breaking and Phase Transitions in Driven Diffusive Systems

We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of equilibrium are derived. These transitions manifest themselves as singularities in the large deviation function, resulting in enhanced current fluctuations. Microscopic models which implement each of the scenarios are presented, with possible experimental realizations. Depending on the model, the singularity is associated either with a particle-hole symmetry breaking, which leads to a continuous transition, or in the absence of the symmetry with a first-order phase transition. An exact Landau theory which captures the different singular behaviors is derived.

The theory of spin noise spectroscopy: a review

Direct measurements of spin fluctuations are becoming the mainstream approach for studies of complex condensed matter, molecular, nuclear, and atomic systems. This review covers recent progress in the field of optical spin noise spectroscopy (SNS) with an additional goal to establish an introduction into its theoretical foundations. Various theoretical techniques that have been recently used to interpret results of SNS measurements are explained alongside examples of their applications.

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Universality in Higher Order Spin Noise Spectroscopy

Higher order time correlators of spin fluctuations reveal considerable information about spin interactions. We argue that in a broad class of spin systems, one can justify a phenomenological approach to explore such correlators. We predict that the third and fourth order spin cumulants are described by a universal function that can be parametrized by a small set of parameters. We show that the fluctuation theorem constrains this function so that such correlators are fully determined by lowest nonlinear corrections to the free energy and the mean and variance of microscopic spin currents. We also provide an example of microscopic calculations for conduction electrons.

Intermittency and dynamical Lee-Yang zeros of open quantum systems

We use high-order cumulants to investigate the Lee-Yang zeros of generating functions of dynamical observables in open quantum systems. At long times the generating functions take on a large-deviation form with singularities of the associated cumulant generating functions-or dynamical free energies-signifying phase transitions in the ensemble of dynamical trajectories. We consider a driven three-level system as well as the dissipative Ising model. Both systems exhibit dynamical intermittency in the statistics of quantum jumps. From the short-time behavior of the dynamical Lee-Yang zeros, we identify critical values of the counting field which we attribute to the observed intermittency and dynamical phase coexistence. Furthermore, for the dissipative Ising model we construct a trajectory phase diagram and estimate the value of the transverse field where the stationary state changes from being ferromagnetic (inactive) to paramagnetic (active).

Extreme current fluctuations in lattice gases: beyond nonequilibrium steady states

We use the macroscopic fluctuation theory (MFT) to study large current fluctuations in nonstationary diffusive lattice gases. We identify two universality classes of these fluctuations, which we call elliptic and hyperbolic. They emerge in the limit when the deterministic mass flux is small compared to the mass flux due to the shot noise. The two classes are determined by the sign of compressibility of effective fluid, obtained by mapping the MFT into an inviscid hydrodynamics. An example of the elliptic class is the symmetric simple exclusion process, where, for some initial conditions, we can solve the effective hydrodynamics exactly. This leads to a super-Gaussian extreme current statistics conjectured by Derrida and Gerschenfeld [J. Stat. Phys. 137, 978 (2009)] and yields the optimal path of the system. For models of the hyperbolic class, the deterministic mass flux cannot be neglected, leading to a different extreme current statistics.

Waiting time distributions for the transport through a quantum-dot tunnel coupled to one normal and one superconducting lead

We have studied the waiting time distributions (WTDs) for subgap transport through a single-level quantum-dot tunnel coupled to one normal and one superconducting lead. The WTDs reveal the internal dynamics of the system, in particular, the coherent transfer of Cooper pairs between the dot and the superconductor. The WTDs exhibit oscillations that can be directly associated to the coherent oscillation between the empty and doubly occupied dot. The oscillation frequency is equal to the energy splitting between the Andreev bound states. These effects are more pronounced when the empty state and double-occupied state are in resonance.

Trajectory phase transitions and dynamical Lee-Yang zeros of the Glauber-Ising chain

We examine the generating function of the time-integrated energy for the one-dimensional Glauber-Ising model. At long times, the generating function takes on a large-deviation form and the associated cumulant generating function has singularities corresponding to continuous trajectory (or "space-time") phase transitions between paramagnetic trajectories and ferromagnetically or antiferromagnetically ordered trajectories. In the thermodynamic limit, the singularities make up a whole curve of critical points in the complex plane of the counting field. We evaluate analytically the generating function by mapping the generator of the biased dynamics to a non-Hermitian Hamiltonian of an associated quantum spin chain. We relate the trajectory phase transitions to the high-order cumulants of the time-integrated energy which we use to extract the dynamical Lee-Yang zeros of the generating function. This approach offers the possibility to detect continuous trajectory phase transitions from the finite-time behavior of measurable quantities.

Braid group and topological phase transitions in nonequilibrium stochastic dynamics

We show that distinct topological phases of the band structure of a non-Hermitian Hamiltonian can be classified with elements of the braid group. As the proof of principle, we consider the non-Hermitian evolution of the statistics of nonequilibrium stochastic currents. We show that topologically nontrivial phases have detectable properties, including the emergence of decaying oscillations of parity and state probabilities, and discontinuities in the steady state statistics of currents.

Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state

We describe how to characterize dynamical phase transitions in open quantum systems from a purely dynamical perspective, namely, through the statistical behavior of quantum jump trajectories. This approach goes beyond considering only properties of the steady state. While in small quantum systems dynamical transitions can only occur trivially at limiting values of the controlling parameters, in many-body systems they arise as collective phenomena and within this perspective they are reminiscent of thermodynamic phase transitions. We illustrate this in open models of increasing complexity: a three-level system, the micromaser, and a dissipative version of the quantum Ising model. In these examples dynamical transitions are accompanied by clear changes in static behavior. This is however not always the case, and, in general, dynamical phases need to be uncovered by observables which are strictly dynamical, e.g., dynamical counting fields. We demonstrate this via the example of a class of models of dissipative quantum glasses, whose dynamics can vary widely despite having identical (and trivial) stationary states.

Quantum heat fluctuations of single-particle sources

Optimal single electron sources emit regular streams of particles, displaying no low-frequency charge current noise. Because of the wave packet nature of the emitted particles, the energy is, however, fluctuating, giving rise to heat current noise. We investigate theoretically this quantum source of heat noise for an emitter coupled to an electronic probe in the hot-electron regime. The distribution of temperature and potential fluctuations induced in the probe is shown to provide direct information on the single-particle wave function properties and display strong nonclassical features.

Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics

We investigate Lee-Yang zeros of generating functions of dynamical observables and establish a general relation between phase transitions in ensembles of trajectories of stochastic many-body systems and the time evolution of high-order cumulants of such observables. This connects dynamical free energies for full counting statistics in the long-time limit, which can be obtained via large-deviation methods and whose singularities indicate dynamical phase transitions, to observables that are directly accessible in simulation and experiment. As an illustration, we consider facilitated spin models of glasses and show that from the short-time behavior of high-order cumulants, it is possible to infer the existence and location of dynamical or "space-time" transitions in these systems.

Fluctuation relations for spintronics

Fluctuation relations are derived in systems where the spin degree of freedom and magnetic interactions play a crucial role. The form of the nonequilibrium fluctuation theorems relies on the assumption of a local balance condition. We demonstrate that in some cases the presence of magnetic interactions violates this condition. Nevertheless, fluctuation relations can be obtained from the microreversibility principle sustained only at equilibrium as a symmetry of the cumulant generating function for spin currents. We illustrate the spintronic fluctuation relations for a quantum dot coupled to partially polarized helical edge states.

Full-counting statistics of heat transport in harmonic junctions: transient, steady states, and fluctuation theorems

We study the statistics of heat transferred in a given time interval t_{M}, through a finite harmonic chain, called the center, which is connected to two heat baths, the left (L) and the right (R), that are maintained at two temperatures. The center atoms are driven by external time-dependent forces. We calculate the cumulant generating function (CGF) for the heat transferred out of the left lead, Q_{L}, based on the two-time quantum measurement concept and using the nonequilibrium Green's function method. The CGF can be concisely expressed in terms of Green's functions of the center and an argument-shifted self-energy of the lead. The expression of the CGF is valid in both transient and steady-state regimes. We consider three initial conditions for the density operator and show numerically, for a one-atom junction, how their transient behaviors differ from each other but, finally, approach the same steady state, independent of the initial distributions. We also derive the CGF for the joint probability distribution P(Q_{L},Q_{R}), and discuss the correlations between Q_{L} and Q_{R}. We calculate the CGF for total entropy production in the reservoirs. In the steady state we explicitly show that the CGFs obey steady-state fluctuation theorems. We obtain classical results by taking ℏ→0. We also apply our method to the counting of the electron number and electron energy, for which the associated self-energy is obtained from the usual lead self-energy by multiplying a phase and shifting the contour time, respectively.

Full counting statistics of a Luttinger liquid conductor

Nonequilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the time resolved full counting statistics of the transmitted charge is derived. It is given by the Fredholm determinant of the counting operator with a time-dependent scattering phase. The result has a form of counting statistics of noninteracting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the noninteracting leads.

Fluctuation relations and rare realizations of transport observables

Fluctuation relations establish rigorous identities for the nonequilibrium averages of observables. Starting from a general transport master equation with time-dependent rates, we employ the stochastic path integral approach to study statistical fluctuations around such averages. We show how under nonequilibrium conditions, rare realizations of transport observables are crucial and imply massive fluctuations that may completely mask such identities. Quantitative estimates for these fluctuations are provided. We illustrate our results on the paradigmatic example of a mesoscopic RC circuit.

Magnetic-field-induced non-Gaussian fluctuations in macroscopic equilibrium systems

We calculate the magnetic-field-dependent nonlinear conductance and noise in a two-dimensional macroscopic inhomogeneous system. If the system does not possess a specific symmetry, the magnetic field induces a nonzero third cumulant of the current even at equilibrium. This cumulant is related to the first and second voltage derivatives of the spectral density and average current in the same way as for mesoscopic quantum-coherent systems, but these quantities may be much larger. The system provides a robust test of a nonequilibrium fluctuation relation.

Switching exponent scaling near bifurcation points for non-Gaussian noise

We study noise-induced switching of a system close to bifurcation parameter values where the number of stable states changes. For non-Gaussian noise, the switching exponent, which gives the logarithm of the switching rate, displays a non-power-law dependence on the distance to the bifurcation point. This dependence is found for Poisson noise. Even weak additional Gaussian noise dominates switching sufficiently close to the bifurcation point, leading to a crossover in the behavior of the switching exponent.

Variational principle of counting statistics in master equations

We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the similar path integral formulation without the assumption of mesoscopic systems. It has been clarified that the saddle point method for the path integral is not an approximation, but a valid procedure in the present derivation. Hence, a variational principle in the counting statistics is naturally derived. In order to obtain the variational principle, we employ many independent replicas of the same system. In addition, the Euler-Maclaurin formula is used in order to connect the discrete and continuous properties of the system.

Detection of non-Gaussian fluctuations in a quantum point contact

An experimental study of current fluctuations through a tunable transmission barrier, a quantum point contact, is reported. We measure the probability distribution function of transmitted charge with precision sufficient to extract the first three cumulants. To obtain the intrinsic quantities, corresponding to voltage-biased barrier, we employ a procedure that accounts for the response of the external circuit and the amplifier. The third cumulant, obtained with a high precision, is found to agree with the prediction for the statistics of transport in the non-Poissonian regime.

Universal geometric theory of mesoscopic stochastic pumps and reversible ratchets

We construct a unifying theory of geometric effects in mesoscopic stochastic kinetics. We demonstrate that the adiabatic pump and the reversible ratchet effects, as well as similar new phenomena in other domains, such as in epidemiology, all follow from very similar geometric phase contributions to the effective action in the stochastic path integral representation of the moment generating function. The theory provides the universal technique for identification, prediction, and calculation of pumplike phenomena in an arbitrary mesoscopic stochastic framework.

Stochastic dynamics of a Josephson junction threshold detector

We generalize the stochastic path integral formalism by considering Hamiltonian dynamics in the presence of general Markovian noise. Kramers' solution of the activation rate for escape over a barrier is generalized for non-Gaussian driving noise in both the overdamped and underdamped limit. We apply our general results to a Josephson junction detector measuring the electron counting statistics of a mesoscopic conductor. The activation rate dependence on the third current cumulant includes an additional term originating from the backaction of the measurement circuit.

Full-counting statistics for voltage and dephasing probes

We present a stochastic path integral method to calculate the full-counting statistics of conductors with energy conserving dephasing probes and dissipative voltage probes. The approach is explained for the experimentally important case of a Mach-Zehnder interferometer, but is easily generalized to more complicated setups. For all geometries where dephasing may be modeled by a single one-channel dephasing probe we prove that our method yields the same full-counting statistics as phase averaging of the cumulant generating function.

Full counting statistics in strongly interacting systems: non-Markovian effects

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.

Distribution of current in nonequilibrium diffusive systems and phase transitions

We consider diffusive lattice gases on a ring and analyze the stability of their density profiles conditionally to a current deviation. Depending on the current, one observes a phase transition between a regime where the density remains constant and another regime where the density becomes time dependent. Numerical data confirm this phase transition. This time dependent profile persists in the large drift limit and allows one to understand on physical grounds the results obtained earlier for the totally asymmetric exclusion process on a ring.

Measurement of counting statistics of electron transport in a tunnel junction

We present measurements of the time-dependent fluctuations of electrical current in a voltage-biased tunnel junction. We were able to simultaneously extract the first three moments of the current counting statistics. Detailed comparison of the second and the third moments reveals that the statistics is accurately described as Poissonian, expected for spontaneous current fluctuations due to electron charge discreteness, realized in tunneling transport at negligible coupling to environment.

Quantum-to-classical crossover in full counting statistics

The reduction of quantum scattering leads to the suppression of shot noise. In this Letter, we analyze the crossover from the quantum transport regime with universal shot noise to the classical regime where noise vanishes. By making use of the stochastic path integral approach, we find the statistics of transport and the transmission properties of a chaotic cavity as a function of a system parameter controlling the crossover. We identify three different scenarios of the crossover.

Noise and full counting statistics of incoherent multiple Andreev reflection

We present a general theory for the full counting statistics of multiple Andreev reflections in incoherent superconducting-normal-superconducting contacts. The theory, based on a stochastic path integral approach, is applied to a superconductor-double-barrier system. It is found that all cumulants of the current show a pronounced subharmonic gap structure at voltages V=2Delta/en. For low voltages V<<Delta/e, the counting statistics results from diffusion of multiple charges in energy space, giving the pth cumulant Q(p) proportional, variantV(2-p), diverging for p> or =3. We show that this low-voltage result holds for a large class of incoherent superconducting-normal-superconducting contacts.

Current fluctuations in stochastic lattice gases

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation theory for the space-time fluctuations of the empirical current which include the previous results. We then estimate the probability of a fluctuation of the average current over a large time interval. It turns out that recent results by Bodineau and Derrida [Phys. Rev. Lett. 92, 180601 (2004)]] in certain cases underestimate this probability due to the occurrence of dynamical phase transitions.

Transport statistics of bistable systems

We consider the transport statistics of classical bistable systems driven by noise. The stochastic path integral formalism is used to investigate the dynamics and distribution of transmitted charge. Switching rates between the two stable states are found from an instanton calculation, leading to an effective two-state system on a long time scale. In the bistable current range, the telegraph noise dominates the distribution, whose logarithm is found to be universally described by a tilted ellipse.

Rare event statistics in reaction-diffusion systems

We present an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction-diffusion systems. This method is based on a semiclassical treatment of an underlying "quantum" Hamiltonian, encoding the system's evolution. To this end, we formulate the corresponding canonical dynamical system and investigate its phase portrait. This method is presented for a number of pedagogical examples.

Current fluctuations in nonequilibrium diffusive systems: an additivity principle

We formulate a simple additivity principle allowing one to calculate the whole distribution of current fluctuations through a large one dimensional system in contact with two reservoirs at unequal densities from the knowledge of its first two cumulants. This distribution (which in general is non-Gaussian) satisfies the Gallavotti-Cohen symmetry and generalizes the one predicted recently for the symmetric simple exclusion process. The additivity principle can be used to study more complex diffusive networks including loops.

Frequency scales for current statistics of mesoscopic conductors

We calculate the third cumulant of current in a chaotic cavity with contacts of arbitrary transparency as a function of frequency. Its frequency dependence drastically differs from that of the conventional noise. In addition to a dispersion at the inverse RC time characteristic of charge relaxation, it has a low-frequency dispersion at the inverse dwell time of electrons in the cavity. This effect is suppressed if both contacts have either large or small transparencies.

Environmental effects in the third moment of voltage fluctuations in a tunnel junction

We present the first measurements of the third moment of the voltage fluctuations in a conductor. This technique can provide new and complementary information on the electronic transport in conducting systems. The measurement was performed on nonsuperconducting tunnel junctions as a function of voltage bias, for various temperatures and bandwidths up to 1 GHz. The data demonstrate the significant effect of the electromagnetic environment of the sample.

Full counting statistics of multiple Andreev reflection

We derive the full counting statistics of charge transfer through a voltage biased superconducting junction. We find that, for measurement times much longer than the inverse Josephson frequency, the counting statistics describes a correlated transfer of quanta of multiple electron charges, each quantum associated with the transfer of a single quasiparticle. An expression for the counting statistics in terms of the quasiparticle scattering amplitudes is derived.