Hanbury Brown-Twiss correlations to probe the population statistics of GHz photons emitted by conductors

We present the first study of the statistics of GHz photons in quantum circuits, using Hanbury Brown and Twiss correlations. The super-Poissonian and Poissonian photon statistics of thermal and coherent sources, respectively, made of a resistor and a radio frequency generator, are measured down to the quantum regime at milli-Kelvin temperatures. As photon correlations are linked to the second and fourth moments of current fluctuations, this experiment, which is based on current cryogenic electronics, may become a standard for probing electron/photon statistics in quantum conductors.     

Describing supercontinuum noise and rogue wave statistics using higher-order moments

We show that the noise properties of fiber supercontinuum generation and the appearance of long-tailed “rogue wave” statistics can be accurately quantified using statistical higher-order central moments. Statistical measures of skew and kurtosis, as well as the coefficient of variation provide improved insight into the nature of spectral fluctuations across the supercontinuum and allow regions of long-tailed statistics to be clearly identified. These moments – that depend only on analyzing intensity fluctuations – provide a complementary tool to phase-dependent coherence measures to interpret supercontinuum noise.     

Inverse statistics of smooth signals: the case of two dimensional turbulence

The problem of inverse statistics (statistics of distances for which the signal fluctuations are larger than a certain threshold) in differentiable signals with power law spectrum, E(k) approximately k(-alpha), 3< or =alpha<5, is discussed. We show that for these signals, with random phases, exit-distance moments follow a bifractal distribution. We also investigate two dimensional turbulent flows in the direct cascade regime, which display a more complex behavior. We give numerical evidences that the inverse statistics of 2D turbulent flows is described by a multifractal probability distribution; i.e., the statistics of laminar events is not simply captured by the exponent alpha characterizing the spectrum.     

Microscopic Features of Bosonic Quantum Transport and Entropy Production

The microscopic features of bosonic quantum transport in a nonequilibrium steady state, which breaks time reversal invariance spontaneously, are investigated. The analysis is based on the probability distributions, generated by the correlation functions of the particle current and the entropy production operator. The general approach is applied to an exactly solvable model with a point‐like interaction driving the system away from equilibrium. The quantum fluctuations of the particle current and the entropy production are explicitly evaluated in the zero frequency limit. It is shown that all moments of the entropy production distribution are non‐negative, which provides a microscopic version of the second law of thermodynamics. On this basis a concept of efficiency, taking into account all quantum fluctuations, is proposed and analyzed. The role of the quantum statistics in this context is also discussed.     

Coexistence of localized and delocalized surface plasmon modes in percolating metal films

Near-field intensity statistics in semicontinuous silver films over a wide range of surface coverage are investigated using near-field scanning optical microscopy. The variance of intensity fluctuations and the high-order moments of intensity enhancement exhibit local minima at the percolation threshold. This reduction in local field fluctuations results from resonant excitation of delocalized surface plasmon modes. By probing the modification of the critical indices for high-order moments of intensity enhancement caused by the delocalized states, we provide the first experimental evidence for the coexistence of localized and delocalized surface plasmon modes in percolating metal films.     

Thickness fluctuations in turbulent soap films

Rapidly flowing soap films provide a simple and attractive system to study two-dimensional hydrodynamics and turbulence. By measuring the rapid fluctuations of the thickness of the film in the turbulent regime, we find that the statistics of these fluctuations closely resemble those of a passive scalar field in a turbulent flow. The scalar spectra are well described by Kolmogorov-like scaling while the high-order moments show clear deviations from regular scaling just like dye or temperature fluctuations in 3D turbulent flows.     

Steady state statistics of driven diffusions

We consider overdamped diffusion processes driven out of thermal equilibrium and we analyze their dynamical steady fluctuations. We discuss the thermodynamic interpretation of the joint fluctuations of occupation times and currents; they incorporate respectively the time-symmetric and the time-antisymmetric sector of the fluctuations. We highlight the canonical structure of the joint fluctuations. The novel concept of traffic complements the entropy production for the study of the occupation statistics. We explain how the occupation and current fluctuations get mutually coupled out of equilibrium. Their decoupling close-to-equilibrium explains the validity of entropy production principles.     

Mesoscopic full counting statistics and exclusion models

We calculate the distribution of current fluctuations in two simple exclusion models. Although these models are classical, we recover even for small systems such as a simple or a double barrier, the same distibution of current as given by traditional formalisms for quantum mesoscopic conductors. Due to their simplicity, the full counting statistics in exclusion models can be reduced to the calculation of the largest eigenvalue of a matrix, the size of which is the number of internal configurations of the system. As examples, we derive the shot noise power and higher order statistics of current fluctuations (skewness, full counting statistics, ....) of various conductors, including multiple barriers, diffusive islands between tunnel barriers and diffusive media. A special attention is dedicated to the third cumulant, which experimental measurability has been demonstrated lately.     

Counting statistics of single electron transport in a quantum dot

We have measured the full counting statistics of current fluctuations in a semiconductor quantum dot (QD) by real-time detection of single electron tunneling with a quantum point contact. This method gives direct access to the distribution function of current fluctuations. Suppression of the second moment (related to the shot noise) and the third moment (related to the asymmetry of the distribution) in a tunable semiconductor QD is demonstrated experimentally. With this method we demonstrate the ability to measure very low current and noise levels.     

Switching noise as a probe of statistics in the fractional quantum Hall effect

We propose an experiment to probe the unconventional quantum statistics of quasiparticles in fractional quantum Hall states by measurement of current noise. The geometry we consider is that of a Hall bar where two quantum point contacts introduce two interfering amplitudes for backscattering. Thermal fluctuations of the number of quasiparticles enclosed between the two point contacts introduce current noise, which reflects the statistics of the quasiparticles. We analyze Abelian nu=1/q states and the non-Abelian nu=5/2 state.     

Josephson junctions as threshold detectors for full counting statistics

We discuss how threshold detectors can be used for a direct measurement of the full distribution of current fluctuations and how to exploit Josephson junctions in this respect. We propose a scheme to characterize the full counting statistics from the current dependence of the escape rate measured. We illustrate the scheme with explicit results for tunnel, diffusive, and quasiballistic mesoscopic conductors.     

Joint moments of the wave beam amplitude and inverse power in an absorbing random medium with lens properties

This paper presents a derivation of a system of closed equations for joint moments of the amplitude and inverse power of a wave beam propagating in a regularly inhomogeneous dissipative random medium. The radiation transfer in the medium is characterized by non-conservation of the total radiation energy flux and by the existence of power fluctuations. The statistics of the wave beam power fluctuations have been studied. Information on the power statistical characteristics is applied to close the system of equations for joint moments. For task parameters which are not very strict (an effective radius of the wave beam should be considerably less than the outer scale of the turbulence) a system of independent equations for arbitrary joint moments has been obtained. The equations for the first two lower joint moments of the beam intensity and inverse power have been solved analytically. With the solutions obtained the effective wave beam parameters were calculated, i.e. the beam mean displacement, effective broadening and tremble variance (the beam wandering variance) for the propagation of radiation in the refractive channel of an absorbing turbulent medium. Radically new characteristics of the behaviour of the effective parameters in random absorbing and transparent media have been revealed.     

Joint moments of the wave beam amplitude and inverse power in an absorbing random medium with lens properties

Abstract

This paper presents a derivation of a system of closed equations for joint moments of the amplitude and inverse power of a wave beam propagating in a regularly inhomogeneous dissipative random medium. The radiation transfer in the medium is characterized by non-conservation of the total radiation energy flux and by the existence of power fluctuations. The statistics of the wave beam power fluctuations have been studied. Information on the power statistical characteristics is applied to close the system of equations for joint moments. For task parameters which are not very strict (an effective radius of the wave beam should be considerably less than the outer scale of the turbulence) a system of independent equations for arbitrary joint moments has been obtained. The equations for the first two lower joint moments of the beam intensity and inverse power have been solved analytically. With the solutions obtained the effective wave beam parameters were calculated, i.e. the beam mean displacement, effective broadening and tremble variance (the beam wandering variance) for the propagation of radiation in the refractive channel of an absorbing turbulent medium. Radically new characteristics of the behaviour of the effective parameters in random absorbing and transparent media have been revealed.     

X-ray circular magnetic dichroism in the presence of strong spin fluctuations

The use of X-ray magnetic circular dichroism (XMCD) spectra for determininghe t magnitude of atomic magnetic moments in compounds of rare-earth and transition elements is discussed. The standard sum rule approach often yields a magnitude of moments that is often smaller than values obtained from magnetic measurements. We attribute this to strong spin fluctuations in the surface layers in which XMCD signals form. A way of determining the values of local magnetic moments in the presence of strong fluctuations is proposed and tested.     

Circuit theory for full counting statistics in multiterminal circuits

We propose a theory that treats the current, noise, and, generally, the full current statistics of electron transfer in a mesoscopic system in a unified, simple, and efficient way. The theory appears to be a circuit theory of 2 x 2 matrices associated with Keldysh Green functions. We illustrate the theory by considering the big fluctuations of currents in various three-terminal circuits.     

Stochastic path integral formulation of full counting statistics

We derive a stochastic path integral representation of counting statistics in semiclassical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to find the propagator for charge distributions with an arbitrary number of counting fields and generalized charges. The counting statistics is given by the saddle-point approximation to the path integral, and fluctuations around the saddle point are suppressed in the semiclassical approximation. We use this approach to derive the current cumulants of a chaotic cavity in the hot-electron regime.     

Spontaneous symmetry breaking at the fluctuating level

Phase transitions not allowed in equilibrium steady states may happen, however, at the fluctuating level. We observe for the first time this striking and general phenomenon measuring current fluctuations in an isolated diffusive system. While small fluctuations result from the sum of weakly correlated local events, for currents above a critical threshold the system self-organizes into a coherent traveling wave which facilitates the current deviation by gathering energy in a localized packet, thus breaking translation invariance. This results in Gaussian statistics for small fluctuations but non-Gaussian tails above the critical current. Our observations, which agree with predictions derived from hydrodynamic fluctuation theory, strongly suggest that rare events are generically associated with coherent, self-organized patterns which enhance their probability.     

Statistical properties of Lyapunov exponents and of quantum conductance of random systems in the regime of hopping transport

The statistics of the zero-temperature conductance and the Lyapunov exponents of one-, two- and three-dimensional disordered systems in the regime of strong localization is studied numerically. In one dimension, the origin of the universality of the moments of the conductance is explained. The relation between the most probable value of the conductance and its configurational average is discussed. The relative fluctuations of the conductance (and of the resistance) are shown to grow exponentially with the system length. In higher dimensions the conductance is almost entirely determined by the smallest of the Lyapunov exponents. The statistics of the conductance is therefore the same as in the one dimensional case. A model is proposed for the treatment of the fluctuations in hopping transport at finite temperatures. An exponential dependence of the relative fluctuations of the conductance/resistance on the temperature is predicted, log (δg/g) ∞ T^?a with α = 1/(d+1). It is concluded that the presently available experimental data on the temperature dependence of the conductance fluctuations in the hopping regime can be understood by replacing the system size in the zerotemperature result for the fluctuations of the conductance by the hopping length.     

Effect of polarized current on the magnetic state of an antiferromagnet

We provide evidence for the effects of spin polarized current on a nanofabricated antiferromagnet incorporated into a spin-valve structure. The signatures of the current-induced effects include bipolar steps in differential resistance, current-induced changes of exchange bias correlated with these steps, and deviations from the statistics expected for thermally activated switching of spin valves. We explain our observations by a combination of spin torque exerted on the interfacial antiferromagnetic moments and electron-magnon scattering in an antiferromagnet.     

Intermittent distribution of inertial particles in turbulent flows

We consider inertial particles suspended in an incompressible turbulent flow. Because of particles' inertia their flow is compressible, which leads to fluctuations of concentration significant for heavy particles. We show that the statistics of these fluctuations is independent of details of the velocity statistics, which allows us to predict that the particles cluster on the viscous scale of turbulence and describe the probability distribution of concentration fluctuations. We discuss the possible role of the clustering in the physics of atmospheric aerosols, in particular, in cloud formation.