Circuit theory for full counting statistics in multiterminal circuits

Ballistic modes as a source of anomalous charge noise

Steady-state currents generically occur both in systems with continuous translation invariance and in nonequilibrium settings with particle drift. In either case, thermal fluctuations advected by the current act as a source of noise for slower hydrodynamic modes. This noise is unconventional, since it is highly correlated along spacetime rays. We argue that, in quasi-one-dimensional geometries, the correlated noise from ballistic modes generically gives rise to anomalous full counting statistics (FCS) for diffusively spreading charges. We present numerical evidence for anomalous FCS in two settings: (1) a two-component continuum fluid and (2) the totally asymmetric exclusion process initialized in a nonequilibrium state.

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 for noninteracting fermions: exact finite-temperature results and generalized long-time approximation

Exact numerical results for the full counting statistics (FCS) of a one-dimensional tight-binding model of noninteracting electrons are presented at finite temperatures using an identity recently published by Abanov and Ivanov. A similar idea is used to derive an explicit expression for the cumulant generating function for a system consisting of two quasi-one-dimensional leads connected by a quantum dot in the long-time limit, generalizing the Levitov-Lesovik formula for two single-channel leads to systems with an arbitrary number of transverse channels.

Full counting statistics for noninteracting fermions: joint probability distributions

The joint probability distribution in the full counting statistics (FCS) for noninteracting electrons is discussed for an arbitrary number of initially separate subsystems which are connected at t = 0 and separated again at a later time. A simple method to obtain the leading-order long-time contribution to the logarithm of the characteristic function is presented which simplifies earlier approaches. New explicit results for the determinant involving the scattering matrices are found. The joint probability distribution for the charges in two leads is discussed for Y junctions and dots connected to four leads.

Statistics of temperature fluctuations in an electron system out of equilibrium

We study the statistics of the fluctuating electron temperature in a metallic island coupled to reservoirs via resistive contacts and driven out of equilibrium by either a temperature or voltage difference between the reservoirs. The fluctuations of temperature are well defined provided that the energy relaxation rate inside the island exceeds the rate of energy exchange with the reservoirs. We quantify these fluctuations in the regime beyond the Gaussian approximation and elucidate their dependence on the nature of the electronic contacts.

Full counting statistics with spin-sensitive detectors reveals spin singlets

We study the full counting statistics of electric current to several drain terminals with spin-dependent entrance conductances. We show that the statistics of charge transfers can be interpreted in terms of single electrons and spin-singlet pairs coming from the source. If the source contains transport channels of high transparency, a significant fraction of electrons comes in spin-singlet pairs.

Full current statistics in the regime of weak coulomb interaction

We evaluate the full statistics of the current via a Coulomb island that is strongly coupled to the leads. This strong coupling weakens Coulomb interaction. We show that in this case the effects of the interaction can be incorporated into the renormalization of transmission eigenvalues of the scatterers that connect the island and the leads. We evaluate the Coulomb blockade gap in the current-voltage characteristics, the value of the gap being exponentially suppressed as compared to the classical charging energy of the island.

Andreev reflection eigenvalue density in mesoscopic conductors

The energy-dependent Andreev reflection eigenvalues determine the transport properties of normal-superconducting systems. We evaluate the eigenvalue density to get insight into the formation of resonant electron-hole transport channels. The circuit-theory-like method developed can be applied to any generic mesoscopic conductor or combinations thereof. We present the results for experimentally relevant cases of a diffusive wire and a double tunnel junction.

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.

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.