Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0701620

Full counting statistics for noninteracting fermions: Exact results and the Levitov-Lesovik formula

K. Schoenhammer
View original source ↗Read source document ↗Export metadata ↓

Abstract

Exact numerical results for the full counting statistics (FCS) for a one-dimensional tight-binding model of noninteracting electrons are presented without using an idealized measuring device. The two initially separate subsystems are connected at t=0 and the exact time evolution for the large but finite combined system is obtained numerically. At zero temperature the trace formula derived by Klich is used to to calculate the FCS via a finite dimensional determinant. Even for surprisingly short times the approximate description of the time evolution with the help of scattering states agrees well with the exact result for the local current matrix elements. An additional approximation has to be made to recover the Levitov-Lesovik formula in the limit where the system size becomes infinite and afterwards the long time limit is addressed. The new derivation of the Levitov-Lesovik formula is generalized to more general geometries like a Y-junction enclosing a magnetic flux.

Explore related subjects

cond-mat.mes-hall

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

K. Schoenhammer. 2007-05-02. Full counting statistics for noninteracting fermions: Exact results and the Levitov-Lesovik formula. https://doi.org/10.1103/physrevb.75.205329

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Conductivity of charge-neutral multicomponent 2D electron-hole system

The interplay between distinct carrier species in systems with broken Galilean invariance can give rise to a rich landscape of interaction-driven transport phenomena. Here, we develop a comprehensive theory of the electrical conductivity of a two-dimensional mixture of massless Dirac and massive fermions, a system realized in HgTe quantum wells tuned to the charge-neutrality point. In this regime, all carriers are thermally activated, enabling a self-consistent, temperature-dependent interplay between the two species. Crucially, the charge-neutrality condition ensures that the chemical potential is not externally pinned but is determined self-consistently, thereby making the system's transport response an intrinsic probe of inter-species quantum friction. We demonstrate that the conductivity changes with temperature : at low temperatures, transport is dominated by massless Dirac carriers, yielding a nearly temperature-independent conductivity reminiscent of the charge-neutrality point in pristine graphene. As the temperature rises, massive holes become thermally excited, and their mutual scattering with Dirac carriers induces a specific nonmonotonic temperature dependence of the conductivity in both clean and disordered structures. In particular, in nearly clean structures with strong screening modeled by a short-range interparticle interaction potential, the system's conductivity can exhibit an inverse-quadratic temperature dependence. Conversely, in disordered structures with a long-range interparticle interaction, it varies quadratically with temperature. Our findings establish HgTe quantum wells at charge neutrality as a clean, highly tunable platform for isolating and quantitatively studying interaction-driven transport in the absence of Galilean invariance, offering a direct pathway to explore regimes where interparticle collisions dominate over disorder.

cond-mat.mes-hall↗
arXiv2026

Spin-conserving and spin-flip magnetic scattering in the altermagnetic spin-splitter effect

Critical magnetic fluctuations scatter electrons strongly near an ordering transition, but they barely degrade the charge current, because they scatter mostly through small angles. In an altermagnet the electric field also drives a spin current, and a nearly forward spin flip moves an electron to the other spin band at almost unchanged velocity. We develop a Boltzmann theory of the spin splitter ratio that keeps the full collision operator of quasistatic magnetic fluctuations and its change with the magnetic order. Fluctuations of equal total strength give the same resistivity for every fraction of spin flips, yet they can move the spin splitter ratio in opposite directions. Spin conserving fluctuations relax the spin current at about the charge relaxation rate, whereas forward flips equalize the two spin populations at equal energy at the quasiparticle rate, which in two dimensions grows linearly with the correlation length. Energy conservation on the split bands protects the part of the spin current carried by the band shift of the occupied states at every scattering strength, and the splitting blocks forward flips once the spin Fermi lines lie farther apart than the inverse correlation length. When flips dominate, a quarter to a half of the lattice band ratio survives. The transport time approximation reproduces the initial growth of the resistivity but recovers only a quarter to a half of the initial fall of the ratio, and a disorder series at fixed reduced temperature measures this fall independent of the order amplitude.

cond-mat.mes-hall↗
arXiv2026

Spin conservation protects the altermagnetic spin-splitter current from critical scattering

Near a magnetic transition, critical fluctuations scatter electrons strongly, but the charge current survives, because long wavelength fluctuations barely turn the electron velocity. In an altermagnet the electric field also drives a spin current, the spin splitter effect, and a nearly forward scattering event that flips spin moves an electron to the other spin band at almost unchanged velocity. We show that the spin current shares the protection of the charge current only when the fluctuations conserve spin. Solving the Boltzmann equation with the full collision operator, including its change with the magnetic order, we find that forward flips equalize the two spin populations at equal energy at the quasiparticle rate, which in two dimensions grows linearly with the correlation length, whereas spin conserving fluctuations relax the spin current at a rate comparable to the charge relaxation rate. Fluctuations with the same resistivity can thus move the spin splitter ratio in opposite directions. Energy conservation protects the part of the spin current that follows the band shift of the occupied states, and the splitting blocks forward flips once the spin Fermi lines lie farther apart than the inverse correlation length. A disorder series at fixed reduced temperature measures the initial fall of the ratio with the magnetic resistivity independent of the order amplitude, and the growth of this slope toward the transition identifies spin flip critical fluctuations.

cond-mat.mes-hall↗