A note on "Exact Solution of Bipartite Fluctuations in One-Dimensional Fermions"

We consider current statistics for a two species exclusion process of particles hopping in opposite directions on a one-dimensional lattice. We derive an exact formula for the Green's function as well as for a joint current distribution of the model, and study its long time behavior. For a step type initial condition, we show that the limiting distribution is a product of the Gaussian and the GUE Tracy-Widom distribution. This is the first analytic confirmation for a multi-co...

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 presented by Abanov and Ivanov. A similar idea is used to derive a new 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. This provides a generalization of the Levitov-Lesovik f...

We compute thermal and quantum fluctuations in the background of a domain wall in a scalar field theory at finite temperature using the exact scalar propagator in the subspace orthogonal to the wall's translational mode. The propagator makes it possible to calculate terms of any order in the semiclassical expansion of the partition function of the system. The leading term in the expansion corresponds to the fluctuation determinant, which we compute for arbitrary temperature i...

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins $\uparrow \downarrow (\downarrow \uparrow)$ can exchange to assume the configuration $\downarrow \uparrow (\uparrow \downarrow)$, with rate $\beta (\alpha)$, through energy decreasing moves only. We report exact solution for the case when one of the rates, $\alpha$ or $\beta$, is zero. The irreversibility of such dynamics results in strong dependence on the initial conditions. Domain wall argu...

In this letter the fractional fermion number of thick domain walls is computed. The analysis is achieved by developing the heat kernel expansion of the spectral eta functon of the Dirac Hamiltonian governing the fermionic fluctuations around the domain wall. A formula is derived showing that a non null fermion number is always accompanied by a Hall conductivity induced on the wall. In the limit of thin and impenetrable walls the chiral bag boundary conditions arise, and the H...

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 ...

We revisit the problem of full counting statistics of particles on a segment of a one-dimensional gas of free fermions. Using a combination of analytical and numerical methods, we study the crossover between the counting of discrete particles and of the continuous particle density as a function of smoothing in the counting procedure. In the discrete-particle limit, the result is given by the Fisher--Hartwig expansion for Toeplitz determinants, while in the continuous limit we...

We study $N$ noninteracting fermions in a domain bounded by a hard wall potential in $d \geq 1$ dimensions. We show that for large $N$, the correlations at the edge of the Fermi gas (near the wall) at zero temperature are described by a universal kernel, different from the universal edge kernel valid for smooth potentials. We compute this $d$ dimensional hard edge kernel exactly for a spherical domain and argue, using a generalized method of images, that it holds close to any...

In a series of ten papers, of which this is the first, we prove that the temperature zero renormalized perturbation expansions of a class of interacting many-fermion models in two space dimensions have nonzero radius of convergence. The models have "asymmetric" Fermi surfaces and short range interactions. One consequence of the convergence of the perturbation expansions is the existence of a discontinuity in the particle number density at the Fermi surface. Here, we present a...

We revisit the problem of finding the probability distribution of a fermionic number of one-dimensional spinless free fermions on a segment of a given length. The generating function for this probability distribution can be expressed as a determinant of a Toeplitz matrix. We use the recently proven generalized Fisher--Hartwig conjecture on the asymptotic behavior of such determinants to find the generating function for the full counting statistics of fermions on a line segmen...