Transport through a finite Hubbard chain connected to reservoirs

The dc conductance through a finite Hubbard chain of size N coupled to two noninteracting leads is studied at T = 0 in an electron-hole symmetric case. Assuming that the perturbation expansion in U is valid for small N (=1,2,3,...) owing to the presence of the noninteracting leads, we obtain the self-energy at \omega = 0 analytically in the real space within the second order in U. Then, we calculate the inter-site Green's function which connects the two boundaries of the chain, G_{N1}, solving the Dyson equation. The conductance can be obtained through G_{N1}, and the result shows an oscillatory behavior as a function of N. For odd N, a perfect transmission occurs independent of U. This is due to the inversion and electron-hole symmetries, and is attributed to a Kondo resonance appearing at the Fermi level. On the other hand, for even N, the conductance is a decreasing function of N and U.Comment: 11 pages, RevTeX, 6 figures, to be published in Phys. Rev. B 59 (1999

Mixed-state aspects of an out-of-equilibrium Kondo problem in a quantum dot

We reexamine basic aspects of a nonequilibrium steady state in the Kondo problem for a quantum dot under a bias voltage using a reduced density matrix, which is obtained in the Fock space by integrating out one of the two conduction channels. The integration has been carried out by discretizing the conduction channels preserving the two-fold degeneracy due to the left-going and right-going scattering states. The remaining subspace is described by a single-channel Anderson model, and the statistical weight is determined by the reduced density matrix. In the noninteracting case, it can be constructed as the mixed states that show a close similarity to the high-temperature distribution in equilibrium. Specifically, if the system has an inversion symmetry, the one-particle states in an energy window between the two chemical potentials \mu_R and \mu_L are occupied, or unoccupied, completely at random with an equal weight. The Coulomb interaction preserves these aspects, and the correlation functions can be expressed in a Lehmann-representation form using the mixed-state statistical weight.Comment: 8 pages, 3 figure

The Cosmic Microwave Background Spectrum and a Determination of Fractal Space Dimensionality

The possibility to constrain fractal space dimensionality from Astrophysics and other areas is briefly reviewed. Assuming such dimensionality to be $3 + \epsilon$, a limit to $\epsilon$ can be inferred from COBE satellite data. The available data for the cosmic microwave background radiation spectrum are fitted by a Planck's radiation distribution generalized to non integer space dimensionality. Our analysis shows that the shape of the CMBR spectrum, which does not depend on the absolute normalization, is correctly described from this distribution provided the absolute temperature is equal to 2.726 $\pm$ $0.003\times 10^{-2}$ K and $\epsilon = - (0.957 \pm 0.006) \times 10^{-5}$. This value for $\epsilon$ is shown to be consistent with what is found on a very different spatial scale based on a quantum field phenomenon. The $|\epsilon|$ is interpreted as an upper limit for how much space dimensionality could have deviated from three. In other words, this is the maximum fluctuation space dimensionality should have experienced in a spatial and temporal scale compared to that of the decoupling era.Comment: 6 pages, 2 figure

Fermi liquid theory for the Anderson model out of equilibrium

We study low-energy properties of the Anderson impurity under a finite bias voltage $V$ using the perturbation theory in $U$ of Yamada and Yosida in the nonequilibrium Keldysh diagrammatic formalism, and obtain the Ward identities for the derivative of the self-energy with respect to $V$. The self-energy is calculated exactly up to terms of order $\omega^2$, $T^2$ and $V^2$, and the coefficients are defined with respect to the equilibrium ground state. From these results, the nonlinear response of the current through the impurity has been deduced up to order $V^3$.Comment: 8 pages, 1 figur

NRG approach to the transport through a finite Hubbard chain connected to reservoirs

We study the low-energy properties of a Hubbard chain of finite size N_C connected to two noninteracting leads using the numerical renormalization group (NRG) method. The results obtained for N_C = 3 and 4 show that the low-lying eigenstates have one-to-one correspondence with the free quasi-particle excitations of a local Fermi liquid. It enables us to determine the transport coefficients from the fixed-point Hamiltonian. At half-filling, the conductance for even N_C decreases exponentially with increasing U showing a tendency towards the development of a Mott-Hubbard gap. In contrast, for odd N_C, the Fermi-liquid nature of the low-energy states assures perfect transmission through the Kondo resonance. Our formulation to deduce the conductance from the fixed-point energy levels can be applied to various types of interacting systems.Comment: One typo found in Eq.(3) in previous version has been correcte

Fermi-liquid theory for a conductance through an interacting region attached to noninteracting leads

We study the relation between the dc conductance and the transmission through an interacting region based on the Kubo formalism using the perturbation analysis in the Coulomb interaction developed by Yamada-Yosida and Shiba. We find that the contributions of the vertex correction to the dc conductance disappear at T=0 if the currents are measured in the noninteracting leads. Consequently, the dc conductance is written in a Landauer-type form using the transmission coefficient for single-particle-like excitation at the Fermi energy. The results are generalized to a system with a number of scattering channels, and may be regarded as an extension of the relation derived by Fisher-Lee.Comment: text is not changed, 6 PS figures were replaced by 6 EPS figures in order to prevent the control-D problem of the PS file