1,933 research outputs found
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
Determination of the phase shifts for interacting electrons connected to reservoirs
We describe a formulation to deduce the phase shifts, which determine the
ground-state properties of interacting quantum-dot systems with the inversion
symmetry, from the fixed-point eigenvalues of the numerical renormalization
group (NRG). Our approach does not assume the specific form of the Hamiltonian
nor the electron-hole symmetry, and it is applicable to a wide class of quantum
impurities connected to noninteracting leads. We apply the method to a triple
dot which is described by a three-site Hubbard chain connected to two
noninteracting leads, and calculate the dc conductance away from half-filling.
The conductance shows the typical Kondo plateaus of Unitary limit in some
regions of the gate voltages, at which the total number of electrons N_el in
the three dots is odd, i.e., N_el =1, 3 and 5. In contrast, the conductance
shows a wide minimum in the gate voltages corresponding to even number of
electrons, N_el = 2 and 4.
We also discuss the parallel conductance of the triple dot connected
transversely to four leads, and show that it can be deduced from the two phase
shifts defined in the two-lead case.Comment: 9 pages, 12 figures: Fig. 12 has been added to discuss T_
Fermi liquid theory for the Anderson model out of equilibrium
We study low-energy properties of the Anderson impurity under a finite bias
voltage using the perturbation theory in 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 . The self-energy is
calculated exactly up to terms of order , and , 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 .Comment: 8 pages, 1 figur
Perturbation Study of the Conductance through an Interacting Region Connected to Multi-Mode Leads
We study the effects of electron correlation on transport through an
interacting region connected to multi-mode leads based on the perturbation
expansion with respect to the inter-electron interaction. At zero temperature
the conductance defined in the Kubo formalism can be written in terms of a
single-particle Green's function at the Fermi energy, and it can be mapped onto
a transmission coefficient of the free quasiparticles described by an effective
Hamiltonian. We apply this formulation to a two-dimensional Hubbard model of
finite size connected to two noninteracting leads. We calculate the conductance
in the electron-hole symmetric case using the order self-energy. The
conductance shows several maximums in the dependence in some parameter
regions of , where () is the hopping matrix element in the
- (-) directions. This is caused by the resonance occurring in some of
the subbands, and is related with the dependence of the eigenvalues of the
effective Hamiltonian.Comment: 17 pages, 12 figures, to be published in J.Phys.Soc.Jpn. 71(2002)No.
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
Arc sensitivity to cluster ellipticity, asymmetries and substructures
We investigate how ellipticity, asymmetries and substructures separately
affect the ability of galaxy clusters to produce strong lensing events, i.e.
gravitational arcs, and how they influence the arc morphologies and fluxes.
This is important for those studies aiming, for example, at constraining
cosmological parameters from statistical lensing, or at determining the inner
structure of galaxy clusters through gravitational arcs. We do so by creating
two-dimensional gradually smoothed, differently elliptical and asymmetric
versions of some numerical models. On average, we find that the contributions
of ellipticity, asymmetries and substructures amount to ~40%, ~10% and ~30% of
the total strong lensing cross section, respectively. However, our analysis
shows that substructures play a more important role in less elliptical and
asymmetric clusters, even if located at large distances from the cluster
centers (~1Mpc/h). Conversely, their effect is less important in highly
asymmetric lenses. The morphology, position and flux of individual arcs are
strongly affected by the presence of substructures in the clusters. Removing
substructures on spatial scales <~50kpc/h, roughly corresponding to mass scales
<~5 10^{10}M_\odot/h, alters the image multiplicity of ~35% of the sources used
in the simulations and causes position shifts larger than 5'' for ~40% of the
arcs longer than 5''. We conclude that any model for cluster lens cannot
neglect the effects of ellipticity, asymmetries and substructures. On the other
hand, the high sensitivity of gravitational arcs to deviations from regular,
smooth and symmetric mass distributions suggests that strong gravitational
lensing is potentially a powerfull tool to measure the level of substructures
and asymmetries in clusters.Comment: 16 pages, 18 figures. Accepted version. Version with full resolution
images can be found at
http://www.ita.uni-heidelberg.de/~massimo/sub/publications.htm
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
Two New Gravitationally Lensed Double Quasars from the Sloan Digital Sky Survey
We report the discoveries of the two-image gravitationally lensed quasars,
SDSS J0746+4403 and SDSS J1406+6126, selected from the Sloan Digital Sky Survey
(SDSS). SDSS J0746+4403, which will be included in our lens sample for
statistics and cosmology, has a source redshift of z_s=2.00, an estimated lens
redshift of z_l~0.3, and an image separation of 1.08". SDSS J1406+6126 has a
source redshift of z_s=2.13, a spectroscopically measured lens redshift of
z_l=0.27, and an image separation of 1.98". We find that the two quasar images
of SDSS J1406+6126 have different intervening MgII absorption strengths, which
are suggestive of large variations of absorbers on kpc scales. The positions
and fluxes of both the lensed quasar systems are easily reproduced by simple
mass models with reasonable parameter values. These objects bring to 18 the
number of lensed quasars that have been discovered from the SDSS data.Comment: 25 pages, 6 figures, The Astronomical Journal accepte
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