1,590 research outputs found
Effects on the Non-Relativistic Dynamics of a Charged Particle Interacting with a Chern-Simons Potential
The hydrogen atom in two dimensions, described by a Schr\"odinger equation
with a Chern-Simons potential, is numerically solved. Both its wave functions
and eigenvalues were determined for small values of the principal quantum
number . The only possible states correspond to . How the result
depends on the topological mass of the photon is also discussed. In the case
, the energy of the fundamental state corresponding to different choice
for the photon mass scale are found to be comprehended in the interval , corresponding to a mean
radius of the electron in the range ~cm
~cm. In any case, the planar
atom is found to be very weekly bounded showing some features similar to the
Rydberg atoms in three dimensions with a Coulombian interaction.Comment: 6 pages, 5 figure
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
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.
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 , a limit to 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
K and .
This value for is shown to be consistent with what is found on a
very different spatial scale based on a quantum field phenomenon. The
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 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
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
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