1,318 research outputs found
``Linearized'' Dynamical Mean-Field Theory for the Mott-Hubbard transition
The Mott-Hubbard metal-insulator transition is studied within a simplified
version of the Dynamical Mean-Field Theory (DMFT) in which the coupling between
the impurity level and the conduction band is approximated by a single pole at
the Fermi energy. In this approach, the DMFT equations are linearized, and the
value for the critical Coulomb repulsion U_{\rm c} can be calculated
analytically. For the symmetric single-band Hubbard model at zero temperature,
the critical value is found to be given by 6 times the square root of the
second moment of the free (U=0) density of states. This result is in good
agreement with the numerical value obtained from the Projective Selfconsistent
Method and recent Numerical Renormalization Group calculations for the Bethe
and the hypercubic lattice in infinite dimensions. The generalization to more
complicated lattices is discussed. The ``linearized DMFT'' yields plausible
results for the complete geometry dependence of the critical interaction.Comment: 8 page
Numerical Renormalization Group for Impurity Quantum Phase Transitions: Structure of Critical Fixed Points
The numerical renormalization group method is used to investigate zero
temperature phase transitions in quantum impurity systems, in particular in the
particle-hole symmetric soft-gap Anderson model. The model displays two stable
phases whose fixed points can be built up of non-interacting single-particle
states. In contrast, the quantum phase transitions turn out to be described by
interacting fixed points, and their excitations cannot be described in terms of
free particles. We show that the structure of the many-body spectrum of these
critical fixed points can be understood using renormalized perturbation theory
close to certain values of the bath exponents which play the role of critical
dimensions. Contact is made with perturbative renormalization group
calculations for the soft-gap Anderson and Kondo models. A complete description
of the quantum critical many-particle spectra is achieved using suitable
marginal operators; technically this can be understood as epsilon-expansion for
full many-body spectra.Comment: 14 pages, 12 figure
MATERIAL BALANCE IN SEWAGE TREATMENT
The most important characteristics of sewage purification is: cell retention time (CRT),
sludge loading, ratio of recirculation or rather excess sludge removal. Of course, these parameters
are in close connection with each other. To examine these connections, material balance
seems to be the most suitable for either the aeration tank or for the aeration tank and sedimentation
basin together. These equations are suitable to examine the method of sludge load, the
most basic possibility of regulation. the ratio of recirculation and also the excess sludge can be
determined
On X-ray-singularities in the f-electron spectral function of the Falicov-Kimball model
The f-electron spectral function of the Falicov-Kimball model is calculated
within the dynamical mean-field theory using the numerical renormalization
group method as the impurity solver. Both the Bethe lattice and the hypercubic
lattice are considered at half filling. For small U we obtain a single-peaked
f-electron spectral function, which --for zero temperature-- exhibits an
algebraic (X-ray) singularity () for . The
characteristic exponent depends on the Coulomb (Hubbard) correlation
U. This X-ray singularity cannot be observed when using alternative
(Keldysh-based) many-body approaches. With increasing U, decreases and
vanishes for sufficiently large U when the f-electron spectral function
develops a gap and a two-peak structure (metal-insulator transition).Comment: 8 pages, 8 figures, revte
Spectral Densities of Response Functions for the O(3) Symmetric Anderson and Two Channel Kondo Models
The O(3) symmetric Anderson model is an example of a system which has a
stable low energy marginal Fermi liquid fixed point for a certain choice of
parameters. It is also exactly equivalent, in the large U limit, to a localized
model which describes the spin degrees of freedom of the linear dispersion two
channel Kondo model. We first use an argument based on conformal field theory
to establish this precise equivalence with the two channel model. We then use
the numerical renormalization group (NRG) approach to calculate both
one-electron and two-electron response functions for a range of values of the
interaction strength U. We compare the behaviours about the marginal Fermi
liquid and Fermi liquid fixed points and interpret the results in terms of a
renormalized Majorana fermion picture of the elementary excitations. In the
marginal Fermi liquid case the spectral densities of all the Majorana fermion
modes display a |omega| dependence on the lowest energy scale, and in addition
the zero Majorana mode has a delta function contribution. The weight of this
delta function is studied as a function of the interaction U and is found to
decrease exponentially with U for large U. Using the equivalence with the two
channel Kondo model in the large U limit, we deduce the dynamical spin
susceptibility of the two channel Kondo model over the full frequency range. We
use renormalized perturbation theory to interpret the results and to calculate
the coefficient of the ln omega divergence found in the low frequency behaviour
of the T=0 dynamic susceptibility.Comment: 26 pages, 18 figures, to be published in Eur. Phys. J.
Testing for redshift evolution of Type Ia supernovae using the strongly lensed PS1-10afx at
The light from distant supernovae (SNe) can be magnified through
gravitational lensing when a foreground galaxy is located along the line of
sight. This line-up allows for detailed studies of SNe at high redshift that
otherwise would not be possible. Spectroscopic observations of lensed
high-redshift Type Ia supernovae (SNe Ia) are of particular interest since they
can be used to test for evolution of their intrinsic properties. The use of SNe
Ia for probing the cosmic expansion history has proven to be an extremely
powerful method for measuring cosmological parameters. However, if systematic
redshift-dependent properties are found, their usefulness for future surveys
could be challenged. We investigate whether the spectroscopic properties of the
strongly lensed and very distant SN Ia PS1-10afx at deviates from the
well-studied populations of normal SNe Ia at nearby or intermediate distance.
We created median spectra from nearby and intermediate-redshift
spectroscopically normal SNe Ia from the literature at -5 and +1 days from
light-curve maximum. We then compared these median spectra to those of
PS1-10afx. We do not find signs of spectral evolution in PS1-10afx. The
observed deviation between PS1-10afx and the median templates are within what
is found for SNe at low- and intermediate-redshift. There is a noticeable broad
feature centred at ~\AA{}, which is present only to a
lesser extent in individual low and intermediate redshift SN Ia spectra. From a
comparison with a recently developed explosion model, we find this feature to
be dominated by iron peak elements, in particular, singly ionized cobalt and
chromium.Comment: accepted for publication in section 4. Extragalactic astronomy of
Astronomy and Astrophysic
Numerical Renormalization Group Calculations for the Self-energy of the impurity Anderson model
We present a new method to calculate directly the one-particle self-energy of
an impurity Anderson model with Wilson's numerical Renormalization Group method
by writing this quantity as the ratio of two correlation functions. This way of
calculating Sigma(z) turns out to be considerably more reliable and accurate
than via the impurity Green's function alone. We show results for the
self-energy for the case of a constant coupling between impurity and conduction
band (ImDelta = const) and the effective Delta(z) arising in the Dynamical Mean
Field Theory of the Hubbard model. Implications to the problem of the
metal-insulator transition in the Hubbard model are also discussed.Comment: 18 pages, 9 figures, submitted to J. Phys.: Condens. Matte
Spectral scaling and quantum critical behaviour in the pseudogap Anderson model
The pseudogap Anderson impurity model provides a classic example of an
essentially local quantum phase transition. Here we study its single-particle
dynamics in the vicinity of the symmetric quantum critical point (QCP)
separating generalized Fermi liquid and local moment phases, via the local
moment approach. Both phases are shown to be characterized by a low-energy
scale that vanishes at the QCP; and the universal scaling spectra, on all
energy scales, are obtained analytically. The spectrum precisely at the QCP is
also obtained; its form showing clearly the non-Fermi liquid, interacting
nature of the fixed point.Comment: 7 pages, 2 figure
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