8,029 research outputs found
Reversal of particle-hole scattering-rate asymmetry in Anderson impurity model
We study the particle-hole asymmetry of the scattering rate in strongly
correlated electron systems by examining the cubic and
terms in the imaginary part of the self-energy of the Anderson impurity model.
We show that the sign is opposite in the weak-coupling and strong-coupling
limits, explaining the differences found in theoretical approaches taking the
respective limits as the starting points. The sign change in fact precisely
delineates the cross-over between the weak and strong correlation regimes of
the model. For weak interaction the sign reversal occurs for small values
of the doping , while for interaction of order , being the hybridization strength, the cross-over curve
rapidly shifts to the large-doping range. This curve based on the impurity
dynamics is genuinely different from other cross-over curves defined through
impurity thermodynamic and static properties.Comment: 4 pages, 5 figure
On the Capacity of the Finite Field Counterparts of Wireless Interference Networks
This work explores how degrees of freedom (DoF) results from wireless
networks can be translated into capacity results for their finite field
counterparts that arise in network coding applications. The main insight is
that scalar (SISO) finite field channels over are analogous
to n x n vector (MIMO) channels in the wireless setting, but with an important
distinction -- there is additional structure due to finite field arithmetic
which enforces commutativity of matrix multiplication and limits the channel
diversity to n, making these channels similar to diagonal channels in the
wireless setting. Within the limits imposed by the channel structure, the DoF
optimal precoding solutions for wireless networks can be translated into
capacity optimal solutions for their finite field counterparts. This is shown
through the study of the 2-user X channel and the 3-user interference channel.
Besides bringing the insights from wireless networks into network coding
applications, the study of finite field networks over also
touches upon important open problems in wireless networks (finite SNR, finite
diversity scenarios) through interesting parallels between p and SNR, and n and
diversity.Comment: Full version of paper accepted for presentation at ISIT 201
Reduced Complexity Filtering with Stochastic Dominance Bounds: A Convex Optimization Approach
This paper uses stochastic dominance principles to construct upper and lower
sample path bounds for Hidden Markov Model (HMM) filters. Given a HMM, by using
convex optimization methods for nuclear norm minimization with copositive
constraints, we construct low rank stochastic marices so that the optimal
filters using these matrices provably lower and upper bound (with respect to a
partially ordered set) the true filtered distribution at each time instant.
Since these matrices are low rank (say R), the computational cost of evaluating
the filtering bounds is O(XR) instead of O(X2). A Monte-Carlo importance
sampling filter is presented that exploits these upper and lower bounds to
estimate the optimal posterior. Finally, using the Dobrushin coefficient,
explicit bounds are given on the variational norm between the true posterior
and the upper and lower bounds
Musical chairs: a comment on the credit crisis.
Uncertainty –that is, a rise in unknown and immeasurable risk rather than the measurable risk that the financial sector specializes in managing– is at the heart of the recent liquidity crisis. The financial instruments and derivative structures underpinning the recent growth in credit markets are complex. Because of the rapid proliferation of these instruments, market participants cannot refer to a historical record to measure how these financial structures will behave during a time of stress. These two factors, complexity and lack of history, are the preconditions for rampant uncertainty. We explain how a rise in uncertainty can cause a liquidity crisis and discuss central bank policies in this context.
Doping a correlated band insulator: A new route to half metallic behaviour
We demonstrate in a simple model the surprising result that turning on an
on-site Coulomb interaction U in a doped band insulator leads to the formation
of a half-metallic state. In the undoped system, we show that increasing U
leads to a first order transition between a paramagnetic, band insulator and an
antiferomagnetic Mott insulator at a finite value U_{AF}. Upon doping, the
system exhibits half metallic ferrimagnetism over a wide range of doping and
interaction strengths on either side of U_{AF}. Our results, based on dynamical
mean field theory, suggest a novel route to half-metallic behavior and provide
motivation for experiments on new materials for spintronics.Comment: 5 pages, 7 figure
Variational Monte Carlo and Configurational Interaction Studies of and its Fragments
The molecule and its fragments are studied using Configuration
Interaction (CI) and Variational Monte Carlo (VMC) techniques, within the
Hubbard model. Using benzene as a test case, we compare the results of the
approximate calculations with exact calculations. The fragments of
studied are pyracylene, fluoranthene and corannulene. The energies, bond
orders, spin-spin and charge-correlation functions of these systems are
obtained for various values of the Hubbard parameter, . The analysis of bond
orders and correlation functions of these individual molecules allow us to
visualise pyracylene as a naphthalene unit with two ethylenic moieties and
fluoranthene as weakly bridged benzene and naphthalene units. Corannulene is
the largest fragment of that we have studied. The hexagon-hexagon(h-h)
bond orders are slightly larger than those of the hexagon-pentagon bonds(h-p),
a feature also found in other fragments. We also find bonds between two
co-ordinated carbon sites to be stronger than bonds involving three coordinated
carbon sites. In , the h-h bonds are stronger than in corannulene and
the h-p bonds weaker than in corannulene for all correlation strengths.
Introducing bond alternation in the buckyball enhances this difference.Comment: 42 pages, 5 figures available on request, to appear in J. Phys. Che
Phase Diagram of the Half-Filled Ionic Hubbard Model
We study the phase diagram of the ionic Hubbard model (IHM) at half-filling
using dynamical mean field theory (DMFT), with two impurity solvers, namely,
iterated perturbation theory (IPT) and continuous time quantum Monte Carlo
(CTQMC). The physics of the IHM is governed by the competition between the
staggered potential and the on-site Hubbard U. In both the methods we
find that for a finite and at zero temperature, anti-ferromagnetic
(AFM) order sets in beyond a threshold via a first order phase
transition below which the system is a paramagnetic band insulator. Both the
methods show a clear evidence for a transition to a half-metal phase just after
the AFM order is turned on, followed by the formation of an AFM insulator on
further increasing U. We show that the results obtained within both the methods
have good qualitative and quantitative consistency in the intermediate to
strong coupling regime. On increasing the temperature, the AFM order is lost
via a first order phase transition at a transition temperature within both the methods, for weak to intermediate values of U/t. But
in the strongly correlated regime, where the effective low energy Hamiltonian
is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition
from the AFM phase to the paramagnetic phase, but the CTQMC does. As a result,
at any finite temperature T, DMFT+CTQMC shows a second phase transition (not
seen within DMFT+IPT) on increasing U beyond . At , when
the Neel temperature for the effective Heisenberg model becomes lower
than T, the AFM order is lost via a second order transition. In the
3-dimensonal parameter space of , there is a line of
tricritical points that separates the surfaces of first and second order phase
transitions.Comment: Revised versio
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