8,070 research outputs found
Complexity of links in 3-manifolds
We introduce a natural-valued complexity c(X) for pairs X=(M,L), where M is a
closed orientable 3-manifold and L is a link contained in M. The definition
employs simple spines, but for well-behaved X's we show that c(X) equals the
minimal number of tetrahedra in a triangulation of M containing L in its
1-skeleton. Slightly adapting Matveev's recent theory of roots for graphs, we
carefully analyze the behaviour of c under connected sum away from and along
the link. We show in particular that c is almost always additive, describing in
detail the circumstances under which it is not. To do so we introduce a certain
(0,2)-root for a pair X, we show that it is well-defined, and we prove that X
has the same complexity as its (0,2)-root. We then consider, for links in the
3-sphere, the relations of c with the crossing number and with the hyperbolic
volume of the exterior, establishing various upper and lower bounds. We also
specialize our analysis to certain infinite families of links, providing rather
accurate asymptotic estimates.Comment: 24 pages, 6 figure
Universal low-temperature crossover in two-channel Kondo models
An exact expression is derived for the electron Green function in two-channel
Kondo models with one and two impurities, describing the crossover from
non-Fermi liquid (NFL) behavior at intermediate temperatures to standard Fermi
liquid (FL) physics at low temperatures. Symmetry-breaking perturbations
generically present in experiment ensure the standard low-energy FL
description, but the full crossover is wholly characteristic of the unstable
NFL state. Distinctive conductance lineshapes in quantum dot devices should
result. We exploit a connection between this crossover and one occurring in a
classical boundary Ising model to calculate real-space electron densities at
finite temperature. The single universal finite-temperature Green function is
then extracted by inverting the integral transformation relating these Friedel
oscillations to the t matrix. Excellent agreement is demonstrated between exact
results and full numerical renormalization group calculations.Comment: 26 pages, 14 figures: updated version including new a section and
figure comparing exact results to finite-temperature numerical
renormalization group calculation
Total electronic Raman scattering in the charge-density-wave phase of the spinless Falicov-Kimball model
The total electronic Raman scattering spectrum, including the nonresonant,
mixed and resonant components, is determined for the charge-density-wave (CDW)
phase of the spinless Falicov-Kimball model at half filling within dynamical
mean-field theory. Its frequency dependence is investigated for different
values of the energy of the incident photons. The spectra reflect the different
structures in the density of states and how they are modified by screening and
resonance effects. The calculations are performed for the , and symmetries (which are typically examined in experiment).
Our results for the resonance effects of the Raman spectra, found by tuning the
energy of the incident photons, give information about the many-body charge
dynamics of the CDW-ordered phase.Comment: 8 pages, contribution to the proceedings of the 3rd Conference
"Statistical Physics: Modern Trends and Applications", June 23-25, 2009 Lviv,
Ukrain
Smearing of Coulomb Blockade by Resonant Tunneling
We study the Coulomb blockade in a grain coupled to a lead via a resonant
impurity level. We show that the strong energy dependence of the transmission
coefficient through the impurity level can have a dramatic effect on the
quantization of the grain charge. In particular, if the resonance is
sufficiently narrow, the Coulomb staircase shows very sharp steps even if the
transmission through the impurity at the Fermi energy is perfect. This is in
contrast to the naive expectation that perfect transmission should completely
smear charging effects.Comment: 4 pages, 3 figure
Enhanced Two-Channel Kondo Physics in a Quantum Box Device
We propose a design for a one-dimensional quantum box device where the charge
fluctuations are described by an anisotropic two-channel Kondo model. The
device consists of a quantum box in the Coulomb blockade regime, weakly coupled
to a quantum wire by a single-mode point contact. The electron correlations in
the wire produce strong back scattering at the contact, significantly
increasing the Kondo temperature as compared to the case of non-interacting
electrons. By employing boundary conformal field theory techniques we show that
the differential capacitance of the box exhibits manifest two-channel Kondo
scaling with temperature and gate voltage, uncontaminated by the
one-dimensional electron correlations. We discuss the prospect to
experimentally access the Kondo regime with this type of device.Comment: EPL style, 5 pages, 1 figure, final published versio
The Yang Lee Edge Singularity on Feynman Diagrams
We investigate the Yang-Lee edge singularity on non-planar random graphs,
which we consider as the Feynman Diagrams of various d=0 field theories, in
order to determine the value of the edge exponent.
We consider the hard dimer model on phi3 and phi4 random graphs to test the
universality of the exponent with respect to coordination number, and the Ising
model in an external field to test its temperature independence. The results
here for generic (``thin'') random graphs provide an interesting counterpoint
to the discussion by Staudacher of these models on planar random graphs.Comment: LaTeX, 6 pages + 3 figure
Transport through a quantum dot with SU(4) Kondo entanglement
We investigate a mesoscopic setup composed of a small electron droplet (dot)
coupled to a larger quantum dot (grain) also subject to Coulomb blockade as
well as two macroscopic leads used as source and drain. An exotic Kondo ground
state other than the standard SU(2) Fermi liquid unambiguously emerges: an
SU(4) Kondo correlated liquid. The transport properties through the small dot
are analyzed for this regime, through boundary conformal field theory, and
allow a clear distinction with other regimes such as a two-channel spin state
or a two-channel orbital state.Comment: 13 pages, 3 figure
Zeros of the Partition Function for Higher--Spin 2D Ising Models
We present calculations of the complex-temperature zeros of the partition
functions for 2D Ising models on the square lattice with spin , 3/2, and
2. These give insight into complex-temperature phase diagrams of these models
in the thermodynamic limit. Support is adduced for a conjecture that all
divergences of the magnetisation occur at endpoints of arcs of zeros protruding
into the FM phase. We conjecture that there are such arcs for , where denotes the integral part of .Comment: 8 pages, latex, 3 uuencoded figure
The Challenge of Light-Front Quantisation: Recent Results
We explain what is the challenge of light-front quantisation, and how we can
now answer it because of recent progress in solving the problem of zero modes
in the case of non-Abelian gauge theories. We also give a description of the
light-front Hamiltonian for SU(2) finite volume gluodynamics resulting from
this recent solution to the problem of light-front zero modes.Comment: 17 pages, lecture delivered by GBP at the XXXIV PNPI Winter School,
Repino, St.Petersburg, Russia, February 14-20, 2000, version to appear in the
Proceeding
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