7,259 research outputs found
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
Algebro-Geometric Solutions of the Boussinesq Hierarchy
We continue a recently developed systematic approach to the Bousinesq (Bsq)
hierarchy and its algebro-geometric solutions. Our formalism includes a
recursive construction of Lax pairs and establishes associated
Burchnall-Chaundy curves, Baker-Akhiezer functions and Dubrovin-type equations
for analogs of Dirichlet and Neumann divisors. The principal aim of this paper
is a detailed theta function representation of all algebro-geometric
quasi-periodic solutions and related quantities of the Bsq hierarchy.Comment: LaTeX, 48 page
Optical and dc transport properties of a strongly correlated charge density wave system: exact solution in the ordered phase of the spinless Falicov-Kimball model with dynamical mean-field theory
We derive the dynamical mean-field theory equations for transport in an
ordered charge-density-wave phase on a bipartite lattice. The formalism is
applied to the spinless Falicov-Kimball model on a hypercubic lattice at half
filling. We determine the many-body density of states, the dc charge and heat
conductivities, and the optical conductivity. Vertex corrections continue to
vanish within the ordered phase, but the density of states and the transport
coefficients show anomalous behavior due to the rapid development of thermally
activated subgap states. We also examine the optical sum rule and sum rules for
the first three moments of the Green's functions within the ordered phase and
see that the total optical spectral weight in the ordered phase either
decreases or increases depending on the strength of the interactions.Comment: 14 pages, 14 figures, submitted to Phys. Rev.
Some New Results on Complex-Temperature Singularities in Potts Models on the Square Lattice
We report some new results on the complex-temperature (CT) singularities of
-state Potts models on the square lattice. We concentrate on the problematic
region (where ) in which CT zeros of the partition function
are sensitive to finite lattice artifacts. From analyses of low-temperature
series expansions for , we establish the existence, in this
region, of complex-conjugate CT singularities at which the magnetization and
susceptibility diverge. From calculations of zeros of the partition function,
we obtain evidence consistent with the inference that these singularities occur
at endpoints of arcs protruding into the (complex-temperature
extension of the) FM phase. Exponents for these singularities are determined;
e.g., for , we find , consistent with .
By duality, these results also imply associated arcs extending to the (CT
extension of the) symmetric PM phase. Analytic expressions are suggested for
the positions of some of these singularities; e.g., for , our finding is
consistent with the exact value . Further discussions of
complex-temperature phase diagrams are given.Comment: 26 pages, latex, with eight epsf figure
Inelastic Processes in the Collision of Relativistic Highly Charged Ions with Atoms
A general expression for the cross sections of inelastic collisions of fast
(including relativistic) multicharged ions with atoms which is based on the
genelazition of the eikonal approximation is derived. This expression is
applicable for wide range of collision energy and has the standard
nonrelativistic limit and in the ultrarelativistic limit coincides with the
Baltz's exact solution ~\cite{art13} of the Dirac equation. As an application
of the obtained result the following processes are calculated: the excitation
and ionization cross sections of hydrogenlike atom; the single and double
excitation and ionization of heliumlike atom; the multiply ionization of neon
and argon atoms; the probability and cross section of K-vacancy production in
the relativistic collision. The simple analytic formulae
for the cross sections of inelastic collisions and the recurrence relations
between the ionization cross sections of different multiplicities are also
obtained. Comparison of our results with the experimental data and the results
of other calculations are given.Comment: 25 pages, latex, 7 figures avialable upon request,submitted to PR
Observation of Quantum Fluctuations of Charge on a Quantum Dot
We have incorporated an aluminum single electron transistor directly into the
defining gate structure of a semiconductor quantum dot, permitting precise
measurement of the charge in the dot. Voltage biasing a gate draws charge from
a reservoir into the dot through a single point contact. The charge in the dot
increases continuously for large point contact conductance and in a step-like
manner in units of single electrons with the contact nearly closed. We measure
the corresponding capacitance lineshapes for the full range of point contact
conductances. The lineshapes are described well by perturbation theory and not
by theories in which the dot charging energy is altered by the barrier
conductance.Comment: Revtex, 5 pages, 3 figures, few minor corrections to the reference
Finite Size Effects in Addition and Chipping Processes
We investigate analytically and numerically a system of clusters evolving via
collisions with clusters of minimal mass (monomers). Each collision either
leads to the addition of the monomer to the cluster or the chipping of a
monomer from the cluster, and emerging behaviors depend on which of the two
processes is more probable. If addition prevails, monomers disappear in a time
that scales as with the total mass , and the system reaches a
jammed state. When chipping prevails, the system remains in a quasi-stationary
state for a time that scales exponentially with , but eventually, a giant
fluctuation leads to the disappearance of monomers. In the marginal case,
monomers disappear in a time that scales linearly with , and the final
supercluster state is a peculiar jammed state, viz., it is not extensive.Comment: 18 pages, 8 figures, 45 reference
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