139 research outputs found
Multilateral inversion of A_r, C_r and D_r basic hypergeometric series
In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic
hypergeometric matrix inverse with applications to bilateral basic
hypergeometric series. This matrix inversion result was directly extracted from
an instance of Bailey's very-well-poised 6-psi-6 summation theorem, and
involves two infinite matrices which are not lower-triangular. The present
paper features three different multivariable generalizations of the above
result. These are extracted from Gustafson's A_r and C_r extensions and of the
author's recent A_r extension of Bailey's 6-psi-6 summation formula. By
combining these new multidimensional matrix inverses with A_r and D_r
extensions of Jackson's 8-phi-7 summation theorem three balanced
very-well-poised 8-psi-8 summation theorems associated with the root systems
A_r and C_r are derived.Comment: 24 page
Orientational order in dipolar fluids consisting of nonspherical hard particles
We investigate fluids of dipolar hard particles by a certain variant of
density-functional theory. The proper treatment of the long range of the
dipolar interactions yields a contribution to the free energy which favors
ferromagnetic order. This corrects previous theoretical analyses. We determine
phase diagrams for dipolar ellipsoids and spherocylinders as a function of the
aspect ratio of the particles and their dipole moment. In the nonpolar limit
the results for the phase boundary between the isotropic and nematic phase
agree well with simulation data. Adding a longitudinal dipole moment favors the
nematic phase. For oblate or slightly elongated particles we find a
ferromagnetic liquid phase, which has also been detected in computer
simulations of fluids consisting of spherical dipolar particles. The detailed
structure of the phase diagram and its evolution upon changing the aspect ratio
are discussed in detail.Comment: 35 pages LaTeX with epsf style, 11 figures in eps format, submitted
to Phys. Rev.
Evidence for short range orbital order in paramagnetic insulating (Al,V)_2O_3
The local structure of (Al_0.06V_0.94)_2O_3 in the paramagnetic insulating
(PI) and antiferromagnetically ordered insulating (AFI) phase has been
investigated using hard and soft x-ray absorption techniques. It is shown that:
1) on a local scale, the symmetry of the vanadium sites in both the PI and the
AFI phase is the same; and 2) the vanadium 3d - oxygen 2p hybridization, as
gauged by the oxygen 1s absorption edge, is the same for both phases, but
distinctly different from the paramagnetic metallic phase of pure V_2O_3. These
findings can be understood in the context of a recently proposed model which
relates the long range monoclinic distortion of the antiferromagnetically
ordered state to orbital ordering, if orbital short range order in the PI phase
is assumed. The measured anisotropy of the x-ray absorption spectra is
discussed in relation to spin-polarized density functional calculations.Comment: 8 pages, 5 figure
Collinear effective theory at subleading order and its application to heavy-light currents
We consider a collinear effective theory of highly energetic quarks with
energy E, interacting with collinear and soft gluons by integrating out
collinear degrees of freedom to subleading order. The collinear effective
theory offers a systematic expansion in power series of a small parameter
lambda ~ p_{\perp}/E, where p_{\perp} is the transverse momentum of a collinear
particle. We construct the effective Lagrangian to first order in ,
and discuss its features including additional symmetries such as collinear
gauge invariance and reparameterization invariance. Heavy-light currents can be
matched from the full theory onto the operators in the collinear effective
theory at one loop and to order lambda. We obtain heavy-light current operators
in the effective theory, calculate their Wilson coefficients at this order, and
the renormalization group equations for the Wilson coefficients are solved. As
an application, we calculate the form factors for decays of B mesons to light
energetic mesons to order lambda and at leading-logarithmic order in alpha_s.Comment: 29 pages, 5 figures, revised versio
Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators
We present a stability theory for kink propagation in chains of coupled
oscillators and a new algorithm for the numerical study of kink dynamics. The
numerical solutions are computed using an equivalent integral equation instead
of a system of differential equations. This avoids uncertainty about the impact
of artificial boundary conditions and discretization in time. Stability results
also follow from the integral version. Stable kinks have a monotone leading
edge and move with a velocity larger than a critical value which depends on the
damping strength.Comment: 11 figure
Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics
In this article, we analyze the third of three papers, in which Einstein
presented his quantum theory of the ideal gas of 1924-1925. Although it failed
to attract the attention of Einstein's contemporaries and although also today
very few commentators refer to it, we argue for its significance in the context
of Einstein's quantum researches. It contains an attempt to extend and exhaust
the characterization of the monatomic ideal gas without appealing to
combinatorics. Its ambiguities illustrate Einstein's confusion with his initial
success in extending Bose's results and in realizing the consequences of what
later became to be called Bose-Einstein statistics. We discuss Einstein's
motivation for writing a non-combinatorial paper, partly in response to
criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments
are based on Einstein's belief in the complete analogy between the
thermodynamics of light quanta and of material particles and invoke
considerations of adiabatic transformations as well as of dimensional analysis.
These techniques were well-known to Einstein from earlier work on Wien's
displacement law, Planck's radiation theory, and the specific heat of solids.
We also investigate the possible role of Ehrenfest in the gestation of the
theory.Comment: 57 pp
Single Spin Measurement using Single Electron Transistors to Probe Two Electron Systems
We present a method for measuring single spins embedded in a solid by probing
two electron systems with a single electron transistor (SET). Restrictions
imposed by the Pauli Principle on allowed two electron states mean that the
spin state of such systems has a profound impact on the orbital states
(positions) of the electrons, a parameter which SET's are extremely well suited
to measure. We focus on a particular system capable of being fabricated with
current technology: a Te double donor in Si adjacent to a Si/SiO2 interface and
lying directly beneath the SET island electrode, and we outline a measurement
strategy capable of resolving single electron and nuclear spins in this system.
We discuss the limitations of the measurement imposed by spin scattering
arising from fluctuations emanating from the SET and from lattice phonons. We
conclude that measurement of single spins, a necessary requirement for several
proposed quantum computer architectures, is feasible in Si using this strategy.Comment: 22 Pages, 8 Figures; revised version contains updated references and
small textual changes. Submitted to Phys. Rev.
Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies
Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local
reductions of Hamiltonian flows generated by monodromy invariants on the dual
of a loop algebra. Following earlier work of De Groot et al, reductions based
upon graded regular elements of arbitrary Heisenberg subalgebras are
considered. We show that, in the case of the nontwisted loop algebra
, graded regular elements exist only in those Heisenberg
subalgebras which correspond either to the partitions of into the sum of
equal numbers or to equal numbers plus one . We prove that the
reduction belonging to the grade regular elements in the case yields
the matrix version of the Gelfand-Dickey -KdV hierarchy,
generalizing the scalar case considered by DS. The methods of DS are
utilized throughout the analysis, but formulating the reduction entirely within
the Hamiltonian framework provided by the classical r-matrix approach leads to
some simplifications even for .Comment: 43 page
Threshold criterion for wetting at the triple point
Grand canonical simulations are used to calculate adsorption isotherms of
various classical gases on alkali metal and Mg surfaces. Ab initio adsorption
potentials and Lennard-Jones gas-gas interactions are used. Depending on the
system, the resulting behavior can be nonwetting for all temperatures studied,
complete wetting, or (in the intermediate case) exhibit a wetting transition.
An unusual variety of wetting transitions at the triple point is found in the
case of a specific adsorption potential of intermediate strength. The general
threshold for wetting near the triple point is found to be close to that
predicted with a heuristic model of Cheng et al. This same conclusion was drawn
in a recent experimental and simulation study of Ar on CO_2 by Mistura et al.
These results imply that a dimensionless wetting parameter w is useful for
predicting whether wetting behavior is present at and above the triple
temperature. The nonwetting/wetting crossover value found here is w circa 3.3.Comment: 15 pages, 8 figure
Axiomatic quantum field theory in curved spacetime
The usual formulations of quantum field theory in Minkowski spacetime make
crucial use of features--such as Poincare invariance and the existence of a
preferred vacuum state--that are very special to Minkowski spacetime. In order
to generalize the formulation of quantum field theory to arbitrary globally
hyperbolic curved spacetimes, it is essential that the theory be formulated in
an entirely local and covariant manner, without assuming the presence of a
preferred state. We propose a new framework for quantum field theory, in which
the existence of an Operator Product Expansion (OPE) is elevated to a
fundamental status, and, in essence, all of the properties of the quantum field
theory are determined by its OPE. We provide general axioms for the OPE
coefficients of a quantum field theory. These include a local and covariance
assumption (implying that the quantum field theory is locally and covariantly
constructed from the spacetime metric), a microlocal spectrum condition, an
"associativity" condition, and the requirement that the coefficient of the
identity in the OPE of the product of a field with its adjoint have positive
scaling degree. We prove curved spacetime versions of the spin-statistics
theorem and the PCT theorem. Some potentially significant further implications
of our new viewpoint on quantum field theory are discussed.Comment: Latex, 44 pages, 2 figure
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