48,721 research outputs found
A Quasi-Exactly Solvable N-Body Problem with the sl(N+1) Algebraic Structure
Starting from a one-particle quasi-exactly solvable system, which is
characterized by an intrinsic sl(2) algebraic structure and the
energy-reflection symmetry, we construct a daughter N-body Hamiltonian
presenting a deformation of the Calogero model. The features of this
Hamiltonian are (i) it reduces to a quadratic combination of the generators of
sl(N+1); (ii) the interaction potential contains two-body terms and interaction
with the force center at the origin; (iii) for quantized values of a certain
cohomology parameter n it is quasi-exactly solvable, the multiplicity of states
in the algebraic sector is (N+n)!/(N!n!); (iv) the energy-reflection symmetry
of the parent system is preserved.Comment: Latex, 12 page
Chapman-Enskog expansion of the Boltzmann equation and its diagrammatic interpretation
We perform a Chapman-Enskog expansion of the Boltzmann equation keeping up to
quadratic contributions. We obtain a generalized nonlinear Kubo formula, and a
set of integral equations which resum ladder and extended ladder diagrams. We
show that these two equations have exactly the same structure, and thus provide
a diagrammatic interpretation of the Chapman-Enskog expansion of the Boltzmann
equation, up to quadratic order.Comment: 5 pages, 2 figures in eps, talk given at XXXI International Symposium
on Multiparticle Dynamics, Sept 1-7, 2001, Datong China. URL
http://ismd31.ccnu.edu.cn
Top-Antitop-Quark Production and Decay Properties at the Tevatron
At the Tevatron, the collider experiments CDF and DO have data sets at their
disposal that comprise a few thousand reconstructed top-antitop-quark pairs and
allow for precision measurements of the cross section as well as production and
decay properties. Besides comparing the measurements to standard model
predictions, these data sets open a window to physics beyond the standard
model. Dedicated analyses look for new heavy gauge bosons, fourth generation
quarks, and flavor-changing neutral currents. In this mini-review the current
status of these measurements is summarized.Comment: Mini-review to be submitted to Mod. Phys. Lett. A, was derived from
the proceedings of the 21st Rencontres de Blois: Windows on the Universe,
Blois, France, 21. - 27. June 2009. 19 pages. 2nd revision: correct a few
minor mistakes, update references
Robust pricing and hedging under trading restrictions and the emergence of local martingale models
We consider the pricing of derivatives in a setting with trading
restrictions, but without any probabilistic assumptions on the underlying
model, in discrete and continuous time. In particular, we assume that European
put or call options are traded at certain maturities, and the forward price
implied by these option prices may be strictly decreasing in time. In discrete
time, when call options are traded, the short-selling restrictions ensure no
arbitrage, and we show that classical duality holds between the smallest
super-replication price and the supremum over expectations of the payoff over
all supermartingale measures. More surprisingly in the case where the only
vanilla options are put options, we show that there is a duality gap. Embedding
the discrete time model into a continuous time setup, we make a connection with
(strict) local-martingale models, and derive framework and results often seen
in the literature on financial bubbles. This connection suggests a certain
natural interpretation of many existing results in the literature on financial
bubbles
The Dynamical Yang-Baxter Relation and the Minimal Representation of the Elliptic Quantum Group
In this paper, we give the general forms of the minimal matrix (the
elements of the -matrix are numbers) associated with the Boltzmann
weights of the interaction-round-a-face (IRF) model and the minimal
representation of the series elliptic quantum group given by Felder
and Varchenko. The explicit dependence of elements of -matrices on spectral
parameter are given. They are of five different forms (A(1-4) and B). The
algebra for the coefficients (which do not depend on ) are given. The
algebra of form A is proved to be trivial, while that of form B obey
Yang-Baxter equation (YBE). We also give the PBW base and the centers for the
algebra of form B.Comment: 23 page
Chemoviscosity modeling for thermosetting resin systems, part 3
A new analytical model for simulating chemoviscosity resin has been formulated. The model is developed by modifying the well established Williams-Landel-Ferry (WLF) theory in polymer rheology for thermoplastic materials. By introducing a relationship between the glass transition temperature (T sub g (t)) and the degree of cure alpha(t) of the resin system under cure, the WLF theory can be modified to account for the factor of reaction time. Temperature-dependent functions of the modified WLF theory parameters C sub 1 (T) and C sub 2 (T) were determined from the isothermal cure data. Theoretical predictions of the model for the resin under dynamic heating cure cycles were shown to compare favorably with the experimental data. This work represents a progress toward establishing a chemoviscosity model which is capable of not only describing viscosity profiles accurately under various cure cycles, but also correlating viscosity data to the changes of physical properties associated with the structural transformations of the thermosetting resin systems during cure
q-deformed Supersymmetric t-J Model with a Boundary
The q-deformed supersymmetric t-J model on a semi-infinite lattice is
diagonalized by using the level-one vertex operators of the quantum affine
superalgebra . We give the bosonization of the boundary
states. We give an integral expression of the correlation functions of the
boundary model, and derive the difference equations which they satisfy.Comment: LaTex file 18 page
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