17,793 research outputs found
On Thermodynamics of Rational Maps. II: Non-Recurrent Maps
The pressure function p(t) of a non-recurrent map is real analytic on some interval (0,t_*) with t_* strictly greater than the dimension of the Julia set. The proof is an adaptation of the well known tower techniques to the complex dynamics situation. In general, p(t) need not be analytic on the whole positive axis
Form-factors of the sausage model obtained with bootstrap fusion from sine-Gordon theory
We continue the investigation of massive integrable models by means of the
bootstrap fusion procedure, started in our previous work on O(3) nonlinear
sigma model. Using the analogy with SU(2) Thirring model and the O(3) nonlinear
sigma model we prove a similar relation between sine-Gordon theory and a
one-parameter deformation of the O(3) sigma model, the sausage model. This
allows us to write down a free field representation for the
Zamolodchikov-Faddeev algebra of the sausage model and to construct an integral
representation for the generating functions of form-factors in this theory. We
also clear up the origin of the singularities in the bootstrap construction and
the reason for the problem with the kinematical poles.Comment: 16 pages, revtex; references added, some typos corrected. Accepted
for publication in Physical Review
Analytic Results for Massless Three-Loop Form Factors
We evaluate, exactly in d, the master integrals contributing to massless
three-loop QCD form factors. The calculation is based on a combination of a
method recently suggested by one of the authors (R.L.) with other techniques:
sector decomposition implemented in FIESTA, the method of Mellin--Barnes
representation, and the PSLQ algorithm. Using our results for the master
integrals we obtain analytical expressions for two missing constants in the
ep-expansion of the two most complicated master integrals and present the form
factors in a completely analytic form.Comment: minor revisions, to appear in JHE
On a general analytical formula for U_q(su(3))-Clebsch-Gordan coefficients
We present the projection operator method in combination with the
Wigner-Racah calculus of the subalgebra U_q(su(2)) for calculation of
Clebsch-Gordan coefficients (CGCs) of the quantum algebra U_q(su(3)). The key
formulas of the method are couplings of the tensor and projection operators and
also a tensor form for the projection operator of U_q(su(3)). We obtain a very
compact general analytical formula for the U_q(su(3)) CGCs in terms of the
U_q(su(2)) Wigner 3nj-symbols.Comment: 9 pages, LaTeX; to be published in Yad. Fiz. (Phys. Atomic Nuclei),
(2001
Free field representation for the O(3) nonlinear sigma model and bootstrap fusion
The possibility of the application of the free field representation developed
by Lukyanov for massive integrable models is investigated in the context of the
O(3) sigma model. We use the bootstrap fusion procedure to construct a free
field representation for the O(3) Zamolodchikov- Faddeev algebra and to write
down a representation for the solutions of the form-factor equations which is
similar to the ones obtained previously for the sine-Gordon and SU(2) Thirring
models. We discuss also the possibility of developing further this
representation for the O(3) model and comment on the extension to other
integrable field theories.Comment: 14 pages, latex, revtex v3.0 macro package, no figures Accepted for
publication in Phys. Rev.
Formation of homophily in academic performance: Students change their friends rather than performance
Homophily, the tendency of individuals to associate with others who share similar traits, has been identified as a major driving force in the formation and evolution of social ties. In many cases, it is not clear if homophily is the result of a socialization process, where individuals change their traits according to the dominance of that trait in their local social networks, or if it results from a selection process, in which individuals reshape their social networks so that their traits match those in the new environment. Here we demonstrate the detailed temporal formation of strong homophily in academic achievements of high school and university students. We analyze a unique dataset that contains information about the detailed time evolution of a friendship network of 6,000 students across 42 months. Combining the evolving social network data with the time series of the academic performance (GPA) of individual students, we show that academic homophily is a result of selection: students prefer to gradually reorganize their social networks according to their performance levels, rather than adapting their performance to the level of their local group. We find no signs for a pull effect, where a social environment of good performers motivates bad students to improve their performance. We are able to understand the underlying dynamics of grades and networks with a simple model. The lack of a social pull effect in classical educational settings could have important implications for the understanding of the observed persistence of segregation, inequality and social immobility in societies
On the nature of the solar-wind-Mars interaction
Plasma measurements near Mars on the U.S.S.R. Mars-2, -3, and -5 spacecraft are considered. The data are compared with simultaneous magnetic measurements. Strong evidence is obtained in favor of a direct interaction and mass exchange between the solar wind plasma and the gaseous envelope of Mars
Optical measurement of electron spins in quantum dots: Quantum Zeno effects
We describe the effects of the quantum back action under continuous optical
measurement of electron spins in quantum dots. We consider the system
excitation by elliptically polarized light close to the trion resonance, which
allows for the simultaneous spin orientation and measurement. We
microscopically demonstrate that the nuclei-induced spin relaxation can be both
suppressed and accelerated by the continuous spin measurement due to the
quantum Zeno and anti-Zeno effects, respectively. Our theoretical predictions
can be directly compared with the future experimental results and
straightforwardly generalized for the pump-probe experiments.Comment: 9 pages, 4 figure
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