16,477 research outputs found
Coping with dating errors in causality estimation
We consider the problem of estimating causal influences between observed processes from time series possibly corrupted by errors in the time variable (dating errors) which are typical in palaeoclimatology, planetary science and astrophysics. "Causality ratio" based on the Wiener-Granger causality is proposed and studied for a paradigmatic class of model systems to reveal conditions under which it correctly indicates directionality of unidirectional coupling. It is argued that in the case of a priori known directionality, the causality ratio allows a characterization of dating errors and observational noise. Finally, we apply the developed approach to palaeoclimatic data and quantify the influence of solar activity on tropical Atlantic climate dynamics over the last two millennia. A stronger solar influence in the first millennium A.D. is inferred. The results also suggest a dating error of about 20 years in the solar proxy time series over the same period
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
The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions
We consider the application of the DRA method to the case of several master
integrals in a given sector. We establish a connection between the homogeneous
part of dimensional recurrence and maximal unitarity cuts of the corresponding
integrals: a maximally cut master integral appears to be a solution of the
homogeneous part of the dimensional recurrence relation. This observation
allows us to make a necessary step of the DRA method, the construction of the
general solution of the homogeneous equation, which, in this case, is a coupled
system of difference equations.Comment: 17 pages, 2 figure
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
Kondo enhancement of current induced spin accumulation in a quantum dot
Weak spin-orbit coupling produces very limited current induced spin
accumulation in semiconductor nanostructures. We demonstrate a possibility to
increase parametrically the spin polarization using the Kondo effect. As a
model object we consider a quantum dot side coupled to a quantum wire taking
into account the spin dependent electron tunneling from the wire to the dot.
Using the nonequilibrium Green's functions, we show that the many body
correlations between the quantum dot and the quantum wire can increase the
current induced spin accumulation at low temperatures by almost two orders of
magnitude for the moderate system parameters. The enhancement is related to the
Kondo peak formation in the density of states and the spin instability due to
the strong Coulomb interaction. This effect may be useful to electrically
manipulate the localized electron spins in quantum dots for their quantum
applications.Comment: 7+5 pages, 3+1 figure
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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