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471.
Let ? be the function algebra on a semisimple orbit, M, in the coadjoint representation of a simple Lie group, g, with the Lie algebra ?. We study one and two parameter quantizations ?
h
and ?
t,h
of ? such that the multiplication on the quantized algebra is invariant under action of the Drinfeld–Jimbo quantum group,
U
h
(?). In particular, the algebra ?
t,h
specializes at h= 0 to a U(?)-invariant ($G$-invariant) quantization, %Ascr;
t
,0.
We prove that the Poisson bracket corresponding to ?
h
must be the sum of the so-called r-matrix and an invariant bracket. We classify such brackets for all semisimple orbits, M, and show that they form a dim H
2(M) parameter family, then we construct their quantizations.
A two parameter (or double) quantization, $?
t,h
, corresponds to a pair of compatible Poisson brackets: the first is as described above and the second is the Kirillov-Kostant-Souriau
bracket on M. Not all semisimple orbits admit a compatible pair of Poisson brackets. We classify the semisimple orbits for which such
pairs exist and construct the corresponding two parameter quantization of these pairs in some of the cases.
Received: 15 August 1998 / Accepted: 13 January 1999 相似文献
472.
Electrostatic interaction energies in a disordered monodisperse system of metallic granules are calculated. The calculation
is performed in the dipole approximation for particles that cannot be regarded as point charges. The dependences of the charging
energies of the particles on the concentration of the metallic phase as well as the dependences of the interaction energy
of the charged particles on the distances between them are obtained.
Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 100–105 (25 July 1999) 相似文献
473.
A. V. Gurevich K. P. Zybkin G. A. Él’ 《Journal of Experimental and Theoretical Physics》1999,88(1):182-195
The behavior of the solution of the Korteweg-de Vries equation for large-scale oscillating periodic initial conditions prescribed
on the entire x axis is considered. It is shown that the structure of small-scale oscillations arising in a Korteweg-de Vries system as t→∞ loses its dynamical properties as a consequence of phase mixing. This process can be called the generation of soliton turbulence.
The infinite system of interacting solitons with random phases developing under these conditions leads to oscillations having
a stochastic character. Such a system can be described using the terms applied to a continuous random process, the probability
density and correlation function. It is shown that for this it suffices to determine from the prescribed initial conditions
amplitude distribution function of the solitons and their mean spatial density. The limiting stochastic characteristics of
the mixed state for problems with initial data in the form of an infinite sequence of isolated small-scale pulses are found.
Also, the problem of stochastic mixing under arbitrary initial conditions in the dispersionless limit (the Hopf equation)
is completely solved.
Zh. éksp. Teor. Fiz. 115, 333–360 (January 1999) 相似文献