On Bohr-Sommerfeld bases

This paper combines algebraic and Lagrangian geometry to construct a special basis in every space of conformal blocks, the Bohr-Sommerfeld (BS) basis. We use the method of [D. Borthwick, T. Paul and A. Uribe, Legendrian distributions with applications to the non-vanishing of Poincar\'e series of large weight, Invent. math, 122 (1995), 359-402, preprint hep-th/9406036], whereby every vector of a BS basis is defined by some half-weighted Legendrian distribution coming from a Bohr-Sommerfeld fibre of a real polarization of the underlying symplectic manifold. The advantage of BS bases (compared to bases of theta functions in [A. Tyurin, Quantization and ``theta functions'', Jussieu preprint 216 (Apr 1999), e-print math.AG/9904046, 32pp.]) is that we can use information from the skillful analysis of the asymptotics of quantum states. This gives that Bohr-Sommerfeld bases are unitary quasi-classically. Thus we can apply these bases to compare the Hitchin connection with the KZ connection defined by the monodromy of the Knizhnik-Zamolodchikov equation in combinatorial theory (see, for example, [T. Kohno, Topological invariants for 3-manifolds using representations of mapping class group I, Topology 31 (1992), 203-230; II, Contemp. math 175} (1994), 193-217]).Comment: 43 pages, uses: latex2e with amsmath,amsfonts,theore

Special lagrangian fibrations on flag variety F3F^3

One constructs lagrangian fibrations on the flag variety $F^3$ and proves that the fibrations are special.Comment: 19 page

Radiation-induced hydrogen transfer in metals

The paper presents processes of hydrogen (deuterium) diffusion and release from hydrogen-saturated condensed matters in atomic, molecular and ionized states under the influence of the electron beam and X-ray radiation in the pre-threshold region. The dependence is described between the hydrogen isotope release intensity and the current density and the electron beam energy affecting sample, hydrogen concentration in the material volume and time of radiation exposure to the sample. The energy distribution of the emitted positive ions of hydrogen isotopes is investigated herein. Mechanisms of radiation-induced hydrogen transfer in condensed matters are suggested

Spin content of constituent quarks and one-spin asymmetries in inclusive processes

We consider mechanism for one-spin asymmetries observed in inclusive hadron production. The main role belongs to the orbital angular momentum of the quark-antiquark cloud in the internal structure of constituent quarks. We argue that the origin of the asymmetries in pion production is a result of retaining of this internal angular orbital momentum by the perturbative phase of QCD under transition from the non-perturbative phase. The non-perturbative hadron structure is based on the results of chiral quark models. PACS number(s): 11.30.Qc, 12.40.Pp, 13.75.Ni, 13.88.+eComment: 21 pages LaTeX + 8 figures (not included

Sum rules for spin asymmetries

Starting from rotational invariance we derive sum rules for the single-spin asymmetries in inclusive production and binary processes. We also get sum rules for spin correlation parameters in elastic pp-scattering.Comment: 4 page

Billiard algebra, integrable line congruences, and double reflection nets

The billiard systems within quadrics, playing the role of discrete analogues of geodesics on ellipsoids, are incorporated into the theory of integrable quad-graphs. An initial observation is that the Six-pointed star theorem, as the operational consistency for the billiard algebra, is equivalent to an integrabilty condition of a line congruence. A new notion of the double-reflection nets as a subclass of dual Darboux nets associated with pencils of quadrics is introduced, basic properies and several examples are presented. Corresponding Yang-Baxter maps, associated with pencils of quadrics are defined and discussed.Comment: 18 pages, 8 figure

Determination of some parameters of a porous medium-liquid system by the pulsed field gradient NMR

A possibility was considered to estimate the parameter of a porous medium S/Vp, where S and Vp are the surface area and the volume of pores, respectively, as well as the power of nuclear magnetic energy sinks ρ of a porous medium-liquid system by the example of randomly packed glass spheres 53-63 μm in diameter and acetone, water, or decane as a liquid medium. Estimates were made by analyzing the time dependences of the effective self-diffusion coefficient D(t) and P(t), the probability of return of a molecule to its initial position by time t. It was shown that the short-time parts of D(t) dependence allow us to obtain parameters S/Vp and ρ, whereas those of P(t), only the S/Vp, parameter. The values of ρ, obtained from D(t), and from the time of relaxation of longitudinal nuclear magnetization, differ from each other by an order of magnitude. As expected, the value of S/Vp, obtained for a given porous medium, is independent of the nature of introduced liquid