Normal ordering and quantum groups

The irreducible R-matrices associated with the quantum Liouville and sine-Gordon equations were classified by the su(2) index l, 2l integer. We find that the associated quantum field theories must have the following equal time operator product expansions in the lattice approximation

On the Uniqueness of Weak Weyl Representations of the Canonical Commutation Relation

Let (T, H) be a weak Weyl representation of the canonical commutation relation (CCR) with one degree of freedom. Namely T is a symmetric operator and H is a self-adjoint operator on a complex Hilbert space satisfying the weak Weyl relation: for all (the set of real numbers), e^−itH D(T) ⊂ D(T) (i is the imaginary unit and D(T) denotes the domain of T) and . In the context of quantum theory where H is a Hamiltonian, T is called a strong time operator of H. In this paper we prove the following theorem on uniqueness of weak Weyl representations: Let be separable. Assume that H is bounded below with and , where is the set of complex numbers and, for a linear operator A on a Hilbert space, σ(A) denotes the spectrum of A. Then ( is the closure of T) is unitarily equivalent to a direct sum of the weak Weyl representation on the Hilbert space , where is the multiplication operator by the variable and with . Using this theorem, we construct a Weyl representation of the CCR from the weak Weyl representation . This work is supported by the Grant-in-Aid No.17340032 for Scientific Research from Japan Society for the Promotion of Science (JSPS).     

Kramers Degeneracy Theorem in Nonrelativistic QED

Degeneracy of the eigenvalues of the Pauli–Fierz Hamiltonian with spin 1/2 is proven by the Kramers degeneracy theorem. The Pauli–Fierz Hamiltonian at fixed total momentum is also investigated.      

Refined interpretation of Christiansen-filter experiments and neutron scattering lengths of the lead-isotopes

A refined interpretation of Christiansen filter experiments is described, which allows for the effects of inhomogeneities in the powder column of the filter. Using this procedure the evaluation of experiments on enriched samples of lead isotopes provided the neutron coherent scattering lengths (in fm) for the separated isotopes:b (204) =10.6 ± 2.0;b (206)=9.23 ± 0.05;b (207)=9.28 ± 0.04 andb (208)=9.50 ± 0.06. The corresponding potential scattering radius R was obtained by taking account of resonance contributions as earlier used in the determination of the neutron's electric polarizability. The found R=9.74 ± 0.07 fm is in good argreement with the literature. This confirms the correctness of the used resonance contributions.Work partially supported by the Bundesministerium für Forschung und Technologie     

On the Instability Intervals of the Mathieu–Hill Operator

Consider the Mathieu–Hill operator

On the competiting role of mean-field and residual interactions in flow observables

Theoretical analyses of heavy-ion reactions are performed in the framework of the semi-classical Landau-Vlasov approach. The incident energies are investigated in the range from intermediate to low energy regimes, where transverse collective motion has been experimentally evidenced. The influence of the equation of state (E.O.S.) parameters on various collective observables is studied in relation with the action of the residual interactions. From the sensitivity to both aspects, and taking into account the experimental biases limitations, our investigation indicates that E.O.S. signatures should be more expected at energies below 100 MeV per nucleon.     

Spectral Asymptotic for the High-Dimensional Euler Top

In this paper, we compute the leading coefficient in the asymptotic expansion of the joint eigenvalues for the high-dimensional Euler Top. We also prove a central limit theorem for the same eigenvalues.      

New bounds on the number of bound states for Schrödinger operators

We consider the Schrödinger operatorH = – +V(|x|) onR ³. Letn denote the number of bound states with angular momentum (not counting the 2 + 1 degeneracy). We prove the following bounds onn . LetV 0 and d/dr r ^1-2p (-V)^{1 –p} 0 for somep [1/2, 1) then

On the Hochschild Homology of Elliptic Sklyanin Algebras

In this paper, we compute the Hochschild homology of elliptic Sklyanin algebras. These algebras are deformations of polynomial algebra with a Poisson bracket called the Sklyanin Poisson bracket.      

On the chaining dynamics of inclusions in SmC* free standing films

A simplified model of an inclusion represented by (+1)-wedge disclination and an accompanying hyperbolic defect ((−1)-wedge disclination) in smectic C* free standing films is used to describe the early stage of the ordering process of inclusions into chains. The elastic interaction between inclusions and their associated hyperbolic defects is used to discuss the dynamics observed experimentally during the inclusion chaining when inclusions are at distances much larger than their radii. This work was also supported by Grant No. 202/02/0840 of the Grant Agency of the Czech Republic and by the research project AV0Z1-010-914.     

Stretching excitations of tetrahedral molecules in an anharmonically coupled local mode model

Summary  An anharmonically coupled local mode model is used to study highly excited stretching vibrational spectra and intensities of infrared transition in a tetrahedral molecule. This model is successfully applied to silane and silicon tetrafluoride. The author is very grateful to Prof. Zhong-Qi Ma for his continuing interest, support and sound advice. This work was supported by the National Natural Science Foundation of China and Grant No. LWTZ-1298 of the Chinese Academy of Sciences.     

On the measurement of the tensor analysing power in proton induced deuteron break-up experiments

The tensor analysing powerA _zz is calculated in the reaction with polarized deuteron break-up d+pp+p + n. Peculiarities and possibilities of the experiments with different kinematical set-up are discussed from the point of view what information can be extracted about the high-momentum component of the deuteron wave function.The authors are indebted to S. L. Belostotsky, B. Metsch, H. R. Petry and O. G. Grebenyuk for useful discussions. One of us (L.D.) is grateful to Deutsche Forschungsgemeinschaft for the financial support during the visit to the Bonn University.     

Absorption measurements in InSe:Ho single crystal under an electric field

InSe:Ho single crystal was grown by Bridgman-Stockberger method. Electric field effects on the absorption measurements have been investigated as a function of temperature in InSe:Ho single crystal. The absorption edge shifted towards longer wavelengths and a decrease of intensity in absorption spectra occurred under an electric field of 7.5 kV/cm. Using absorption measurements, steepness parameter and Urbach energy were calculated under electric field. Applied electric field caused an increase in the Urbach energy. At 10 K and 320 K, the first exciton energies were calculated as 1.322 and 1.301 eV for zero voltage and 1.245 and 1.232 eV for applied electric field, respectively.     

On the limits of induced radiation concept in FELs

We discuss a restriction of the induced radiation concept in classical beam systems due to accompanying spontaneous radiation (radiation friction). For short wave FELs, spontaneous radiation renders a noticeable influence on the phasing of particles, which is the base mechanism of induced radiation in classical systems. It leads to an essential restriction on the radiating system length and gain which cannot be compensated by an increase in the beam current. The text was submitted by the authors in English.     

Isotopic dependence of electron screening in fusion reactions

The fusion reactions⁶Li(p, )³He,⁶Li(d, )⁴He, and⁷Li(p, )⁴He have been studied over the c.m. energy rangeE=10 to 1450 keV. Each reaction involved the use of hydrogen projectiles and LiF solid targets as well as Li projectiles and hydrogen molecular gas targets. In all cases the effects of electron screening on the low-energy fusion cross sections (exponential enhancement) have been observed; the effects are somewhat stronger in the case of atomicp ord projectiles compared to the case of molecularH ₂ orD ₂ gas targets. If isotopic effects on electron screening are negligible, all three reactions should exhibit the same enhancements for each set of experimental techniques. The measurements confirmed this expectation to a large extent.Supported in part by the Landesamt Nordrhein-Westfalen (IVA5-10600387), the Deutsche Forschungsgemeinschaft (Ro429/ 18-2 and Ro429/21-1), and the Comision Interministerial de Ciencia y Tecnologia (AEN90-0932)     

Estimates of hypernuclear production via the exclusive (p,K+) reaction

We investigate the possibility of producing hypernuclei with proton beams via (p, K ⁺) reaction. We present differential cross sections calculations utilizing the distorted wave impulse approximation in momentum space. We consider the reactions¹²C(p,K ⁺) ¹³ and¹⁶O(p,K ⁺) ¹⁷ within the energy region 0.8 GeV1.2 GeV. We study both the case of formation of in S-state (¹²C) and P-state (¹⁶O). We take into account the contribution of both one-step and two-step processes when K pair is produced directly by incoming proton and intermediate pion, respectively. It is found that practically in all cases the two-step processes give significant contribution.Work supported by KFA Julich     

Study of fast target protons in high energy hadron-nucleus collisions

Intranuclear cascade model calculations are carried out on the recent measurements (WA80 Collaborations) for the multiplicity, energy and angular distributions of singly charged target fragments of energy in the range 30 E < 400=" mev=" (the=" so-called=" grey=" particles)=" produced=" in=" proton-nucleus=" interactions=" at=" 200=" gev/c.=" it=" is=" shown=" that=" these=" distributions=" are=" reasonably=" well=" understood=" in=" terms=" of=" the=" intranuclear=" cascade=" model=" which=" considers=" that=" grey=" particles=" are=" only=" produced=" in=" the=" first=" two=" generations=" of=" the=" cascade.=" the=" obtained=" distributions,=" mean=" values=" and=" target=" mass=" dependence=" are=" more=" consistent=" with=" the=" experimental=" data=" than=" other=" models=" using=" monte=" carlo=">     

On the Space of KdV Fields

The space of functions A over the phase space of KdV-hierarchy is studied as a module over the ring generated by commuting derivations. A -free resolution of A is constructed by Babelon, Bernard and Smirnov by taking the classical limit of the construction in quantum integrable models assuming a certain conjecture. We propose another -free resolution of A by extending the construction in the classical finite dimensional integrable system associated with a certain family of hyperelliptic curves to infinite dimension assuming a similar conjecture. The relation between the two constructions is given.