The Canonical Solutions of the Q-Systems¶ and the Kirillov–Reshetikhin Conjecture

We study a class of systems of functional equations closely related to various kinds of integrable statistical and quantum mechanical models. We call them the finite and infinite $Q$-systems according to the number of functions and equations. The finite Q-systems appear as the thermal equilibrium conditions (the Sutherland–Wu equation) for certain statistical mechanical systems. Some infinite Q-systems appear as the relations of the normalized characters of the KR modules of the Yangians and the quantum affine algebras. We give two types of power series formulae for the unique solution (resp. the unique canonical solution) for a finite (resp. infinite) Q-system. As an application, we reformulate the Kirillov–Reshetikhin conjecture on the multiplicities formula of the KR modules in terms of the canonical solutions of Q-systems. Received: 2 August 2001 / Accepted: 27 December 2001     

Color centers in irradiated MgF2

Abstract

Color centers in rutile-structured MgF₂ single crystals irradiated at 20K/360K by reactor neutrons are investigated spectroscopically at LNT. Four different types of the F-F vacancy bond in MgF₂ are possibly identified to the observed absorption bands as due to the F₂ centers; instead of previous assignments, the 300nm band to the F₂(D_2h), the 325nm band to the F₂(C₁), the 355nm band to the F₂(C_2v), and the 400nm band to the F₂(C_2h) centers.     

Studies of phase characteristics of various photon echoes with a phase sensitive detection method

Various optical coherent transient signals in ruby have been examined by using an optical phase sensitive detection (PSD) technique. The PSD is performed by comparing the phase of the heterodyne beat signals obtained by the Stark switching technique with that of a local oscillator whose frequency is equal to the heterodyne beat frequency. The optical FID, two-pulse photon echoes, radiation locked echoes and notched echoes have been detected as υ-mode signals with small u-mode signals probably due to the asymmetry of the inhomogeneous broadening. The dependence of the phase of the radiation locked and notched echoes upon the driving pulses is also examined. The experimental results are in good agreement with theoretical predictions based on Bloch equations.     

Coherent transients observed by Stark switching in ruby having narrow optical hole burning

By using the Stark switching technique we observed new coherent transient signals in ruby at low laser intensities, which are unique in solids where T₁ ? T₂. It was confirmed that the existence of narrow optical hole burning before the switching plays an essential role in giving rise to the signals. The effects of the multiple optical hole burning were also observed in the time domain. Assuming the existence of the holes, the signals can well be interpreted by linear system analysis.     

Excitation and decay of the isovector giant monopole resonances via the 208Pb(3He,t p) reaction at 410 MeV

The excitation and subsequent proton decay of the isovector spin-flip giant monopole resonance (IVSGMR) is studied via the 208Pb(3He,t) reaction at 410 MeV. In the inclusive spectrum (60+/-5)% of the non-energy-weighted sum-rule strength for this 2 variant Planck's over 2h omega resonance was found in the region 29相似文献   

Magnetic properties of the bilayer manganese oxide (Pr0.6La0.4)1.2Sr1.8Mn2O7 under pressure

We investigated the effect of pressure on the magnetic properties of a single crystal of the bilayer manganese oxide (Pr_0.6La_0.4)_1.2Sr_1.8Mn₂O₇ by means of DC magnetization measurements under pressure. The ferromagnetic transition, which is accompanied by a metal-insulator transition, is highly sensitive to pressure. The pressure causes a structural variation, which affects the magnetic properties. We discuss the pressure dependence of the 3d electronic state of the Mn ion in this system.     

Induction in linear logic

Linear logic, introduced by Girardet al., has a great power of expression, but no method for induction. This paper proposes a method of induction using knowledge represented by linear logical formulas. In linear logic, the number of propositions is controlled by logical operators. When a background theory and a hypothesis prove an example, the number of propositions on each side must be equivalent.