More surprises in the general theory of lattice systems

I use Israel's methods to prove new theorems of ubiquitous pathology for classical and quantum lattice systems. The main result is the following: Let be any interaction and be any translation-invariant equilibrium state for (extremal or not). Then there exists a sequence { _k } of interactions converging to , having extremal (or even unique) translation-invariant equilibrium states _k , such that { _k } converges to . In certain situations the perturbations _k – can be chosen to lie in a cone of antiferromagnetic pair interactions. I discuss the connection with results of Daniëls and van Enter, and point out an application to the one-dimensional ferromagnetic Ising model with 1/r ² interaction (Thouless effect).     

The quantum efficiency of the internal photo-electric effect in indium antimonide

A method is described for measuring the relative quantum efficiency of the internal photo-electric effect in semi-conductors by simultaneously measuring the photo-magnetoelectric and photo-conductive effect. The results of measurements on indium antimonide are given. The quantum efficiency begins to increase if the energy of the photon exceeds 0·47 eVat room temperature. The quantum efficiency as a function of the energy of the photon is analysed on the basis of the conception of impact ionization and it is shown that a study of the structure of this curve can supply information on the, band structure of a semi-conductor in the region of high energies of electrons and holes.

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. . , 0,47 eV . , .

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The authors thank M. Závtová and M. Vantuchová for efficient help with the measurements, K. mirous and V. Vrchovská for preparing the material, E. Antoník for critical remarks and M. Matyá and A. Müller for determining the constants of the material.     

Локалъная чувствите лъностъ фотокатодов фотоумножителей

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The local sensitivity of photo-multiplier photo-cathodes

The influence of the non-uniform distribution of the sensitivity of a photo-multiplier photo-cathode on the spectrum shape of the output pulses from a scintillation detector is studied. Methods of scanning the local sensitivity and determining its distribution function are described. The theory was compared qualitatively with measurement on a slow-neutron detector from a mixture of zinc sulphate and boric acid.

     

Changes in EPR spectrum of free radical species inγ-irradiated polyformaldehyde

We have found that gamma-irradiated polyformaldehyde does not exhibit the effect of the disappearance of the hyperfine structure of EPR spectrum as a function of the dose or the time passed since the end of irradiation, as was found earlier for a group of polymers having only C-C-C-C-atoms in the polymer chain. This difference in the change in the EPR of the polyformaldehyde (PFA) spectrum compared with the polymers with a -C-C-C-C- chain is explained by the impossibility of forming a conjugate double bond in the -C-O-C-O- chain in PFA.

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, , -, , , atom C-C-C-C-. ( ) C-C-C-C- , C-O-C-O- qu .

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The author thanks K. Vacek for many valuable discussions which helped this work.     

Von neumann entropy as information rate

Recently it has been shown that quantum theory can be viewed as a classical probability theory by treating Hilbert space as a measure space (H, B(H)) of events or hidden states. Each density operator defines a set of probability measures such that(E _n )=w _n (alln). Coding elements H by subspacesE _n entails distortion. We show that the von Neumann entropyS() = -trInequals the effective rate at which the Hilbert space produces information with zero expected distortion, and comment on the meaning of this.     

Equilibrium state of toroidal electron beam

The paper deals with the collective behaviour of electrons which rotate in a magnetic field used in a betatron. It is shown experimentally that there exists strong interaction between the electrons, which leads to the rapid formation of the equilibrium state with characteristic distribution of the charge density in the cross-section of the toroidal beam. The corresponding relaxation time is of the order of 1 sec. A statistical theory of the equilibrium beam is elaborated. Its main result is that the effective radius of the beam is a function of two parameters, one of which is proportional to the thermal energy of the electrons and the other to the perveance of the beam. The charge contained in a toroidal beam of given effective cross-section is equal to the product of the charge the beam would contain at zero temperature and a coefficient, which is a function of the temperature of the beam. Its value is unity at zero temperature and rapidly decreases with increasing temperature. The cause of cooling of the beam is shown.

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, . , , . 1S. . , , — I/(E₀/q)^3/2 (I — , ₀ — q ). , , , , , . . .

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Now Institute of Vacuum Electronics, Czechosl. Acad. Sci., Prague.

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In conclusion the author thanks J. Luká and L. Hyttych for invaluable help in the experiments, A. Rajský for constructing the electronic apparatus and J. Sokol for preparing the miniature probe.     

Change in primary extinction during decomposition of supersaturated solid solution II. Al-Cu 4% alloy-formation of G.P. zones

The change in integrated intensity of the (200) reflections of a solid solution during the formation of G.P. zones was measured and compared with the change in the character of the diffuse streaks corresponding to them. It was found that the. formation of G.P. zones does not lead to a decrease in primary extinction despite the great changes in the distribution of the copper atoms. It was shown that the formation of a precipitate accompanied by the formation of crystallographically incoherent boundaries greatly decreases the primary extinction.

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. II. 1-u 4%: [. . ]

(200) . . , . , . . , . , , , .

     

The influence of compression on the absorption of AgBr single crystals

The influence of compression on the edge of self absorption of AgBr single crystals was studied. The measurements were performed at a temperature of –180°C. The shift of the edge of self absorption was studied both in the field of elastic and plastic deformations. The shift of the absorption edge towards the UV end of the spectrum was determined in the field of elastic deformations and towards the i.r. end in the field of plastic deformations. After the ending of the deformation and after unloading the crystal the return of the absorption edge towards the original position was observed.

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AgBr

AgBr. –180°C. , . , — . .

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The author thanks Prof. Dr. L. Zachoval and K. K. Vacek C. Sc. for their interest in this work and for many comments given during the work.     

Paramagnetic resonance of Fe3+ ion in CdWO4 monocrystal

The paramagnetic spectrum of the Fe³⁺ ion in a CdWO₄ monocrystal was measured on a frequency of 9600 kMHz at 290°K. The spin-Hamiltonian of the Fe³⁺ ion was determined and had the form of (1). The constants derived for the spin-Hamiltonian areE/D=0·144±0·002,D=23·8 kMHz.

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Fe³⁺ CdWO₄

Fe³⁺ CdWO₄ 9600 kMHz 290°K. - Fe³⁺ (1), E/D 0,144±0,002 D 23,8 kMHz.

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In conclusion, the authors thank . Bárta and V. Kment from the Society for Chemical and Metallurgical Production in Ústí n/L for producing and supplying the monocrystals and for much valuable advice.     

ОДНОНУКЛОННАЯ МОДЕЛ Ь ЯДРА. ЧАСТЬ I

. . , - , - , - .     

A note on the Watanabe theory of weak interactions

It is shown that according to the Watanabe theory of weak interactions a resonant scattering of electrons by protons must take place. The resonant energy depends on the massm _B of the intermediate boson. Form _B=2300m _e this energy is about 213 MeV in the centre of the mass system (c. m. s.). The energy width at resonance is 1·4 MeV.

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, . , , . _{m B}=2300_{m B} , 213 MeV -. 1,4 MeV.

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The author would like to thank Professor V. Votruba for suggesting this note and for valuable advice and help during the work.     

Asymptotic theory of multidimensional chaos

A delay-differential equationu(t)+u(t)=f(u(t–1)), 0t < , and its generalization are investigated in the limit 0, when the attractor's dimension increases infinitely. It is shown that a number of statistical characteristics are asymptotically independent of. As for the attractor, it can be regarded as a direct product ofO(1/) equivalent subattractors, their statistical characteristics being asymptotically independent of . The results enable one to predict some characteristics of the attractor with fractal dimensionD 1 for the case 1, when they are inaccessible numerically. The approach developed seems to be applicable for a wide class of spatiotemporal systems.     

Anderson localization for the almost Mathieu equation: A nonperturbative proof

We prove that for any diophantine rotation angle and a.e. phase the almost Mathieu operator (H()) _n = _n–1 + _n+1 +cos(2(+n)) _n has pure point spectrum with exponentially decaying eigenfunctions for 15. We also prove the existence of some pure point spectrum for any 5.4.     

Double quantum transitions in paramagnetic resonance

The theory of double quantum transitions of the M=±2 type, with regard to inhomogeneously broadened spin systems is studied in this paper with the approximation ²T₂T₃ 1. We suppose that the inhomogeneous broadening is formed by an inhomogeneous crystal field. The obtained results describe the magnitude of absorption as a function of the h.f. power and also describe the shape of the absorption curve. It is demonstrated that in inhomogeneously broadened spin systems the absorption curve of double quantum transitions has the form of the difference of two different Lorentz's curves and that at the saturation ( ²T₂T₁ 1) the absorption increases with the cube of the h.f. field intensity. The shape of the curves is expressed by means of phenomenological relaxation constants of the system.

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M=±2 ²T₂T₃ 1. , - . . , ( ²T₂T₁ 1) . .

     

Correlation function formulas for some infrared asymptotic-free scalar field lattice models via the block renormalization group

We consider a class of scalar field lattice models with action 1/2()+V(), V small. After n block renormalization group transformations, new formulas are obtained for the finite lattice generating and correlation functions. For some infrared asymptotic-free models in the thermodynamic and n limits, the formulas for correlation functions are especially simple, isolate the correct dominant long-distance behavior, and can be used to control the subdominant contributions.     

First order phase transition in the plane rotator ferromagnetic model in two dimensions

We show that the two-dimensional isotropic ferromagnetic rotator model exhibits a first order phase transition if the interaction decays asr ^– with 2<<4.Work supported by Fonds National Suisse de la Recherche Scientifique.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Low-temperature and long-time anomalies of a damped quantum particle

The time evolution of a damped quantum particle is discussed. Dissipation is modeled by the bilinear coupling to a set of harmonic oscillators. Using a functional integral technique that accounts for initial correlations between the particle and the reservoir, one can express the dynamics of the damped particle entirely in terms of equilibrium correlation functions. The long-time behavior of these correlations is determined for memory damping arising from the coupling to a reservoir with spectral densityI() at low frequencies, where > 0. The time evolution of nonequilibrium initial states of the damped particle is discussed. At finite temperatures an initially localized state is found to spread subdiffusively or superdiffusively, depending on . For > 2 the damping becomes ineffective for long times, and the width of a state grows kinematically. At zero temperature and for < 1, an initially localized state remains localized for all times. For 1 the state spreads, but with a slower rate than at finite temperatures. Study of arbitrary initial states indicates that the process is ergodic at finite temperatures only for 2 and at zero temperature for 1 2.     

Differential calculi on quantum vector spaces with Hecke-type relations

From a vector spaceV equipped with a Yang-Baxter operatorR one may form the r-symmetric algebraS _R V=TV/v w–R(v w), which is a quantum vector space in the sense of Manin, and the associated quantum matrix algebraM _R V=T(End(V))/f g–R(f g)R ^-1. In the case whenR satisfies a Hecke-type identityR ²=(1–q)R+q, we construct a differential calculus _R V forS _R V which agrees with that constructed by Pusz, Woronowicz, Wess, and Zumino whenR is essentially theR-matrix of GL _q (n). Elements of _R V may be regarded as differential forms on the quantum vector spaceS _R V. We show that _R V isM _R V-covariant in the sense that there is a coaction _*: _R V M _R V _R V with _*d=(1 d)_* extending the natural coaction :S _R V M _R V S _R V.