Derivations commuting with abelian gauge actions on lattice systems

Let be an action of a compact abelian groupG on aC*-algebraA, and assume that the fixed-point subalgebraA is an AF-algebra. We show that if is a closed *-derivation onA commuting with , and the restriction of toA generates a one-parameter group of *-automorphisms, then itself is a generator. In particular, the result applies if is an infinite product action ofG on a UHF algebra. Furthermore, if in this situation ₁ and ₂ are two derivations both satisfying the hypotheses on , and ₁ and ₂ have the same restriction toA , then there exists a one-parameter subgroup of the action with generator ₀ such thatD(₁)D(₂)D(₀) is a joint core for the three derivations, and ₂=₁+₀ on this core.     

Superradiating 4P-4S-3P cascade of sodium vapour arising on the leading edge of the exciting laser pulse

Investigations of the superradiating cascade of sodium vapour 4P-4S-3P ₁ = 2.21 µm and ₂=1.14 µm) arising on the leading edge of the exciting laser pulse were carried out. The dependences of the actual delay time _D of the ₁ pulse on the population rise time of the laser-excited 4P state were measured and compared with those calculated following the existing theoretical model. The dependence of the actual delay time _D on the inverse density of excited atoms 1/N* is also presented. Analysis of this dependence revealed the influence of the Doppler dephasing and of the second, ₂, transition on the formation of the ₁ superradiance.     

Zero value of the Schwarzschild mass for an asymptotically Euclidian system of gravitational waves

A class of the asymptotically Euclidian space-times is shown to exist for which the Schwarzschild mass is equal to zero. The coordinate atlases of these space-times satisfy two additional conditions: _k (-gg ^0k )=0 and _ik ⁰ _0g ^ik - _ik ^k _0g ⁰ⁱ =0. In aT-orthogonal metricgs ²=g ₀₀ dt ² -g dx dx these conditions take a simple form: ₀(detg )=0 and (₀ g )(₀ g )=0.     

Compatibility of higher rho-resonances with the pion form factor data

A realistic pion form factor model respecting the usual fundamental principles supplemented by reasonable assumptions is constructed by means of conformai mapping having some specific uniformization properties. The model includes the contributions of higher rho-resonances without any conflict with analyticity, provides a certain flexibility for the asymptotic behaviour and depends just on the physical parameters. The best fit of all existing data is achieved with(770),'(1600) and the asymptoticst ^–3/2. The predicted values of the pion charge radius, P-wave isovector scattering length, as well as theI=J = 1 scattering amplitude at the experimental measurable region coincide with the world averaged data.Dedicated to the 30th anniversary of the Joint Institute of Nuclear Research.The authors are indebted to Prof. V. A. Meshcheryakov, Dr. S. B. Gerasimov and Dr. D. Krupa for many stimulating and illuminating discussions.     

Gelation and Cluster Growth with Cluster-Wall Interactions

Metallic cluster growth within a reactive polymer matrix is modeled by augmenting coagulation equations to include the influence of side reactions of metal atoms with the polymer matrix: where > 0 and where c _k denotes the concentration of the kth cluster and p denotes the concentration of reactive sites available within the polymer matrix for reaction with metallic atoms. The initial conditions are required to be non-negative and satisfy and p(0) = p ₀. We assume that for 01, which encompasses both bond linking kernels (R _jk = j k ) and surface reaction kernels (R _jk = j + k ). Our analytical and numerical results indicate that the side reactions delay gelation in some cases and inhibit gelation in others. We provide numerical evidence that gelation occurs for the classical coagulation equations ( = 0) with the bond linking kernel (d ) for 1/2<1. We examine the relative fraction of metal atoms, which coagulate compared to those which interact with the polymer matrix, and demonstrate in particular a linear dependence on ^–1 in the limiting case R _{= jk} , p ₀=1.     

The use of the repulsive potential in the quantum theory of solids

A new method is proposed for calculating the energy in certain special points of the Brillouin zone. The wave functions of valence and conduction electrons are given in the form of the linear combination of plane waves and the orthogonality condition of these functions to the wave functions of lower states is replaced by the repulsive potential. The practical application of this very simple method is illustrated on the energy spectrum of silicon in the centre of the Brillouin zone. It is proved that the results are comparable with some other methods, e. g. the orthogonalized plane-wave method.

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The basic thesis of this paper, together with concrete calculation of the energy spectrum of diamond, was delivered at the Czechoslovak-Polish conference in Sopoty in November 1956.

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In conclusion the autor would like to thank K. Trnková for carrying out the numerical calculations.     

A Rigorous Derivation of a Linear Kinetic Equation of Fokker–Planck Type in the Limit of Grazing Collisions

We rigorously derive a linear kinetic equation of Fokker–Planck type for a 2-D Lorentz gas in which the obstacles are randomly distributed. Each obstacle of the Lorentz gas generates a potential V( ), where V is a smooth radially symmetric function with compact support, and >0. The density of obstacles diverges as ^– , where >0. We prove that when 0< <1/8 and =2+1, the probability density of a test particle converges as 0 to a solution of our kinetic equation.     

Correlated majority model

We extend the bichromatic majority model by including (one-dimensional isotropic) correlations and numerically discuss, through Monte Carlo simulations, the simple, 1/3, and 2/3 majority rules. We calculate, as functions of the concentration and correlation degree, the mean finite cluster size, and the order parameterm as well as their respective critical exponents and. We find1 regardless of the correlation degree or the type of majority. Also, a supplementary divergence of is observed at the>0 borderline.     

Local observables and particle statistics I

We consider the family of those states which become asymptotically indistinguishable from the vacuum for observations in far away regions of space. The pure states of this family may be subdivided into superselection sectors labelled by generalized charge quantum numbers. The principle of locality implies that within this family one may define a natural product composition (leading for instance from single particle states ton-particle states). Intrinsically associated with then-fold product of states of one sector there is a unitary representation ofP ⁽ⁿ⁾, the permutation group ofn elements, analogous in its role to that arising in wave mechanics from the permutations of the arguments of ann-particle wave function. We show that each sector possesses a statistics parameter which determines the nature of the representation ofP ⁽ⁿ⁾ for alln and whose possible values are 0, ±d ^–1 (d a positive integer). A sector with 0 has a unique charge conjugate (antiparticle states); if =d ^–1 the states of the sector obey para-Bose statistics of orderd, if =–d ^–1 they obey para-Fermi statistics of orderd. Some conditions which restrict to ± 1 (ordinary Bose or Fermi statistics) are given.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

On the characterization of the stationary state of a class of dynamical semigroups

We consider a representation of the entropy production for a completely positive, trace-preserving dynamical semigroup satisfying detailed balance with respect to its faithful stationary state denned on aW*-algebra(): it is expressed as a positive Hermitian form on(), which is analogous to the quantum correlation functions used in the Kubo theory. By considering this Hermitian form as a variation function of a vector in(), an exact characterization of the stationary states of semigroups in a certain class is obtained. On this basis, the problem of characterizing the stationary states discussed by Spohn and Lebowitz for manyreservoir open systems is solved without the restriction to situations near thermal equilibrium.     

Dynamic structure factor in a random diffusion model

Let {X _t:0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew ^–1(X _t), where {w(x):x^d} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering function F(q,t)=E ₀ (q^d) is completely monotonic int (E ₀ denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factor S(q, w)=2 ₀ cos(t)F(q, t) exists for 0 and is strictly positive. Ind=1, 2 it diverges as 1/||^1/2, resp. –ln(||), in the limit 0; ind3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that ||D |q|², whereD is the diffusion constant.     

Zur Temperaturabhängigkeit einiger Kenngrössen der Verfestigungskurven von Zinkeinkristallen

Zusammenfassung Es werden Ergebnisse beschrieben über die Temperaturabhängigkeit: der kritischen Schubspannung ₀, des Verfestigungskoeffizienten _A , im BereichA der Verfestigungskurve; des Verfestigungskoeffizienten _B im BereichB, der Längea _A des BereichsA und der Schubspannung _A am Ende des BereichsA. Die kritische Schubspannung wächst im Temperaturbereich 225–344°K linear mit abnehmender Temperatur. Der Temperaturverlauf des Verfestigungskoeffizienten _A , stimmt überein mit älteren Messungen an h.k.p. Metallen. Ähnlich verhält sich der Verfestigungskoeffizient _B . Die Schubspannung am Ende des BereichsA wird durch thermisch aktivierte Vorgänge beeinflußt. Der BereichA verkürzt sich im Temperaturbereich 0–85°C linear mit zunehmender Temperatur. Temperaturwechselversuche zeigen, daß im BereichB thermisch irreversible Änderungen in der Versetzungsstruktur auftreten.

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: ₀, _A , _B , _{A A} . 226 344°K . _A . _B . . 0–85°C . , .

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Herrn Dr. F. Kroupa und Ing. B. esták bin ich für das Durchlesen des Manuskripts sowie wertvolle Hinweise zu Dank verpflichtet. Mein besonderer Dank für zahlreiche fruchtbare Diskusionen und Anregungen gilt Herrn P. Kratochvíl. Herrn Prof. Dr. A. Seeger danke ich ganz besonders für Kritik des Manuskripts und wertvolle Ratschläge.     

A natural scalar field in the einstein gravitational theory

In a Riemannian space-time, the difference between the third-order tensor potentialH of the Riemann tensor (presented in a precedent paper) and the Lanczos generating function of the Weyl tensor is here shown to be characterized by a vectorV , obtained by contractionH . The significant role of such a vector, in the context of general relativity, is then discussed. Particular attention is paid to the scalar potential which characterizes the irrotational part ofV : such a scalar field satisfies a space-time wave equation of the Poisson type. Weak fields are also considered: in the particular case of a static metric, the scalar is found to be proportional to the classic Newtonian potential.This work was done in the sphere of activity of the C.N.R. Groups for mathematical research.     

Instability in degenerate two-photon running wave laser

The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k>1+r(k=/,r=/; is the cavity loss of the field and , are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr<k<(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.     

ВЛИЯНИЕ ДАВЛЕНИЯ НА Ч УВСТВИТЕЛЬНОСТЬ ФОТОГРАФИЧЕСКОЙ ЭМУ ЛЬСИИ

- gr, -, . - , - . , , .     

On surface layers on BaTiO3 single crystals

The possibility of explaining the existence of a surface layer on BaTiO₃ crystals by the presence of Schottky defects in the crystal is investigated. The magnitude of the potential difference between the surface and the interior of the crystal and the thickness of the surface layer, which at temperatures of over 400°C agrees with the measured values, are calculated for the cubic phase from a simplified ionic model.

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BaTiO₃

iO₃ . , 400° .

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In conclusion the author would like to thank Dr. M. Trlifaj and V. Janovec, candidates of physics and mathematics, for valuable remarks.     

The interaction of pions with deuterons

Summary There has been remarkable experimental and theoretical progress in the field ofd interactions in the last few years. Within the uncertainties of the theory the experimental data in thed breakup and thed elastic scattering reaction can be fairly well reproduced. Theoretical problems remain in the absorption channel, but there is a hope that with a few additional measurements of tensor polarization and spin transfer observables in this reaction a partial wave amplitude analysis may localize the theoretical difficulties. In addition it is very important to provide data on the deuteron tensor polarizations and the spin transfer parameters for thed elastic scattering reaction in order to obtain a reliable set of phase shifts, which may reveal resonance structures in this reaction channel.Invited talk to the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

Magnetic susceptibility of a one-dimensional Fermi system and dielectric function of a two-dimensional Coulomb gas

A relation between the magnetic susceptibility(k, ) of an interacting 1-D Fermi system and the dielectric function(q) of a 2-D Coulomb gas is established. By applying a cluster-expansion technique and by using known results for the pair-correlation function of the Coulomb gas we obtain a number of expressions for(q) which apply in different regions of theq-plane and in different temperature intervals. These results supplement the existing picture of the transition from non-metallic to metallic behaviour occurring in the 2-D Coulomb gas as the temperature increases. The relation between(q) and(k, ) is then used to derive explicit expressions for(k, ) from these results for(q). The change in the dielectric response of the 2-D Coulomb gas is reflected by a change in the magnetic response of the 1-D Fermi system: as a function of the spin non-flip coupling constant the susceptibility of the Fermi system changes from normal paramagnetic behaviour to non-magnetic behaviour characteristic of a bound singlet-spin ground state, as decreases. Our result for the gap in the spin excitation spectrum of the Fermi system is in agreement with the results of other authors.On sabbatical leave from Institut für Theoretische Physik, TU Hannover, GermanyWork at U.C.S.B. supported in part by the National Science Foundation     

Generating fields from data onH − ⋃H +andH − ⋃I +

There are series solutions for characteristic boundary value problems for fields on black hole backgrounds that converge when the data are given on =^{– +}, or on =^{– +}, but may not converge when the data are given on ^{– –}, or on ^{+ +}. We specialize to oscillatory data of frequency and calculate approximate reflection and transmission coefficientsR() andT(), using a field generated by data on =^{– +}, and again, using a field generated by data on ^{– –}. The first calculation gives qualitatively good results at all frequencies at each order of approximation, and quantitatively better results at higher orders of approximation; the second calculation, using the series which may not converge, gives bad results except at very high frequencies. Thus for the physically unnatural case of a field that vanishes on ^– and goes toe ^iv on ⁺ we have a series that is convergent, and uniformly so with respect to frequency, while for the natural case of a field that vanishes on ^– and goes toe ^iv on ^– we are limited to high frequencies. It is argued that a frequency-dependent renormalization of a series of the first type provides an approximation scheme that is convergent, and uniformly so with respect to frequency, for the physically important problems of the second type. The difficulties posed by the -dependent renormalization for the study of incident pulses are discussed.