An interpretation of the conditions for the existence of Shockley surface states

A study is made of the Shockley surface states in a linear chain of equal atoms, joined by alternately strong bonds. If the simple MO LCAO method is used, which considers the exchange integrals between nearest neighbours and next nearest neighbours, we get the surface states for a semi-infinite chain if the stronger bond is interrupted. The connection between Shockley and Tamm surface states is shown and the hypothesis is put forward that the condition for the existence of Shockley surface states has a generally simple physical interpretation, the validity of which is proved on the models of a semi-infinite crystal studied up to now.

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, . MO LCAO, , , . , , , .

     

Some examples ofq-regularization

An introduction to Hopf algebras as a tool for the regularization of relevant quantities in quantum field theory is given. We deform algebraic spaces by introducingq as a regulator of a noncommutative and noncocommutative Hopf algebra. Relevant quantities are finite providedq 1 and diverge in the limitq 1. We discussq-regularization on differentq-deformed spaces for ⁴ theory as examples to illustrate the idea.     

Current distributions in a two-dimensional random-resistor network

The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&^k, is found to scale with the linear sizeL as (InL)^(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)–, yielding information on the threshold below which the multifractality of (i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.     

Thermostimulierte Exoemission und Lumineszenz von MgO und CaO

Ohne Zusammenfassung

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MgO CaO

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Ich danke bestens Frau K. Listoová für die sorgfältige Durchführung der Versuchsreihen und Ing. S. urovi und Dr. A. Bergstein für das liebenswürdige Überlassen der Präparate.     

Dynamical Behavior of the Multibondic and Multicanonic Algorithm In The 3D q-State Potts Model

We investigate the dynamical behavior of the recently proposed multibondic cluster Monte Carlo algorithm in applications to the three-dimensional q-state Potts models with q= 3, 4, and 5 in the vicinity of their first-order phase transition points. For comparison we also report simulations with the standard multicanonical algorithm. Similar to the findings in two dimensions, we show that for the multibondic cluster algorithm the dependence of the autocorrelation time on the system size Vis well described by the power law V , and that the dynamical exponent is consistent with the optimal random walk estimate = 1. For the multicanonical simulations we obtain, as expected, a larger value of 1.2.     

The van der Waals limit for classical systems. I. A variational principle

We consider the thermodynamic pressurep(, ) of a classical system of particles with the two-body interaction potentialq(r)+ ^v K(r), where is the number of space dimensions, is a positive parameter, and is the chemical potential. The temperature is not shown in the notation. We prove rigorously, for hard-core potentialsq(r) and for a very general class of functionsK(s), that the limit 0 of the pressurep(, ) exists and is given by where the limit and the supremum can be interchanged. Here is a certain class of nonnegative, Riemann integrable functions,D is a cube of volume |D|, anda ⁰() is the free energy density of a system withK=0 and density . A similar result is proved for the free energy.     

Intersubjectivity,relativistic covariance,and conditionals: response to C. I. J. M. Stuart

A misunderstanding persists between Stuart and me, which I do my best to clarify. Bayesian inverse subjectivities versus relativistic covariance and physical intersubjectivity are discussed. A joint number of chances formalism taking care of the propagation of the probability of causes is proposed.     

Solution of coupled differential equations of soliton theory

We present the complete set of solutions of the coupled differential equations of the form ()²=(), ² =(). Equations of this form appear in several physical situations.     

Radiation losses in completely ionized plasma

The losses caused by bremsstahlung during electron-ion and electron-electron collisions in a completely ionized plasma (in Born's approximation) are calculated. The calculation can be carried out analytically for a sufficiently dilute plasma (plasma with infinitely large Debay-Hückel radius). This assumption is satisfied very well by the known classification to actual controlled thermonuclear reaction. A dependence of the formI=an ². (1+3/2), wherea=0·73×10^–16 MeV.cm³.sec^–1,n is the number of ions per cm³ and =kT/mc ², is determined for the amount of energy radiated from 1 cm³ of plasma per sec. In the relativistic temperature regionkTmc ² the influence of electron-electron collisions begins to predominate. A number of important results concerning radiation losses in relativistic plasma will be published in a later paper.

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, ( ). ( -). . , I=an ². (1+3/2), =0,73. 10^–16 MeVcm²s^–1,n — =kT/mc ². kTmc ² . , .

     

The inverse backscattering problem in three dimensions

This article is a study of the mapping from a potentialq(x) onR ³ to the backscattering amplitude associated with the Hamiltonian –+q(x). The backscattering amplitude is the restriction of the scattering amplitudea(, , k), (, , k)S ²×S ²×₊, toa(,–, k). We show that in suitable (complex) Banach spaces the map fromq(x) toa(x/|x|, –x/|x|, |x|) is usually a local diffeomorphism. Hence in contrast to the overdetermined problem of recoveringq from the full scattering amplitude the inverse backscattering problem is well posed.     

Measurement of the reaction γp → K0Σat photon energies up to 2.6 GeV⋆

The reaction p K⁰⁺ was measured in the photon energy range from threshold up to 2.6 GeV with the SAPHIR detector at the electron stretcher facility, ELSA, in Bonn. Results are presented on the reaction cross-section and the polarization of the ⁺ as a function of the kaon production angle in the centre-of-mass system, cos^c.m._K, and the photon energy. The cross-section is lower and varies less with photon energy and kaon production angle than that of p K⁺⁰. The ⁺ is polarized predominantly at cos^c.m._K 0. The data presented here are more precise than previous ones obtained with SAPHIR and extend the photon energy range to higher values. They are compared to isobar model calculations.     

Random walks on lattices with a random distribution of perfect traps

We made an accurate numerical determination of the average number of steps until trapping n of a particle performing a random walk on a square resp. cubic lattice containing traps. We assume a random distribution of perfect trap centers with densityq. Within a large range ofq-values we observe aq-dependence of the form n=–q ^– lnq with 0.817, resp. 0.689. The expression coincides with expansion results aroundq=1 and is compatible with expansion results aroundq=0.     

Hard gamma radiation in the decay of Lu176m

Gamma lines 1·05 MeV(4 × 10^–6 quanta/decay) and 1·14 MeV (9 × 10^–6 quanta/decay), giving evidence of the existence of a new level in Hf¹⁷⁶ with an energy of 1·14 MeV, were found in the decay of Lu^176m with a half-life of 3·7 hours, using the scintillation method. The component of the beta spectrum, exciting this level, has a maximum energy of 0·17 MeV and logft=8·3. The spin of this level proved to be equal to one. The level was interpreted as a single-particle neutron level withn ₀: 5/2^– (512),n ₁: 7/2^– (514);I=1⁺.

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- Lu^176m

Lu^176m 3,7 - 1,05 MeV (4.10^–6 /) 1,14 MeV (9.10^–6 / /), Hf¹⁷⁶ 1,14 MeV. -, , 0,17 MeV logft = =8,3. . cn ₀: 5/2^– (512),n ₁: 7/2^– (514);I = 1⁺h

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The authors thank L. K. Peker from the Leningrad State University for a helpful discussion of their results.     

Symmetries and half-sided modular inclusions of von Neumann algebras

LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , _N , _N the modular operators to (, ), (N, ), resp (N , ). Assume now ^-it N ^it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups ^it , _N ^ir , _N ^is ,t, r, s generate a unitary representation of the group S1(2, )/Z ₂ of positive energy.Another result is related to two half-sided modular inclusions (₁ , ) and (₂ , ). Under proper conditions the three modular groups ^it , ₁ ^ir , ₂ ^is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

A borel-weil-bott approach to representations of sl q (2, ℂ)

We use a quite concrete and simple realization of sl _q (2, ) involving finite difference operators. We interpret them as derivations (in the noncommutative sense) on a suitable graded algebra, which gives rise to the noncommutative scheme ¹ II ^1* as the counterpart of the standard ¹ = Sl(2, )/B.     

The probability distribution of the velocities of gas molecules after collision with a rapidly moving rigid body

The above problem is met, for example, in the case of the collision of molecules of the atmosphere with an artificial earth satellite and leads to the problem of determining the probability distribution of the absolute value of the vector sum of a constant vector and a Maxwell vector (the latter being a vector, whose rectangular components are distributed normally, with the same standard deviation and mean value zero). The resultant probability density is given by equation (18), the complement to the distribution function by (24), the mean value by (27) and the variance by (31). These results are obtained by transforming the corresponding three-dimensional normal distribution to spherical co-ordinates and integrating over the co-ordinate angles and , which yields the required probability density; the other results are then obtained from it by the usual methods.

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, , (. . , ). (18), -(24), -(27) (31). , ; .

     

Mean-Field Critical Behavior for the Contact Process

The contact process is a model of spread of an infectious disease. Combining with the result of ref. 1, we prove that the critical exponents take on the mean-field values for sufficiently high dimensional nearest-neighbor models and for sufficiently spread-out models with d>4:()– _c as _c and ()( _c–)^–1 as _c, where () and () are the spread probability and the susceptibility of the infection respectively, and _c is the critical infection rate. Our results imply that the upper critical dimension for the contact process is at most 4.     

Long-range correlations at depinning transitions

Semi-infinite systems are considered with long-range surface fields B _z ^–(1+r) for large distancesz from the surface. The influence of such fields on the global phase diagram and on the critical singularities of depinning transitions is studied within Landau theory. For |B|0, the correlation length diverges as b ^–1/2 withb=|Bln|B^–(1+r). For finiteB, t ^v withv =(2+r)/(2+2r) wheret measures the distance from bulk coexistence. In the latter case, a Ginzburg criterion leads to the upper critical dimensiond ^*=(2+3r)/(2+r).     

Noncommutative Ricci Curvature and Dirac Operator on C q [SL2] at Roots of Unity

We find a unique torsion free Riemannian spin connection for the natural Killing metric on the quantum group C _q [ SL₂], using a recent frame bundle formulation. We find that its covariant Ricci curvature is essentially proportional to the metric (i.e. an Einstein space). We compute the Dirac operator and find for q an odd rth root of unity that its eigenvalues are given by q-integers [m] _q for m=0,1...,r–1 offset by the constant background curvature. We fully solve the Dirac equation for r=3.     

Fundamental concepts of the theory of dislocations

The fundamental concepts of the theory of dislocations are given in an exact way and some theorems are proved.

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In conclusion the author would like to thank Professor M. Valouch and Professor L. Zachoval for the interest they took in this work and for remarks and advice which helped to improve it.