Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2

LetH _l be the Hamiltonian in aP()₂ theory with sharp space cutoff in the interval (–l/2,l/2). LetE _l =inf(H _l ), (l)=–E _l /l, and let _l be the vacuum forH _l . discuss properties of (l) and _l . In particular, asl, there are finite constants <0 and such that (l), ((l)–)l, and hence (l)=+/l+o(l ^–1). Moreover exp(–c ₁ l) _{l 1}exp(–c ₂ l) forc ₁,c ₂ positive constants, where _{l 1} is theL ¹(Q, d₀) norm of ₁ with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations ofH _l in the infinite volume limit.Research sponsored by AFOSR under Contract No. F44620-71-C-0108.On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.A. Sloan Foundation Fellow.     

Experimental survey of the sticking problem in muon catalyzed dt fusion

The sticking process dt + n, which constitutes the most severe limit to the number of fusions which a muon can catalyze, is reviewed. Many attempts were made to determine by calculations and measurements the probability for initial sticking _s ⁰ (immediately after dt fusion) and for final sticking _s (after the came to rest). Previous results based on neutron disappearance rates and on the observation of -X-rays were controversial and also in some disagreement with theory. New data are reported from PSI on direct observation of final sticking, using a setup with the St. Petersburg ionization chamber. These data mark a significant improvement in reliability and may clarify questions concerning previous discrepancies. The new results is _s(0.56±0.04)%, lower than the theory prediction _s=(0.65±0.03)%, at medium density.     

The change in primary extinction during decomposition of a super saturated solid solution 1. System Al-Ag

On the basis of the correlation of diffraction data (intensity and width) of a precipitate with the intensity of reflection of a matrix solid solution it is shown that the change in primary extinction during the decomposition of a solid solution of Agin Alis caused by the precipitation of the phase Ag₂Aland not by the production of lattice defects (zones, stacking faults).

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I. Al-Ag

( ) , Ag Al Ag₂Al, ( , ).

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Reported in part at the VIth Scientific Technical Conference on the Application of X-rays held in Leningrad in 1958.

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The author thanks M. Mikovský for preparing the single crystals of the alloy Al-Ag having a high primary extinction and J. Laek and Prof. J. Bedná for carefully checking their homogeneity and chemical composition.     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

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A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

An attempt at a phenomenological interpretation of the influence of a polarizing field on piezoelectric resonators

The change in frequency of quartz piezoelectric resonators in a d-c electric polarizing field cannot be explained merely by a change in the dimensions of the resonator due to the polarizing field caused by the inverse piezoelectric effect and electrostriction. We are forced to admit that the elastic constants also change in a polarizing field. A phenomenological interpretation of the influence of a d-c electric polarizing field on the frequency of quartz resonators is proposed here, based on newly introduced quantities characterizing such a change. In conclusion it is shown in what way the quantities, on which the phenomenological theory is based, can be determined experimentally.

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, . , . , , . , , .

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The author would like to thank Dr. J. Tichý for carefully reading the paper, for valuable discussion and numerous remarks on style and subject matter, which greatly helped to improve the text. He is also indebted to V. Janovec, C. Sc., for some new aspects and the exceptional interest with which he reviewed the paper.     

The effect of microsegregation on the generation of dislocations in zinc single crystals

The applicability of Tiller's considerations on the production of dislocations is proved. The density of dislocations appearing during impurity microsegregation increases with increasing rate of growth as a consequence of the corresponding change in the effective distribution coefficient. The real value of C at the microsegregation boundaries is at least twice as great as the average value of the concentration of impurities in the crystal in question.

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. , , . C , .

     

Металлографические методы определепия нлотности дислокаци й В монокристаллах германия

, , . , .1) . .     

Role of Activator and Vacancy Centers in the Decay of the Gamma Scintillators of CsI–Na Crystals

The influence of the concentration of an activator (C _NaI) and of plastic deformation on a change in the contribution of a slow component to the decay of the -scintillations of CsI–Na crystals was investigated, as well as the influence of C _NaI on a change in the shape of the luminescence excitation spectrum in the region of absorption of activator centers (AC) and of vacancy-related centers (VRC) and also on a change in the intercenter time of deexcitation of the centers indicated. It is shown that AC and VRC participate in the photoluminescence and -scintillations of CsI–Na crystals. In the -scintillations, AC are responsible for the component ₁ = 370 nsec, whereas the components ₁ = 460 nsec and ₂ 2 sec are associated with VRC. The reduction of ₁ from 770 to 560 nsec with an increase in C _NaI from 2·10^–3 to 3·10^–2 mole% and from 570 to 470 nsec after plastic deformation of the crystals ( = 5%) along the 111 axis is caused by a decrease in the number of VRC. The mechanisms underlying the -scintillations of the CaI–Na crystals containing AC and VRC and also the decrease in the number of VRC are discussed.     

Mikrophy'sikalische Vorgänge,die die Entstehung der Schnellen Schichtungswellen in der Neonglimmentladung bedingen

Zusammenfassung Im nachstehenden Artikel werden mikrophysikalische Vorgänge behandelt, die das Auftreten schneller Schichtungswellen in Neonglimmentladungen veranlassen können. Es werden sowohl die qualitativen Abhängigkeiten, als auch die ziffernmäigen Werte der Parameter der Schichtungswellen mit den charakteristischen Gröenwerten der in diesem Entladungstypus vor sich gehenden Vorgänge verglichen. Auf Grund der vorgenommenen Vergleiche kann gesagt werden, da die Relaxationszeiten der schnellen Wellen durch die Diffusionslebensdauer der atomaren, bzw. molekularen Ionen gegeben sind.

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,

, . , . , , .

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Zum Schlu danken wir F. Kroupa und V. Krejí für die aufmerksame Lesung der Arbeit und wertvolle Hinweise.     

The inelastic reactions πp→λ(⌆) K with allowance for the contribution of branch cuts

The method of complex angular moments is used to analyze the experimental data on the inelastic reactions p ()K, taking into account branch cuts in the j-plane in the eikonal approximation. An optical model for the backward scattering is considered. Agreement with experiment is obtained in the region of small angles for the reactions (⁰)K⁰. In the case of ^–P K⁰(^–K⁺) processes, agreement is obtained with the experimental results for large (180) scattering angles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–30, August, 1972.     

Electronic processes andZ centres in NaCl and KC1 crystals

The paper gives the experimental results of the team-work study of coloured pure and Ca doped NaCl and KC1 crystals. The mechanism of the formation ofR centres by coagulation ofF centres and of the formation ofZ centres fromF centres, cation vacancies and Ca ions is discussed. An alternative model forZ ₃ centres is proposed. The possible connections between physical and chemical behaviour are indicated.

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Z- NaCl 1

NaCl KCl . R- F- Z- F-, Ca. Z ₃-. .

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This work was presented by the courtesy of Prof. R. Maurer at the Symposium on Color Centers, Corvallis, Oregon (1959).

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The authors wish to express their gratitude to K. Suk, K. Listoová and M. Javrková for carefully carrying out the measurements and I. Kunzlová and L. Nováková for preparing the crystals.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

К теории коэрцитивно й силы и кривой намагничивания

. , , . .     

ЗАВИСИМОСТЬ ПОЧЕРНЕ НИЯ ФОТОГРАФИЧЕСКОЙ ЭМУЛЬСИИ ОТ ЭНЕРГИИβ-ИЗЛУЧЕНИЯ

, - - . , - , , :³²P,³⁵S ⁹⁰Sr+⁹⁰Y.     

Основные соотношени я длн построения механических селект оров нейтронов

, . , , . . , , .     

ЛОКАЛЬНЫЕ КОЛЕБАНлЯ ДВУХАТОМНОЙ ЛлНЕЙНО Й ЦЕПОЧКл С ДЕФЕКТАМл

. n : , . npou u , n . n n npocm .     

Some problems of quantum mechanics possessing a non-negative phase-space distribution function

In order to clarify physical consequences due to the presence of a set of auxiliary functions _k (q,t) in quantum mechanics with a non-negative phase-space distribution function, the simplest quantum-mechanical problems are solved. It is shown that _k (q,t) influence upon the results of a problem. Therefore it is supposed that _k (q, t) reflect some physical reality (subquantum situation), interacting with a mechanical system. In particular the subquantum situation determines the minimum coordinate and momentum uncertainties ((q)² and (p)²) as well as the coordinate distribution of a fixed system and the momentum distribution of a free system. These results provide the opportunity to formulate the notion of a stationary homogeneous isotropic subquantum situation. Supposing thatq andp are small an attempt is made to develop an approximate method of solutions (quasi-orthodox approximation). Energy spectrum of an electron in a hydrogen atom is found in the second order of this approximation.On leave of absence from Peoples' Friendship University, Chair of Theoretical Physics, 3, Ordjonikidze Street, B-302, Moscow, U.S.S.R.     

К процессам в электро дных оБластях в силъноточных кратк овременных электрических разря дах

.

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On processes in electrode spaces of short-time high-intensity electric discharges

The conditions and causes of the interrupted emission of the vapours of the material of short-time high-intensity electric discharge electrodes are discussed on the basis of earlier and new observations.

     

К ТЕОРИИ СПОНТАННОЙ Н АМАГНИЧЕННОСТИ ТОНКИХ СЛОЕВ. II. ЧАСТЬ)

- , . - . - - . , . 1956 .