An asymptotically flat ℋ space

The null geodesic equation is solved for the space of Sparling and Tod. Bondi coordinates are found and it is verified that the space construction is idempotent, i.e., the -space of this space is itself, symbolically ² = . Properties of the solution are used to motivate a definition of asymptotic flatness.S.R.C. Postdoctoral Research Fellow.     

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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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.     

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

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.     

Metastable states in the van der Waals-Maxwell theory

A slight modification of the recent Penrose and Lebowitz treatment of thermodynamic metastable states is presented. For the case of periodic boundary conditions, this modification allows the condition of metastability to be extended to all the metastable states in the van der Waals-Maxwell theory of the liquid-vapor phase transition, that is, for all states satisfyingf ₀()+1/2 ²>f(, 0+) andf₀()+x>0 wheref(, 0+) is the (stable) Helmholtz free energy density of the generalized van der Waals-Maxwell theory andf ₀() is the Helmholtz free energy density of a reference system with no long-range interaction, is a mean field-type term arising from a long-range Kac interaction, is the overall mean particle density, andx is any positive number. For the case of rigid-wall boundary conditions, a more restrictive condition is placed onx.     

К теории коэрцитивно й силы и кривой намагничивания

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Спектралъный метод о пределения изотопно го состава свинца. Частъ II

, . , [1]. 1–4 mg PbJ₂, . (c. m. c.) PbI 4058 Å. , , - , 5–7%. 3–4% –183 °C. , . 10% . , .     

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 slow passage through a steady bifurcation: Delay and memory effects

We consider the following problem as a model for the slow passage through a steady bifurcation: dy/dt = (t) y – y³ +, where is a slowly increasing function oft given by= _i + t ( ⁱ,<0). Both and are small parameters. This problem is motivated by laser experiments as well as theoretical studies of laser problems. In addition, this equation is a typical amplitude equation for imperfect steady bifurcations with cubic nonlinearities. When=0, we have found that=0 is not the point where the bifurcation transition is observed. This transition appears at a value = ^j > 0. We call ^j the delay of the bifurcation transition. We study this delay as a function of ⁱ, the initial position of, and, the imperfection parameter. To this end, we propose an asymptotic study of this equation as 0, small but fixed. Our main objective is to describe this delay in terms of the relative magnitude of and. Since time-dependent imperfections are always present in experiments, we analyze in the second part of the paper the effect of a small-amplitude but time-periodic imperfection given by (t) = cos(t).     

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

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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.     

Calculation of the dispersion of the third-order optical nonlinearity in C60 films

Using wave functions determined from ground-state local-density calculations, we have calculated the wave-dispersed free response of the optical nonlinear polarizability ⁽³⁾(–3;,,), for the C₆₀ molecule and ⁽³⁾(–3;,,) i.e. Third-Harmonic Generation (THG) for films using a sum-over-states approach. The influence of screening was determined by applying an external static electric field in separate selfconsistent calculations to evaluate induced dipole moments which was used to determine the static linear and nonlinear polarizabilities. The polarizabilities calculated in the static limit were used to determine an effective screening parameter which was, in turn, used together with an RPA approach to calculate screened wave-dispersed, third-order nonlinear optical properties such as ⁽³⁾(–3;,,) and ⁽³⁾(–3;,,). Comparing evaluated polarizabilities with experimental values we found that the non-resonant free polarizability compares well in absolute magnitude with experimental results. Inclusion of screening results in a polarizability about two orders of magnitude below the experimental values.Paper presented at the 129th WE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994     

Long range scattering for nonlinear Schrödinger equations in one space dimension

We consider the scattering problem for the nonlinear Schrödinger equation in 1+1 dimensions: where = /x,R{0},R,p>3. We show that modified wave operators for (*) exist on a dense set of a neighborhood of zero in the Lebesgue spaceL ²(R) or in the Sobolev spaceH ¹(R)., The modified wave operators are introduced in order to control the long range nonlinearity |u|² u.Laboratoire associé au Centre National de la Recherche Scientifique     

Operator product expansions on the vacuum in conformal quantum field theory in two spacetime dimensions

Let ₁(x) and ₂(y) be two local fields in a conformal quantum field theory (CQFT) in two dimensional spacetime. It is then shown that the vector-valued distribution ₁(x)₂(y)|0 is a boundary value of a vectorvalued holomorphic function which is defined on a large conformally invariant domain. By group theoretical arguments alone it is proved that ₁(x)₂(y)|0 can be expanded into conformal partial waves. These have all the properties of a global version of Wilson's operator product expansions when applied to the vacuum state |0. Finally, the corresponding calculations are carried out more explicitly in the Thirring model. Here, a complete set of local conformally covariant fields is found, which is closed under vacuum expansion of any two it its elements (a vacuum expansion is an operator product expansion applied to the vacuum).Work supported by Deutsche Forschungsgemeinschaft     

Computational study of propagating fronts in a Lattice-gas model

Velocities and other features of propagating fronts in the lattice-gas model analyzed by Bramsonet al. are computed by Monte Carlo simulation. The propagation velocity() is found to converge slowly to its asymptotic dependence on the exchange-rate parameter. The number density of occupied sites in the interaction zone (extending from the forwardmost occupied to the rearmost unoccupied site) appears to converge to 2/3 for large. Spatial profiles of site occupancy and interface number density for finite are compared to the profiles originally computed by Fisher using the differential equation obeyed in the large- limit. Several significant features inferred from the computations have not yet been explained analytically.     

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.     

Entropy andp-particle observables. I. The general program

An information-theoretic notion of entropy is proposed for a system ofN interacting particles which assesses an observer's limited knowledge of the state of the system, assuming that he or she can measure with arbitrary precision all one-particle observables and correlations involving some numberp of the particles but is completely ignorant of the form of any higher-order correlations involving more thanp particles. The idea is to define a generic measure of entropyS[ ] = –Tr log for an arbitrary density matrix or distribution function , and then, given the trueN-particle, to define a reduced _R ^P which reflects the observer's partial knowledge. The result, at any timet, is a chain of inequalitiesS[ _R ¹ ]S[ _R ² ]...S[ _R ^N ]S[], with true equalityS[ _R ^p ]=S[ _R ^p+1 ] if and only if the true factorizes exactly into a product of contributions involving all possiblep-particle groupings. It follows further than (1) if, at some initial timet ₀, the true factorizes in this way, thenS[ _R ^p (]S[ _R ^p (t ₀)] for all finite timest>t ₀, with equality if and only if the factorization is restored, and (2) the initial response of the system must be to increase itsp-particle entropy.     

Spin glasses with long-range interaction at high temperatures

We study the Ising andN-vector spin glasses with exchange couplings J=(J _ij ;i, jZ ^d ), which are independent random variables with EJ_ij=0 andEJ ⁿ _ij ⁿ n!¦i–j¦ ^–nd , forn, some finite constant >0, and >1/2. For sufficiently small, we show that forE-a.a.J there is a weakly unique, extremal, infinite-volume Gibbs measure _J for which the expectation of a single (component of) spin vanishes and which has the cluster property inL ₂(E) with the same decay as interaction. This work is based on results and methods of Fröhlich and Zegarlinski.     

One criterion of semigroup product convergence

Let exp(-tA) and exp(-tB) be C ₀ contraction semigroups on both K and , where K is a Hilbert space and is a reflexive Banach space such that the linear space K is dense both in K and . Let ^* be a dual pair of Banach spaces. In this paper we study some properties of infinitesimal operators of these semigroups. We show that under suitable assumptions there is some connection between the form-sum A+B and a closure of A ₁+B₁, where -A ₁ is an infinitesimal operator of C ₀ contraction semigroup exp(-tA ₁) which is the extension by continuity on of C ₀ contraction semigroup exp(-tA) Kin . In particular we give some criterion of an m-accretive closability A ₁+B ₁ which may be applied for example to the Schrödinger operators acting in suitable L ^p-spaces. Also this criterion together with properties of semigroups under consideration results in the establishment of the Lie-Trotter formulae.     

Quantum Hall Quantized Cyclotron Entrance Channels

Quantum Hall plateaus are entered via quantized cyclotron (QC) cloud-chamber orbits that have Landau-level (LL) energies and uniquely-defined angular momenta. The conservation of angular momentum in the quantum Hall system requires both canonical and magnetic angular momentum components, which add together to form the invariant kinematic angular momentum. The only LL radial eigenfunctions that satisfy the conservation-law requirements of the QC to LL transition are the u _n,l eigenstates u _n,2n+1, where n = 0, 1, 2, .... These same eigenstates uniquely have the correct scaled sizes to tile the observed families of = 1/(2n + 1) Hall plateaus. Quantum Hall plateau formation is a direct consequence of this tiling.