Phase uniqueness and correlation length in diluted-field Ising models

The diluted-field Ising model, a random nonnegative field ferromagnetic model, is shown to have a unique Gibbs measure with probability I when the field mean is positive. Our methods involve comparisons with ordinary uniform field Ising models. They yield as a corollary a way of obtaining spontaneous magnetization through the application of a vanishing random magnetic field. The correlation lengths of this model defined as (lim _n-(1/n) log ₀; _n)^-1, wheren is the site on the first coordinate axis at distancen from the origin and ₀; _n is the origin ton two-point truncated correlation function, is non-random. We derive an upper bound for it in terms of the correlation length of an ordinary nonrandom model with uniform field related to the field distribution of the diluted model.     

Correlation tensors of the blackbody radiation in rectangular cavities

Electromagnetic equilibrium fluctuations in finite cavities filled with a dissipative medium (dielectric function ()=+i) and bounded by walls of infinite conductivity are considered. Expanding the fields in terms of a complete and orthonormal set of functions and solving the Maxwell equations the response of the EM field to external forces (polarization and magnetization) is obtained. With the aid of the fluctuation dissipation theorem and the linear response functions the 2nd order correlation tensors of the EM field are derived.For rectangular cavities explicit considerations are made. In the case of transparent media (=0) the spectral energy density of the EM radiation is calculated.     

Batalin-Vilkovisky algebras and two-dimensional topological field theories

By a Batalin-Vilkovisky algebra, we mean a graded commutative algebraA, together with an operator :A A ₊₁ such that ² = 0, and [,a]–a is a graded derivation ofA for allaA. In this article, we show that there is a natural structure of a Batalin-Vilkovisky algebra on the cohomology of a topological conformal field theory in two dimensions. We make use of a technique from algebraic topology: the theory of operads.The author is partially supported by a fellowship of the Sloan Foundation and a research grant of the NSF     

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.

---

Z- NaCl 1

NaCl KCl . R- F- Z- F-, Ca. Z ₃-. .

---

---

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

---

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.     

Inequalities for the Schattenp-norm. III

We present some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA is an operator such that ReAa0, then for any operatorX, AX+XA* _p 2aX _p . Also, for any two operatorsA andB, A–B ₂ ² +A*B* ₂ ² 2A–B ₂ ² .     

Electromagnetic Modes in Schwarzschild Geometry in an Annular Region

The fundamental electromagnetic modes in a spherical annular cavity with perfectly conducting walls at r = a and r = b are calculated, in the presence of a weak Schwarzschild gravitational field. Explicit expressions are given for the case of a thin shell, (b - a)/a 1. The modified angular frequency for mode ,m can be written as = = ₀ \{ 1 - (GM/a)[2 - ( + 1)/(₀ a)²] where ₀ is the nongravitational frequency. This formula (being independent of m) holds for the magnetic as well as for the electric modes.     

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     

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.

---

, . , . , , . , , .

---

---

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.     

Gas‐Kinetic Temperature of Planar High‐Frequency Capacitive Discharge Plasma in N2/CO2/He Gas Mixtures

Using methods of emission spectroscopy, we have determined the gaskinetic temperature fields of planar highfrequency capacitive discharge plasma in N₂/CO₂/He gas mixtures depending on the excitation frequency, discharge current, pressure, and chemical composition of the mixture. It is shown that the dominant contribution to the neutral component heating in the center of the discharge chamber is made by the processes of V–T relaxation of vibrationally excited molecules N₂(X ¹, V) and CO₂(X ¹, V), whereas in the zones near the electrodes an important role in the heating is played, along with the V–T relaxation of the N₂(X ¹, V) and CO₂(X ¹, V) molecules, by the processes of deactivation of the metastable states A ³ of the N₂ molecule.     

The ground state energy of Sdhrödinger operators

We studye()=inf spec(-+V) and examine whene()<0 for all 0. We prove thatc ²e()–d ² for suitableV and all small ||.Research partially funded under NSF grant number DMS-9101716.     

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.     

Universal expansion of the powers of a derivation

We give the expansion of the powers of the Lie operator = ⁱ _i in any dimension, where is either a smooth function or a formal power series over an infinite set of commutatives indeterminates. We describe an algorithm for computer treatment and we give, as an example, a table for the orders 1 to 6.     

Phase transformations in Cu-Sn alloys containing Ni,Al, Ge,and In

After quenching from 700C and aging, Cu-Sn alloys containing Ni and Al were found to have a precipitation of-solid solution, with a DO₃ type of ordering, of metastable ,, and phases. It was established that the phase has an 4 type of ordering while the phase has the Cu₃Ti type. Observations revealed that Cu-Sn-Al alloys contained two phases, and, with an identical structure but with different ratios of electron concentration per atom.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 34–37, April, 1981.     

Diffusion in a one-dimensional gas of hard point particles

We simulate the classical diffusion of a particle of massM in an infinite one-dimensional system of hard point particles of massm in equilibrium. Each computer run corresponds to about 10⁸ collisions of the diffusive particle. We find that (t) 1/t fort large enough, and a crossover from an M m regime where=2 to=3 forM=m. The diffusion constant has a sharp maximum atM=m. We study moments x(t)² and x(t)⁴, and examine the behavior ofq ² (t)=x(t)⁴/3x(t)²². We find thatq(t)1 (consistent with a normal distribution) in theM limit (for all timest) and in the t limit for allM. On sabbatical leave from IVIC-Instituto Venezolano de Investigaciones Cientificas.     

The scattering of waves by a periodic surface

The paper derives a general formula for the scattering of electromagnetic (or sound) waves from a periodic, perfectly conducting (or perfectly rigid) surface. No restrictions are imposed on the angle of incidence, the size of the surface or the degree of roughness. Except for the basic Kirchhoff approximation, the method is exact. The results confirm, generalise or correct special cases obtained by more complicated methods.

---

, ( ) . , . . , , .

     

Steady flux in a continuous-space Sinai chain

We examine the steady-state flux of particles diffusing in a one-dimensional finite chain with Sinai-type disorder, i.e., the system in which in addition to the thermal noise, particles are subject to a stationary random-correlated in space Gaussian force. For this model we calculate the disorder average (over configurations of the random force) flux exactly for arbitrary values of system's parameters, such as chain lengthN, strength of the force, and temperature. We prove that within the limitN1 the average flux decreases withN as J(N)=C/N and thus confirm our recent predictions that the flux in the discrete-space Sinai model is anomalous.     

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.     

Maximal violation of Bell's inequalities is generic in quantum field theory

Under weak technical assumptions on a net of local von Neumann algebras {A(O)} in a Hilbert space , which are fulfilled by any net associated to a quantum field satisfying the standard axioms, it is shown that for every vector state in there exist observables localized in complementary wedge-shaped regions in Minkowski space-time that maximally violate Bell's inequalities in the state . If, in addition, the algebras corresponding to wedge-shaped regions are injective (which is known to be true in many examples), then the maximal violation occurs in any state on () given by a density matrix.     

A contribution to direct processes in the Co59(p,n) reaction forE p ∼ 6·5 MeV

Nuclear emulsions were used to study the energy spectrum and forward-backward asymmetry of neutrons from the Co⁵⁹(p,n) reaction forE _p 6·5 MeV. It was found that the decay of the compound nucleus makes a maximum contribution of 50% to the reaction yield. Energies of some excited states of the Ni⁵⁹ nucleus were also determined.

---

Co⁵⁹(p,n) E _p 6,5 MeV

- Co⁵⁹(p,n) E _p 6,5 MeV. , 50%. , Ni⁵⁹.

---

---

The authors would like to thank all those who helped in this work, particularly all members of the cyclotron group of the Nuclear Research Institute of the Czechoslovak Academy of Sciences, who so willingly helped with the irradiation, and H. Koutová from the Faculty of Technical and Nuclear Physics, who carefully measured the emulsions. Our thanks are also due to R. Krejová from the Faculty of Technical and Nuclear Physics for developing the emulsions and J. Kopecký from the Nuclear Research Institute for providing the cobalt target.     

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