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.     

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     

Orbiting test masses for an equivalence principle space experiment

Deviations from the equivalence principle can be found by observations of the orbital periods of masses in a two body system, in a drag free satellite in geosynchronous orbit. At this altitude the Earth gravitational field tides allow close stable circular motion, within a 30 cm lobe, of a small test mass around the centre of the primary mass, of 75 kg. The repulsive fifth force ought to slow the orbital Newtonian period. A precise clock and laser interferometry provide the determination of in the range between 1 and 10²cm and of if larger than 10^–4.2 or 10^–5, for an uncertainty of the value of the constant of gravitation equal to 10^–5 or 10^–6, respectively ( and are the coupling coefficient to gravity and range of action of the fifth force). In the latter case, for around 10 cm, the fifth force may be detected for larger than 10^–5.5. This experiment may verify the principle of equivalence at short range improving the actual limits from one to two and a half orders of magnitude. The range of action,, up to several meters can be observed with this local experimental concept, but only for large values of, which have been excluded recently by ground experiments.     

The room-temperature decomposition of metastable phases precipitated in the Al-Zn alloys at 200 °C

The room-temperature decomposition of metastable phases in the Al-Zn alloys (from 25 to 50 wt. % Zn) was studied by the transmission electron microscopy and X-ray diffraction. Metastable phases, i.e. G.-P. zones, _R-and -phases, were grown at 200 °C and their decomposition into equilibrium -phase at 20 °C was investigated. Ageing times comprised 1 to 999 days.Both the decomposition mechanism and the rate of decomposition of coherent phases were found to be dependent on the particle sizes and their density reached at 200 °C. The local vacancy supersaturation around the -nucleus in a dense system of G.-P. zones leads to an enhanced growth rate of such nucleus and thus to the formation of one large -precipitate at the expense of several neighbouring G.-P. zones. The elastic stress field around this -particle promotes the further nucleation and growth of -precipitates and leads to their gradual spread throughout the matrix. The decomposition of intermediately sized _Rprecipitates results in the development of -precipitates of comparable sizes nucleated on the array of misfit dislocations at the periphery of _R-precipitates. The cooperative effect between neighbouring particles does not influence the decomposition of large _R-precipitated which split then into several smaller -particles. The rate of G.-P. zones or _R to -decomposition increases with the increasing sizes of transition precipitates and with the zinc content of the alloy. The kinetics of to -decomposition was found to be independent both on the annealing time at 200 °C and on the investigated alloy composition. This can be attributed to the constant density of misfit dislocations as nucleation sites for -precipitates along the -matrix interface and to the large mutual separation of -precipitates in all these alloys.In conclusion we would like to express our thanks to Doc. Dr. V.Syneek, CSc. for his valuable discussions and to Ing. V.íma for the preparation of Al-Zn alloys. Our thanks are also due to Mr. Z.iký for his help in the X-ray diffraction measurement and to P.Vyhlídka for the careful chemical analyses of the investigated alloys.     

Bounded perturbations of dynamics

If and are one-parameter automorphism groups of a von Neumann algebraM is said to be a bounded perturbation of if _t – _t 0 ast0. We give a complete characterization of the bounded perturbations of . In particular, we show that if can be implemented by a strongly continuous one-parameter group with self-adjoint generator (Hamiltonian)H, then can be implemented in the same way and the corresponding HamiltonianH can be chosen to be of the formH=VHV ^–1+h, whereV is a unitary ofM andh=h*M.On leave of absence from II. Institut für Theoretische Physik, Universität Hamburg, D-2000 Hamburg 50, Federal Republic of Germany     

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.     

Slowing down of retrieval in the hopfield model

The variation of the convergence time, as a function of the storage capacity is studied numerically for systems ranging in size fromN=1000 toN=16,000 neurons. is found to increase likeexp[–A(_c–)] as one nears the critical storage capacity _c =0.142=0.002.     

Boson fields under a general class of local relativistic invariant interactions

We consider a boson field (x) under an interaction of the form V((x))dx, whereV() is a bounded continuous real function of a real variable . IfV() has a uniformly continuous and bounded first derivative, we prove that the Heisenberg picture field exists as weak limits of the Heisenberg picture fields corresponding to the cut-off interaction.     

Some exact solutions to the sine-Gordon equations

We present some new exact (solitary and traveling) solutions to the sine-Gordon equationsc ²u_xx–u_tt = sinu andcu _xt+ u_tt = sinu, and the dissipative sine-Gordon equationc ²u_xx–u_tt–u_t=₁ sinu+ ₂ sin(2u). Here,, ₁, and ₂ are the coupling constants, real numbers;c is theintrinsic speed of the propagating wave determined by the system; and is the damping factor. The physical implication is briefly discussed.     

Radiative and nonradiative transitions to an unstable state

In this paper an expression is obtained, which enables us to treat radiative and nonradiative transitions in complex molecular systems, when the final state is unstable. Expressions are give for the matrix elements E/v and E|d/dR|v , where the stable state is described by a solution with a Morse potential, and the unstable state by a solution with a Hulthen potential. The possibility of the concrete realization of such transitions is discussed in the example of excimers.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 10, pp. 70–75, October, 1974.     

Energy level crossings in quantum mechanics

From the eigenvalue equationH \ _n () =E _n ()\ _n () withH H ₀ +V one can derive an autonomous system of first order differential equations for the eigenvaluesE _n () and the matrix elementsV _mn () where is the independent variable. To solve the dynamical system we need the initial valuesE _n ( = 0) and \ _n ( = 0). Thus one finds the motion of the energy levelsE _n (). We discuss the question of energy level crossing. Furthermore we describe the connection with the stationary state perturbation theory. The dependence of the survival probability as well as some thermodynamic quantities on is derived. This means we calculate the differential equations which these quantities obey. Finally we derive the equations of motion for the extended caseH =H ₀ +V ₁ + ² V ₂ and give an application to a supersymmetric Hamiltonian.     

Microstructure of fiber-like SiC/Si3N4 composite particulate

The microstructure of fiber-like SiC/Si₃N₄ composite particulate was investigated using high-resolution transmission electron microscopy techniques. The SiC/Si₃N₄ composite particulate consisted of a-SiC core and a -Si₃N₄ outer shell. Two kinds of composite particulate were distinguished when the observed orientation of the SiC core was <110>. In one type of the SiC/Si₃N₄ composite particulate, a crystal relationship of (111)-SiC | (102) -Si₃N₄ and (111)-SiC (114) -Si₃N₄ was identified; in the other type of the SiC/Si₃N₄ composite particulate, a crystal relationship of (111)-SiC (001) -Si₃N₄, and (111)-SiC (101) -Si₃N₄ was observed.     

Upper bounds onT c for one-dimensional Ising systems

We present upper bounds on the critical temperature of one-dimensional Ising models with long-range,l/n interactions, where 1<2. In particular for the often studied case of =2 we have an upper bound onT _c which is less than theT _c found by a number of approximation techniques. Also for the case where is small, such as =1.1, we obtain rigorous bounds which are extremely close, within 1.0%, to those found by approximation methods.     

What determinates the chemical changes of the internal conversion coefficients for inner atomic shells?

Calculations of internal conversion coefficients (ICC) of the E1–E4 and M1–M4 transitions for nuclei in ions show that the relative changes _i / _i of the ICC _i for deep inner subshells can differ significantly from the relative changes _i/_i of the electron densities _i at the nucleus. For the K conversion _i/ _i are many times greater than _i/_i. Especially large deviations of _i/ _i are characteristic of transitions of high multipolarity; however, for the M1 transitions they can also be significant. Illustrations of various dependencies of _i/ _iare presented for the conversion in the regionZ-50.     

Higher Conformal Multifractality

We derive, from conformal invariance and quantum gravity, the multifractal spectrum f() of the harmonic measure (i.e., electrostatic potential, or diffusion field) near any conformally invariant fractal in two dimensions. It gives the Hausdorff dimension of the set of points where the potential varies with distance r to the fractal frontier as r . First examples are a random walk, i.e., a Brownian motion, a self-avoiding walk, or a critical percolation cluster. The generalized dimensions D(n) as well as the multifractal functions f() are derived, and are all identical for these three cases. The external frontiers of a Brownian motion and of a percolation cluster are thus identical to a self-avoiding walk in the scaling limit. The multifractal (MF) function f(,c) of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a Q-state Potts cluster, is given as a function of the central charge c of the associated conformal field theory. The dimensions D _EP of the external perimeter and D _H of the hull of a critical scaling curve or cluster obey the superuniversal duality equation . Finally, for a conformally invariant scaling curve which is simple, i.e., without double points, we derive higher multifractal functions, like the universal function f ₂(,) which gives the Hausdorff dimension of the points where the potential varies jointly with distance r as r on one side of the curve, and as r on the other. The general case of the potential distribution between the branches of a star made of an arbitrary number of scaling paths is also treated. The results apply to critical O(N) loops, Potts clusters, and to the SLE process. We present a duality between external perimeters of Potts clusters and O(N) loops at their critical point, as well as the corresponding duality in the SLE process for =16.     

InGaAs/GaAs multiple-quantum-well modulators and switches

The design, fabrication and characterization of electrooptical modulators and switches based on pseudomorphic InGaAs/GaAs multiple-quantum-well (MQW) structures is presented. The absorption and refractive index changes (, n) of In_0.2Ga_0.8As/GaAs MQW structures due to the quantum-confined Stark effect are examined in detail. The figures of merit /₀ and n/₀ give information on the design of modulation and switching devices. Based on these results, we develop two types of efficient and high-speed modulators, vertical and waveguide modulators, and for the first time an InGaAs/GaAs intersectional X-type switch. Recent experimental results for each device are presented.     

On P-representation for parametric amplifier and parametric frequency converter

The statistical properties of a parametric amplifier and a frequency converter are studied by means of quantum mechanical methods. The Schrödinger picture and the P-representation of the density matrix are used. Carrying out the Fourier transformation of the Liouville equation a partial differential equation for a generating function is obtained. The inverse Fourier transform of a solution of this equation is a time-dependent P-representationPN( ₁, ₂,t). For the parametric amplifier a relation is derived which enables us to compute the functionPA( ₁, ₂,t) = =1< ₁, ₂/ ₁> is shown thatPA is classical distribution ifPN( ₁, ₂,0) is a positive distribution, while the P-representationPN( ₁, ₂,t) need not exist as a distribution and the P-representationPN( ₁, ₂,t) for the parametric frequency converter is constant along classical trajectories.The author wishes to thank Dr. J. Peina for stimulating discussions.     

Interacting spinor and scalar fields: Exact self-consistent solutions in Bianci I space

Exact self-consistent solutions of the equations that describe a system of interacting spinor and massless scalar fields with the interaction Lagrangian L_int=_,^,(S), where (S) is an arbitrary function of the invariant S=, are obtained in Bianci I space. The possibility of excluding the initial singularity is studied for the case of a power-law function (S), and isotropic expansion of the space as t is established.Russian University of International Amity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 53–58, July, 1995.     

The puzzle ofKα bound state

Kaonic atom experiments suggest existence of a narrow nuclear¯K bound state and indicate blocking of¯K absorption. This blocking is explained in terms of ₀ resonance and interactions with the nuclear density gradient.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

Singular continuous spectrum on a cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian

It is rigorously proven that the spectrum of the tight-binding Fibonacci Hamiltonian,H _mn= _{m, n+1}+ _{m, n–1}+ _{m, n} [(n+1)]–[n]) where =(5–1)/2 and [·] means integer part, is a Cantor set of zero Lebesgue measure for all real nonzero, and the spectral measures are purely singular continuous. This follows from a recent result by Kotani, coupled with the vanishing of the Lyapunov exponent in the spectrum.On leave from the Central Research Institute for Physics, Budapest, Hungary.