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.     

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.     

A theory of 1/f noise

Letu() be an absolutely integrable function and define the random process where thet _i are Poisson arrivals and thes _i, are identically distributed nonnegative random variables. Under routine independence assumptions, one may then calculate a formula for the spectrum ofn(t), S _n(), in terms of the probability density ofs, p_s(). If any probability density p_s() having the property p_s() I for small is substituted into this formula, the calculated S_n() is such that S_n() 1 for small . However, this is not a spectrum of a well-defined random process; here, it is termed alimit spectrum. If a probability density having the property p_s() for small , where > 0, is substituted into the formula instead, a spectrum is calculated which is indeed the spectrum of a well-defined random process. Also, if the latter p_s is suitably close to the former p_s, then the spectrum in the second case approximates, to an arbitrary, degree of accuracy, the limit spectrum. It is shown how one may thereby have 1/f noise with low-frequency turnover, and also strict 1/f ^1– noise (the latter spectrum being integrable for > 0). Suitable examples are given. Actually, u() may be itself a random process, and the theory is developed on this basis.     

Some results for the exponential interaction in two or more dimensions

We show that for the regularized exponential interaction :e : ind space-time dimensions the Schwinger functions converge to the Schwinger functions for the free field ifd>2 for all or ifd=2 for all such that ||>₀.Partially sponsored by the I.H.E.S. through the Stiftung Volkswagenwerk     

Quantum Observables,Lie Algebra Homology and TQFT

Let us consider a Lie (super)algebra G spanned by T where T are quantum observables in BV formalism. It is proved that for every tensor c^... that determines a homology class of the Lie algebra G the expression c^...T...T is again a quantum observable. This theorem is used to construct quantum observables in the BV sigma model. We apply this construction to explain Kontsevich's results about the relation between homology of the Lie algebra of Hamiltonian vector fields and topological invariants of manifolds.     

Lattice vibrations in ordered and disordered thiourea

The critical dynamics of the Syozi model for dilute ferromagnetism is considered by the use of master equations. The dynamics is soluble as it is assumed that the time scale of motion on the sublattice on which the impurities move is so much faster than on the other sublattice that fast relaxing variables may be adiabatically eliminated, leaving a new soluble master equation. It is found that the linear and non-linear relaxation of magnetization exponents ^(l) and ^(nl) increase on dilution to ^(l)/(1–) and ^(nl)/(1–) respectively ( is the specific heat exponent for the pure system, which itself changes on dilution to –/(1–)). Thus if the exponents for the pure system obey the scaling law of Rácz and Fisher ^(nl)= ^(l)– ( is the magnetization exponent which changes on dilution to /(1–)) then so do the exponents for the diluted system. Similarly the exponent for spin diffusion changes on dilution to /(1–).     

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.     

Massive spin-two particle in a gravitational field

The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m ² h Finally, variation with respect tog yields the energy-momentum tensor.     

An inequality for partition functions with disturbed Hamiltonians

We consider a thermodynamic system consisting ofn independent subsystems. Each subsystem is described by a HamiltonianH=H ₀+ ⁱ H ₁,i=1, 2,...,n. We answer the question of how the entirety=( ¹, ²,..., ⁿ ) must be varied in order to change the total partition function and the total free energy of the system monotonically.     

Structure factor of substitutional sequences

We study the structure factor for a large class of sequences of two elementsa andb such that longer sequences are generated from shorter ones by a simple substitution rulea ₁(a, b) andb ₂(a, b), where the's are some sequences ofa's andb's. Such sequences include periodic and quasiperiodic systems (e.g., the Fibonacci sequence), as well as systems such as the Thue-Morse sequence, which are neither. We show that there are values of the frequency at which the structure factors of these sequences have peaks that scale withL, the size of the system likeL ⁽⁾. For a given sequence a simple one- or two-dimensional dynamical iterative map of the variable can easily be abstracted from the substitution algorithm. The basin of attraction of a given fixed point or limit cycle of this map is a set of values of at which there are peaks of the structure factor all of which share the same value of. Furthermore, only those values of which are in the basin of attraction of the origin can have()=2. All other peaks will grow less rapidly withL. We show how to construct many sequences which, like the Thue-Morse sequence, have noL ² peaks. Other qualitative features of the structure factors are presented. Our approach unifies the treatment of a large class of apparently very diverse systems. Implications for the band structure of these systems as well as for the analysis of sequences with more than two elements are discussed.     

Quasi-stationary states of hydrogen

We consider the hydrogen atom within the context of a theory of relativistic quantum mechanics that allows for a probabilistic interpretation of the wave function. We find the radial equation that determines the energy levels of bound states, represented by quasi-stationary states. We compute the order of magnitude of the shifts from the usual spectrum obtained from the Dirac equation, and we find that the leading terms for these corrections are of the order of ⁶ log fors-states and ⁶ for other states. They are small compared to the Lamb shift, which is of the order of ⁵ log .     

Beta-decay asymmetries in polarized12B and12N and theG-parity non-conservation

The decay asymmetries (A) in polarized¹²B and¹²N have been measured as a function of -ray energies (E). The coefficients _± inA = ±P(p/E) (1+_± E) have been determined to be _–(¹²B) =+(0.31±0.06)%/MeV and ₊(¹²N) = –(0.21±0.07)%/MeV. The experimental value, _––₊=(0.52±0.09)%/MeV, is larger than the prediction according to conservation of vector current which includes no second-class current, _––_{+ CVC}0.27%/MeV, and indicates the existence of the second-class induced-tensor current.This work has been done in collaboration with I. Tanihata and J. Göring.     

Calculation of hyperfine interactions measured by magnetic decoupling in oxygen ions

Magnetic hyperfine interactions in highly stripped oxygen ions recoiling in vacuum have been measured with perturbed angular correlations. The second excited state of¹⁶O(I =3^–,E _X=6.13 MeV, =26.6 psec, |g|=0.55) was produced with the nuclear reactions¹⁹F(p,)¹⁶O and¹⁶O(,)¹⁶O and the angular correlation of the -rays observed in coincidence with particles emitted at 180°. Five recoil velocities between 1.0 and 3.3% c produced average ion charge states from 2.1 to 5.5. The perturbation of the angular correlation and hence the decoupling of the hyperfine interactions was observed as a function of an external axial magnetic field varied between 0 and 33 kG. The perturbation is expected to arise primarily from hyperfine interactions of unpaired 1s electrons with smaller contributions from 2s electrons and other configurations. The maximum external field was strong enough to decouple all hyperfine interactions except that of the 1s electrons. The decoupling curves obtained were successfully fitted by calculations using the hyperfine interactions of the pertinent atomic Hartree-Fock-Slater orbitals.Supported in part by the National Science Foundation.     

Optical Emission Spectroscopy Used to Study the Characteristics of the Capacitive Radio-Frequency Discharge in Argon

Capacitively coupled radio-frequency (13.56 MHz) glow discharge in argon at low pressure (200 mTorr) has been studied by optical emission spectroscopy (OES) and electrical probe. Increasing power density resulted in lowering of the electron temperature T _e and increase of the electron density n _e. The to transition in this case takes place smoothly. The intensity (I _750.4) of the emission line at 750.4 nm due to 2p₁1s₂ transition closely follows the variation of n _e with power density. Calculation of the electron-energy probability function shows that electron occupation mainly changes in the high-energy tail, which explains close resemblance of I _750.4 to n _e. At moderate pressures, only OES method was applied to observe - transition which is abrupt in this pressure range.     

Feynman rules for probability amplitudes

Starting with very simple assumptions, Feynman rules for the quantum mechanical amplitudes and the associated probabilities are derived. These rules emerge as the only consistent rules for manipulating complex amplitudes assigned to processes. The probability of a process to which an amplitudex has been assigned is determined asp(x)=|x| , 0<2. If virtual processes are allowed,=2.     

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.     

The Einstein 3-form Gα and its Equivalent 1-form Lα in Riemann–Cartan Space

We motivate the definition of the Einstein 3-form G by means of the contracted 2nd Bianchi identity. This definition contains the whole curvature 2-form. The L 1-form, defined via G = L ^*( ) ( is the Hodge-star, the coframe), is equivalent to the Einstein 3-form and contains all the information of the curvature 2-form relevant for the definition of the Einstein 3-form. A variational formula of Salgado on quadratic invariants of the L 1-form is discussed, generalized, and put into proper perspective.     

Precipitation sequences and transformation kinetics in the Al-30 wt.% Zn alloy aged below 160°C

The transformation sequences in the Al-30 wt.% Zn alloy aged below 160 °C have been investigated by X-ray diffraction and transmission electron microscopy. The sequence G.-P. zones _R has been observed between 85 and 161 °C, whereas the direct G.-P. zones to-transformation occurs below 85 °C. The identical isothermal growth kinetics of both the G.-P. zones and the _R -precipitates was found. The log-log plots yielding a set of parallel straight lines from 50 to 150 °C indicate no change in the activation energy of growth of both these precipitates. The change in the precipitation sequence led to the change in the transformation kinetics. The T-T-T curves have been measured for the formation of metastable _R -phase and for the completion of ellipsoidal G.-P. zones or of _R to-transformation. The retardation in reaching equilibrium found below 85 °C was associated with the observed change in the transformation sequence. This was explained by the different accommodation of the misfit at the interfaces between G.-P. zones or _R -precipitates and the-matrix.The authors are much indebted to Doc. Dr. V.Syneek, CSc. for stimulating discussions. Our thanks are also due to Ing. V.íma and Mr. P.Vyhlídka for the preparation and careful chemical analyses of the investigated samples. The assistance of Mr. Z.iký and Mr. V.Petr in X-ray diffraction measurements and the heat-treatment of samples is appreciated.     

Singular Perturbations of Self-Adjoint Operators

Singular finite rank perturbations of an unbounded self-adjoint operator A ₀ in a Hilbert space ₀ are defined formally as A ₍₎=A ₀+GG ^*, where G is an injective linear mapping from = ^d to the scale space _-k(A₀)k , kN, of generalized elements associated with the self-adjoint operator A ₀, and where is a self-adjoint operator in . The cases k=1 and k=2 have been studied extensively in the literature with applications to problems involving point interactions or zero range potentials. The scalar case with k=2n>1 has been considered recently by various authors from a mathematical point of view. In this paper, singular finite rank perturbations A ₍₎ in the general setting ran G – _k (A ₀), kN, are studied by means of a recent operator model induced by a class of matrix polynomials. As an application, singular perturbations of the Dirac operator are considered.     

Nonlinear superposition for Liouville's equation in three spatial dimensions

We derive in 3+0 dimensions exact solutions of Liouville's equation ²=exp , by applying the Bäcklund transformation technique in conjunction with the principle of nonlinear superposition. The procedure, which is later extended to 3+1 dimensions, yield, as a byproduct, particular solutions of ² and ² =exp (² +² ).