Surviving extrema for the action on the twisted SU(∞) one point lattice

We give a simplified construction of twist eating configurations, based on a theorem due to Frobenius. These configurations are defined through the equation:U U U ⁺ U ⁺ =exp(2in /N) withU SU(N), =1 tod andn an antisymmetric matrix with integer entries. In the (Twisted)-Eguchi-Kawai model they yield extrema some of which survive forN. Comparison is made with the Monte Carlo data of the internal energy in the small coupling region.     

Differential calculus on quantum spheres

Three-dimensional differential calculus on quantum spheres S _infc ^sup2 ,]–1, 1[{0}, c[0, ], is introduced and investigated. Spectra of generalized Laplacians are found. These operators are expressed by generalized directional derivatives. Classical limits of these objects are obtained and a simple approach to quantum mechanics on a quantum sphere is presented.     

The paramagnetic state (μ+e−) in silicon and tellurium at high temperature

The paramagnetic state (⁺e^–) in Si and Te was observed in a longitudinal magnetic field. The mean lifetimes of these states were obtained: _Si = 1.45(3) s, _Te = 12.5(8) s at 290 K, _Te = 12(2) s at 250 K.     

Quantization of the Maxwell field in linear conformal invariant gauges

It is shown that the generalized Lorentz gauges provide all linear conformal invariant gauges, i.e. gauges such that A =0.     

Towards slow μ− production via muon catalyzed fusion

Slow ^– production via dd-CF using a two-layer arrangement is investigated. To determine its feasibility, experimental measurements are now in progress using the muonic X-ray detection method. The following experimental steps are being considered: (1) measurement of the number of ^– stopped inside a solid H₂/D₂ layer by detecting p K X-rays, (2) hot d emission detection by placing a secondary target at a distance of 10–30 mm from the layer and by detecting specific delayed X-rays, (3) measurement of the disappearance of d emission as the added D₂ layer is increased, (4) dd-CF measurement by detecting fusion protons, and (5) slow ^– emission detection. Results of the initial test experiment are presented.     

Scaling of Mandelbrot sets generated by critical point preperiodicity

Letzf (z) be a complex holomorphic function depending holomorphically on the complex parameter . If, for =0, a critical point off ₀ falls after a finite number of steps onto an unstable fixed point off ₀, then, in the parameter space, near 0, an infinity of more and more accurate copies of the Mandelbrot set appears. We compute their scaling properties.On leave from the University of Geneva     

Classical theory of the interaction between a spinor field and the gravitational field: First-order field equations

The classical theory of the interaction of a neutral spin-1/2 Dirac field and the gravitational field is studied. For the purely gravitational part of the Lagrangian, written in terms of a vierbein and the local connection coefficient _ab , (regarded as independent field variables), the usual first-order form is adopted. For the Dirac part, however, a different choice is made, in which the covariant derivative of is built with the aid of the vierbein instead of with _ab . This still yields a first-order formalism, but one in which _ab is related to the vierbein in the same way as it would be in the absence of. This ensures that the global connection remains symmetric in andv in the presence of. The way in which the vierbein field equation leads to a familiar Einstein equation with a symmetric and conserved stress tensor on its right side is also analyzed.     

An Approach to Linear Scalable DH-PHEMT Model for Millimeterwave Application

This paper describes a scalable small-signal equivalent circuit for 0.25 m gatelength Double Heterojunction delta-doped PHEMTs. The scaling rules for all elements except the pad capacitances and bondwire inductances have been determined. Good agreement is obtained between simulation results and measured results for 2 times 20 m , 2 times 40 m, 2 times 60 m, 2 times 100 m gate width (number of gate fingers times unit gate width) DH PHEMT.     

Exact gravitational field of the infinitely long rotating hollow cylinder

The vacuum line element inside an infinitely long rotating hollow cylinder is the usual flat space line element. It is fitted in a most general way to the general cylindrical vacuum field outside at the singular hypersurfaceR ₀=const, representing the infinitely thin hollow cylinder. With the use of the jump conditions atR ₀=const the surface densities , of which the energy-momentum-stress tensor of the shell consists, are calculated. The physical properties of the cylinder, as derived from the eigenvalues and -vectors of , and the generated gravitational field are discussed in full detail.     

FIR gain measurements in cw laser pumped CH3OD

Direct measurements of small signal and saturated gain in cw laser pumped CH₃OD are reported for three lasing transitions of 57 m, 82 m and 103 m. The 57 m transition has a measured gain of 0.6/m, the strongest gain in methanol reported so far. Moreover small gain saturation of this line makes it to be one of the strongest known cw FIR laser lines.     

Absolute parallelism: Spherical symmetry and singularities

A one-parameter class of compatible field equations of n-frames h ^a is considered, characterized by the fact that after the substitution h ^a = HPH ^a (H = detH ^a , p is the constant depending on the dimensionality n and on the equation parameter ), the equations can be written in a trilinear form which contains the matrix H_a and its derivatives, but not H ^a . The equations remain regular for degenerated matrices H_a, if r = rank H_a ^< 2, the points with r < n being singular (if n > 1 + 1/). It is shown that there exist spherically symmetric solutions with singularities appearing for r < n; as the singularity develops, there appears a domain bounded by singular points in which, for certain values of and n, the field h ^a becomes complex.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 47–52, September, 1991.The author thanks I. L. Bukhbinder for his interest to this paper and useful discussions during the seminar.     

The spectrum of a quasiperiodic Schrödinger operator

The spectrum (H) of the tight binding Fibonacci Hamiltonian (H _mn= _m,n+1+ _m+1,n + _m,n v(n),v(n)= ((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary     

Uniqueness of Gibbs State for Nonideal Gas in ℝ d : The Case of Pair Potentials

We consider a classical gas of particles in ^d interacting via a pair potential. We prove that in a given region of the (, ) plane, where is the inverse temperature, and is the chemical potential, either the Gibbs state is unique or it does not exist. Our method uses a version of the well-known Dobrushin uniqueness theorem adapted for lattice systems with a noncompact spin space and proved by Dobrushin and Pechersky. The advantage of this version is that using it one needs to check Dobrushin's contraction condition not for all boundary configurations, but only for those that have spin values in some compact subset of the spin space.     

Fabrication and characteristics of double-fused vertical-cavity lasers

We discuss the fabrication process and characteristics of three consecutive runs of double-fused 1.5-m vertical-cavity lasers. We have measured light-current characteristics of over three hundred lasers with ten different diameters between 6 and 60 m and observe a yield of over 95%. The process and design improvements resulted in a low pulsed threshold current of 3 mA on a number of 6- and 8-m-diameter devices and threshold current density of 2 kA cm^–2 on 60-m-diameter devices at room temperature.     

Gravitomagnetic and Gravitoelectric Waves in General Relativity

Lower-order terms in expansions of the equations of General Relativity in powers of v/c (post-Newtonian approximations) have long been a source of analogies with em theory. A classic textbook example is the steadily spinning sphere generating a constant dipole gravitomagnetic field, with its associated vector potential B^* ₀ = × (analog of the magnetic field B of a spinning charged sphere). In the nonsteady case there are associated gravitoelectric fields E* = – _t – * also, where * is the gravitational Coulomb potential. The case of a rigid sphere spun up from rest by an external (nongravitational) torque at t = 0 is enlightening, as it demonstrates the generation of B* and E* wave fields propagating outward with the velocity of light c: for large t, B* B^* ₀. In a coordinate system for which the metric tensor is nearly equal to the Minkowski tensor, the three-vector potential obeys an equation isomorphic to the electrodynamic equation, that is, ² = –*j* with j* = –v, where is the mass density, v the three-velocity, and * = 16Gc^–2 = 3.7 × 10^–26 mksu, G being the gravitational constant. Significantly, one can construct a gauge invariant four-vector potential F* = (ic^–14*, ), obeying field equations isomorphic to Maxwell's in the Lorentz gauge F _, = 0. The traveling transient dipole field exerts torques on matter in its path, setting up shear strains that may be measurable for very large momentum transfers, for example, between massive astronomical bodies. A rough calculation suggests that such strains are in principle observable.     

BRST quantization of a scalar particle in a curved background

The BRST formalism is employed to quantize a scalar particle and interactions with an external scalar field (x ) and vector gauge fieldA (x ) in the background of an arbitrary gravitational field. The second-quantized actions are obtained.     

Continuity of type-I intermittency from a measure-theoretical point of view

We study a simple dynamical system which displays a so-called type-I intermittency bifurcation. We determine the Bowen-Ruelle measure and prove that the expectation (g) of any continuous functiong and the Kolmogoroff-Sinai entropyh() are continuous functions of the bifurcation parameter. Therefore the transition is continuous from a measure-theoretical point of view. Those results could be generalized to any similar dynamical system.     

Uniaxial stress induced frequency shifts for muons in single crystal Fe

We report the first results on uniaxial stress-induced frequency shifts in an Fe single crystal. Stress was applied along the 100 axis, which was also the axis of magnetization induced by an external field. The observed frequency shift was –0.34±0.023 MHz per 100 microstrain, which corresponds to B/=+25.1±1.6 G/100. The positive sign arises from the negative sign of B itself. This result is interpreted as follows: The stress induces a statistical population shift between magnetically inequivalent sites. Extrapolations from the calculations of Sugimoto and Fukai from Nb and V to Fe yield order of magnitude agreement. The 4T(0) site system seems more likely.     

Formation of muonium and a muonic radical in fullerene

Three distinct electronic states were detected for positive muons (⁺) after implantation into a C₆₀ powder sample. About 40% of the ⁺ remained in the bare (diamagnetic) state, essentially an interstitial charged point particle. The rest of the muons were found to thermalize predominantly in two muonium (Mu=⁺ e^–) atomic species. A vacuum Mu state, with hyperfine coupling close to that of free Mu, most likely at the molecular center, and a muonic substituted radical, i.e. a hydrogen-like Mu addition to double bonds on the carbon rings. This opens up a rich subfield of fullerene spectroscopy using muons.     

Heavy quark cascade mechanism of tetramuon production by neutrinos in a scale-breaking model

A few neutrino-induced tetramuon events have recently been reported by two experimental groups with a production rate of 10^–6 for( ^{– – + +})/ ( ^–). However, the rate for such events is not yet determined theoretically. In the present paper, we report on a detailed calculation of the rate in the framework of a heavy quark cascade mechanism, using the QCD-improved parton distribution functions parametrized by Buras and Gaemers, which have successfully fitted various experimental data. Our calculation for( ^{– – + +})/ () accords well with the CDHS and FHPRW rate. The computed rate is also in accord with that obtained via the radiative charm model calculation, whereby the normal charm dimuon production is accompanied by a radiative ^{+ –} pair.