Instability in degenerate two-photon running wave laser with detuning

The previous stability analysis of the degenerate two-photon running wave laser is extended to the inclusion of detuning between frequencies of cavity and atoms. We derive the analytical equation for the critical pumping and prove analytically that for the special case ofr (/) being unity, there is no Hopf bifurcation instability for the bad cavity. The good cavity case is analysed numerically. The role played by detuning is to raise the critical pumping. In the case ofk (or <K) where there is no Hopf bifurcation instability for the perfect tuning case, the large detuning can give rise to self-pulsing instability.     

On the equilibrium of a black hole in a radiation-filled cavity

By using the horizon entropy, Hawking showed that a stable black hole will form inside a radiation cavity of finite energyE and small enough volume,VV _h(E). But two heuristic considerations seem to contradict this. First, a spontaneous fluctuation large enough to form a hole is so improbable that the chance of one developing even in 10¹⁰ years is negligible. Second, any such hole should not be in equilibrium, let alone stable; it should evaporate away again because the radiation, with typical wavelength 16 times larger than the hole, can hardly be accreted. Study of the combined accretion and evaporation resolves this difficulty. It confirms the prediction of stability and it does so without appeal to the concept of horizon entropy. A state of pure radiation is actually favored over one including a hole when 1V/V _h>0.2556, but the reverse holds for smaller cavity volumes. The horizon entropy of a black hole plays a natural role; it helps determine the system's evolution and equilibria through the condition that the total entropy of hole plus radiation always tends to increase. Using the known temperature of the hole and the fact (deduced from the accretion formula) that energy flows from the hot body to the cold, one easily inverts the reasoning to derive a unique value for the black-hole entropy.     

Infinite hierarchy of exponents in a two-component random resistor network

We have studied the voltage distribution for a two-component random mixture of conductances _a and _b. A scaling theory is developed for the moments of the distribution, which predicts, for small values ofh=_a/_b, an infinite number of crossover exponents, one for each moment, for Euclidean dimensiond >2, and only one crossover exponent ford=2. Monte Carlo results on the square lattice confirm this prediction.     

The tangent bundle of a Calabi-Yau manifold-deformations and restriction to rational curves

The tangent bundle _X of a Calabi-Yau threefoldX is the only known example of a stable bundle with non-trivial restriction to any rational curve onX. By deforming the direct sum of _X and the trivial line bundle one can try to obtain new examples. We use algebro-geometric techniques to derive results in this direction. The relation to the finiteness of rational curves on Calabi-Yau threefolds is discussed.     

Frequencies of the axial modes of a composite cavity

The cavity consists of a rod with plane-parallel plates as mirrors. The frequencies differ in loss, which leads to mode selection. There is a periodicity in the frequencies if the various elements are comparable in length. The period ₀ usually substantially exceeds the distance between natural frequencies for the rod. There may be one or two stable frequencies with minimal loss within a period, the decisive factor being the relation between the optical lengths of the components.     

Simple cell model with collapse instability

A cell model is introduced in which pairs of particles interact only within the same cell, and then only with a constant coupling ₀. For positive ₀ the statistical thermodynamics is normal, but as ₀ changes sign, the system manifests a collapse phenomenon with all particles tending to aggregate in the same cell. This collapse instability causes high-temperature series to diverge, but known asymptotic properties of Stirling numbers of the second kind allow one to establish Borel summability. The present model is equivalent to continuum models with bounded pair potentials when in the latter the space dimensionD is permitted to go to 0+.     

Absence of the partially ordered phase in theq-state models

We investigate theq-state models called (N ,N ) model using an infinitesimal Migdal-Kadanoff renormalization-group method. We distinguish two cases namely the isotropic model and the anisotropic model. The first one presents a critical value ofq,q _c such that forq _c we obtain an Ashkin-Teller phase diagrams while forq>q _c the partially ordered phase disappears then the model exhibits only phase transition between ferromagnetic phase and disordered one. The phase diagrams in the second case are qualitatively similar to one obtained forZ(6) model for all values ofq.     

The magnetoelastic interaction of optical phonons in CecLa1?cF3 single crystals

Splitting and renormalisation of doubly-degenerate optical phonons in Ce _c La_1–c F₃ single crystals (0c1) has been observed in Raman-scattering experiments. The effects depend on the 4f-electron concentrationc, the magnetic field and temperature. A quantitative interpretation is given using a Jahn-Teller type Hamiltonian with only one phenomenological coupling constant.     

RF properties of superconducting vanadium

Q values of a superconducting vanadium cavity in theT E ₀₁₁ mode at 9.6 GHz were measured to determine the residual surface resistanceR ₀ and the reduced energy gap 2(0)/kT _c with respect to different surface treatments such as electropolishing, oxipolishing and anodizing. The residual surface resistance was found to be lowest for the oxipolished cavity, corresponding to a residualQ of 2×10⁸ at 1.2 K. Independent of the surface treatment the reduced energy-gap value amounted to 3.52±0.1. The influence of different vanadium oxides on the rf properties of superconducting vanadium was investigated.     

Quenchedn-vectorp-spin model

A disorderedn-vector model withp spin interactions previously introduced is studied for the quenched case by means of the replica method and a generalized Parisi theory. We present formal solutions for generaln andp and then study the casep . The high-temperature solution is stable at all temperatures and there is only one phase transition at a temperatureT _g. Only longitudinal lowtemperature solutions are possible. There is one spin-glass solution, and it is stable for allT _g. The phase transition atT _g is of first order and displays a jump discontinuity in the order parametersq _j ^(L) andd. The spin-glass free energy is temperature dependent forn > 1 while it is constant whenn = 1.     

Symmetries induced by conserved vector currents in the theory of a scalar field

Let us consider a quantum theory of one scalar, real, local, Poincaré covariant fieldA(x) with the restricted spectrum condition (massive one particle states and a unique vacuum). The asymptotic fieldsA _{in out} (x) are assumed to be irreducible. Our conjecture is that under some technical assumptions the charge of every real, hermitean, locally conserved, Poincaré covariant quantum (pseudo) vector fieldj (x) relatively local toA(x), appearing in this theory-vanishes. This means that in a theory of one scalar, real field with a massive particle one can not expect to get symmetry groups induced by conserved (pseudo) vector currents, only by global, selfadjoint, Poincaré invariant generators.Our arguments can be easily extended to a theory of one complex scalar field, in this case the only symmetry transformation induced by a current can be the gauge transformation.We prove also that under very weak assumptions two fields related to each other by a unitary (or similarity) transformation are equal barring some patological cases.     

Experimental study of cw carbon monoxide flame chemical laser of the CS2/O2/CO2 type

The performance of a continuous-wave (cw) CO flame chemical laser (FCL) of the CS₂/O₂/CO₂ type is presented. The laser gives up to 0.7 W cw output power on a number ofP _v (J) lines corresponding to 1110, ..., 76 vibrational bands of CO molecule. The measured values of chemical efficiency based on the reaction O+CSCO^*(v)+S and the specific power are 0.1% and 0.7J/g, respectively. The spectral composition of the CO FCL of the CS₂/O₂/CO₂ type shows lasing in the region from 5.194 to 5.573 m. All experimental measurements are conducted with a nondispersive optical cavity.     

Stimulated raman pumping to H2 (v″=1, J″=1) and resonance-enhanced multiphoton ionization from it using a single laser

Light pulses from one ArF laser are used both a) to produce H₂ in v=1, J=1 of the X-state by means of stimulated Raman pumping (SRP) and b) to analyze for that state via (2+1) resonance-enhanced multiphoton ionization (REMPI). Both SRP and REMPI have been previously measured in H₂, but with a different laser for each process. Some of our laser light is Raman shifted in H₂. The resulting mixture of fundamental (193 nm) and first Stokes (210 nm) light is focused into low-pressure H₂ where the SRP and REMPI both occur. The SRP is efficient and it produces only v=1, J=1. As the laser is tuned, a REMPI spectrum occurs from excitation by two photons of 193 nm, by two photons of 210 nm, or by one photon each of 210 and 193 nm. The features of this approach are a) that the necessary temporal and spatial overlaps are automatically achieved, b) that the frequency difference generated in the Raman shifter is precisely that needed for SRP, c) that large pulse energies are available for the REMPI, and d) that only one laser is needed.     

Space-charge capacitance in thin semiconductor monocrystalline films

The paper describes the solution for the space-charge capacitance in thin semiconductor films under general boundary conditions. The influence of both surfaces and film thickness on this capacitance is discussed in more detail and it is shown that cases exist in which the space-charge capacitance depends on the properties of one surface or on the film thickness only.Notation E _s2 dimensionless surface field intensity - F ₁, F₂, F₃ space-charge functions - k Boltzmann's constant - n bulk electron density - p _b bulk hole density - q electron charge - T absolute temperature - _o permittivity of free space - _s relative permittivity of semiconductor - dimensionless thicknessd/L _D - dimensionless coordinate perpendicular to the surfacez/L _D - dimensionless potential (multiples ofkT/q).     

Integrability conditions for Killing spinors

The conditions for the existence of solutions ofD _µ=±c_µ are discussed. In general, it is not sufficient to consider only the first integrability condition [D _µ,D _v ]=–2c ²_{µv}; in particular, the second integrability condition is needed to explain why, in certain cases, only for one choice of sign does a solution exist. The Killing spinor-tensors, as defined by Walker and Penrose, are shown to be the spinorial equivalent of conformal Killing tensors. Their relationship to the Killing spinors and spinor-vectors used in supergravity, is given.On leave from the Institute for Theoretical Physics of the State University of New York at Stony BrookWork supported in part by the U.S. Department of Energy under Contract No. DEAC-03-81-ER 40050 and Weingart Fellowship     

Particle flow in a jet

The angular distribution of hadrons in a jet is evaluated in perturbative QCD. The predictions are restrictive in the sense they do no depend on the details of the non-perturbative process. The distribution depends on only one phenomenologically adjustable parameter, a cutoff massQ ₀ (in addition to the universal QCD mass-scale ). The fit of the leading order prediction to the TASSO data is obtained withQ ₀270 MeV.The low value ofQ ₀ supports the hypothesis of local partonhadron duality. The particle flow in a gluon jet is also analysed.     

A photolyticallyQ-switched photolytic iodine laser

A novel, repetitively pulsed, photolyticQ-switching scheme has been demonstrated on a 1.315 m (² P _1/2² P _3/2) cw photolytic iodine laser using an intracavity cell containing either IBr or ICl. When the cell is irradiated with a KrF laser (=248 nm), I(² P _3/2) atoms are produced and lasing ceases due to the introduction of loss into the laser cavity. Lasing resumes, however, following recombination of the atoms into the parent molecule. Experimental evidence is presented which indicates that the laser's shut-off time is a function of excimer laser energy and the pressure of buffer gas in the cell.     

A microwave μSR spectrometer

A microwave-SR (WSR) spectrometer has been developed which operates in the frequency region of 1–2 GHz. The spectrometer geometry is that of longitudinal field (LF)SR and is typically used in time integral measurements. The high frequency of this instrument distinguishes it from the currently used RFSR spectrometers and allows high field measurements to be made for normal Mu type systems. This allows one to avoid low field broadening mechanisms that may be present, either from electronic spin-lattice relaxation or nuclear hyperfine interactions.Technical details of the tunable microwave cavity and the RF coupling scheme are presented. Experimental spectra of Mu lines in SiO₂ and GaAs are displayed.     

On galvanomagnetic size effects in metals

The importance of open electron trajectories formed by specular reflections of charge carriers by the sample boundary to the metal electric conductivities in the strong magnetic fieldH is analyzed. It is shown that the electric conductivity of the near-surface layer _skin is rather sensitive to the state of the conductor surface. The electron-hole Umklapp processes during the surface scattering of charge carriers do not change the dependence _skin(H), while skipping from the closed Fermi surface section to the open one is able to affect _skin essentially only in bulk samples. The method is proposed to restore the indicatrix of conduction electron scattering by the sample boundary through an experimental investigation of the Sondheimer effect and the static skin effect.     

A Mössbauer spectroscopic study of cobalt-iron molybdates

Fe _x Co_1–x MoO₄ compounds prepared by coprecipitation were studied by XRD, electrical conductivity and mainly by absorption and emission Mössbauer spectroscopy. FeMoO₄ and CoMoO₄ samples were shown to contain Fe³⁺ and Co³⁺, respectively, in solid solution. Three kinds of Fe _x Co_1–x MoO₄ solids can be described. Forx0.16: one has a -Co(Fe²⁺, Fe³⁺)MoO₄ solid solution. For 0.17x0.25: one has the same solid solution with its surface rich in Fe³⁺. Forx0.26: one has the same solid solution with only bulk Fe³⁺, and ferric molybdate. Studies of reduction by hydrogen and of catalytic reaction of mechanical mixtures of CoMoO₄ and ferric molybdate support these statements.