Instability in degenerate two-photon running wave laser

The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k>1+r(k=/,r=/; is the cavity loss of the field and , are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr<k<(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.     

μ+SR in magnetically ordered BCC metals: Local fields, μ+ sites,quantum diffusion,and strain effects

The paper gives a critical discussion of the procedures for extracting from the ⁺SR signals obtainable on magnetically ordered metals information on ⁺ sites, on local lattice distortions induced by the ⁺, on the local magnetic fields felt by the ⁺, and on quantum diffusion. Results for-Fe are: ⁺ occupy O sites, the tetragonality of the elastic double-force tensor isA–B 2eV, the dipolar magnetic field acting on the ⁺ isB _dip=(0.66±0.02)T. Using this information ⁺ hopping rates and diffusivities in Fe are deduced and compared with diffusivities obtained for hydrogen and deuterium. From this it is concluded that hydrogen in Fe diffuses via the adiabatic mechanism. In addition, the paper contains a brief summary of the theoretical background required for taking advantage of the rather large ¦A– B¦ values expected for ⁺ at O sites in bcc metals in order to gain information on the effects of energy asymmetries between neighbouring ⁺ sites on the ⁺ hopping rates.     

Algebraisch spezielle Einstein-Räume mit einer Bewegungsgruppe

In algebraically special Einstein spaces (R_v=0) with a hypersurfaceorthogonal spacelike Killing vector field _v, the trajectories of the multiple eigen null directions k lie — except one case — in the subspacesV ₃ orthogonal to _v (k=0) and are hypersurface-orthogonal. The solutions with vanishing expansion (k_,;=0, Kundt's class) can be determined explicitly.     

New cascade laser transitions in CH2F2 pumped with the 9R32 line of a cw CO2 laser

New cascade laser transitions of¹²CH₂F₂ at 172.50m, 208.83m, 220.44m, 223.99m and 250.61m are reported. A waveguide FIR laser was pumped with a quasi cw¹²C¹⁶O₂ laser operating on the 9R32 line. Together with the already known lines at 184.3m, 196.1m and 235.9m, the laser lines can be assigned to rotational transitions in the ₉ vibrational band of¹²CH₂F₂ and to refill transitions of the vibrational ground state ₀.     

Singularity theorems and the [General Relativity + additional matter fields] formulation of metric theories of gravitation

By using the [General Relativity + additional matter fields] formulation (which depends on a redefined metrich ) of metric theories of gravitation, the study of singularities characterized by incomplete nonspacelike geodesics is simplified, but may be used only if (at least) the non-spacelike geodesics of the original metricg are conserved under the transformation betweeng and the new metrich . In order that every class of geodesies of a diagonal Bianchi I metric correspond to the same class of geodesies of a diagonal metrich , it is necessary that the transformation between these two metrics be a constant (positive) conformal transformation. We analyse the implications of the previous results for the singularitiesg when the latter is a solution of theories with a quadratic or polynomial Lagrangian.     

Modified London model for the determination of λ and ζ in a high κ superconductor

We present a modified London model suggested by Brandt [1–3] which introduces a finite vortex core size appropriate for isotropic superconductors in which the average internal field is less than approximately (1/4)H _c2. TheSR lineshape resulting from this model possesses a distinctive shape due to the magnetic penetration depth and the vortex core diameter (approximately equal to twice the coherence length ). However, for a given lineshape, there is a large range of values of and which produce nearly the same lineshape. Lineshape smearing caused by disorder in the vortex lattice increases uncertainty in values for and . If well-determined values of either (T) or (T) are not available from another technique, both of them can be determined bySR measurements alone if runs in more than one applied field at the same temperature are fit with and as shared parameters. We also present our method of estimating the degree of disorder in the vortex lattice.     

The unitary bogoliubov transformation for a quantized scalar field in a friedman space-time

The time-dependent creation and annihilation operators for a complex scalar field, in a Friedmann space-time, defining particle states with respect to which the Hamiltonian is diagonal, are related by a Bogoliubov transformation to the creation and annihilation operators defined in strict analogy with the procedure carried out in Minkowski space. The Bogoliubov transformation is here written in terms of a unitary operator,U, and an expression for that operator is found via the generating functionF=i InU. The properties of the representation obtained by makingU act upon the state vector , to give a new state _U, are discussed. It is shown that the particle-number operator remains constant in such a picture so that the evolution of the system with time is clearly seen to depend upon the energy _k on the one hand, and upon the state vector _U on the other. Also, it is pointed out that this new representation permits the in and out states to be defined unambiguously.On leave of absence from Istituto de Fisica G. Galilei (Padova) and Istituto Nazionale di Fisica Nucleare (Sezione di Padova).     

Electrical and optical properties and stabilization of the Fermi level in GaP crystals irradiated by electrons and H+ ions

Electrical and optical properties and Fermi level stabilization are studied in GaP crystals irradiated by electrons (E2.2 MeV, D1·10¹⁹ cm^–2) and H⁺ ions (E5 MeV, D1.7·10¹⁶ cm^–2). It is shown that the limiting position of the Fermi level (F_limE_G/2±0.2 eV) is independent of the initial GaP parameters and the type of bombarding particle, but is determined by the condition of local neutrality of the defective GaP. Resistivity values for the irradiated specimens of _max(D)1·10¹³ ·cm were obtained at 300 K. At maximum integral particle fluxes a decrease in crystal resistivity to (3–6)·10⁹ ·cm was observed. The readjustment of GaP absorption spectra in the region hvE_G upon irradiation is related to recharging of gap states by radiation defects upon motion of the Fermi level toward F_lim.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 37–42, December, 1994.     

Radiation losses in completely ionized plasma

The losses caused by bremsstahlung during electron-ion and electron-electron collisions in a completely ionized plasma (in Born's approximation) are calculated. The calculation can be carried out analytically for a sufficiently dilute plasma (plasma with infinitely large Debay-Hückel radius). This assumption is satisfied very well by the known classification to actual controlled thermonuclear reaction. A dependence of the formI=an ². (1+3/2), wherea=0·73×10^–16 MeV.cm³.sec^–1,n is the number of ions per cm³ and =kT/mc ², is determined for the amount of energy radiated from 1 cm³ of plasma per sec. In the relativistic temperature regionkTmc ² the influence of electron-electron collisions begins to predominate. A number of important results concerning radiation losses in relativistic plasma will be published in a later paper.

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, ( ). ( -). . , I=an ². (1+3/2), =0,73. 10^–16 MeVcm²s^–1,n — =kT/mc ². kTmc ² . , .

     

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.     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

Isotope dependence of particle-decay rates of muonic molecular ions (d3,4Heμ) J=1 below (dμ)1s-3,4He threshold

Rates of particle-emitting decay of the resonant state of the muonic molecular ion (dHe) _J=1 lying below the (d)_1s-He threshold can decay to the d-He scattering state. The resonant state is estimated by scattering calculations with the non-adiabatic coupled-rearrangement-channel method. Strong isotope dependence of the decay rates of (d³He) _J=1 and (d⁴He) _J=1 is predicted, though the calculated radiative decay rates of the states are almost the same. In (d³He) _J=1, the particle decay width is three times larger than the radiative decay width, while the two types of decay widths are almost the same in (d⁴He) _J=1. This results in a strong hindrance of the branching ratio of the radiative decay of (d³He) _J=1 compared with the case of (d⁴He) _J=1. This is consistent with a recent observation of the radiative decay of the two molecular states.     

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.     

Muon catalyzed fusion: old and new aspects of energy production

Muon catalyzed fusion of deuterium and tritium (CF) yields the same energy gain per reaction as fusion with magnetic or inertial confinement (17.6 MeV). The crucial points of Cf are, however, very different, namely (a) the energy costW ₍₎ for production of one ^– and (b) the numbern of reactions a single muon can catalyze on the average. (b) is ultimately limited by theeffective sticking probability _f :n1/ _f. With standard methods one hasW ₍₎5 GeV, _f=0.5%. Hence a standard CF reactor can never reach a net energy gain. To solve this problem, ways discussed since about a decade are to increase the efficiency by both (i) energy multiplication using a fissionable blanket and (ii) breeding. A new way to increase the safety of fission devices mostly due to Yu. Petrov is outlined. On the other hand there is a hope to lowerW ₍₎ slightly and _f drastically, the latter by artificial reactivation. New theoretical results for beam cooling in an omegatron type driven integrated CF reactor, important forW ₍₎ and, in particular, _f, is presented.     

Decay of the Bethe–Salpeter Kernel and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We consider lattice classical ferromagnetic spin systems at high temperature (1) with nearest neighbor interactions and even single-spin distributions (ssd). Associated with each system is an imaginary time lattice quantum field theory. It is known that there is a particle of mass m–ln in the energy-momentum spectrum. If s ⁴–3s ²²<0, where s ^k is the kth moment of the ssd, and is sufficiently small, we show that in the two-particle subspace there is no mass spectrum up to 2m. For >0 we show that the only mass spectrum in (m, 2m) is a bound state of mass m _b=2m+ln(1–)+O(), where =(+2s ²²)^–1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results.     

Heat transfer in unsteady MHD oscillatory flow

Heat transfer in unsteady MHD channel flow (of an incompressible viscous and electrically conducting fluid) under oscillatory pressure gradient when the channel surfaces are conducting and moving with time-dependent velocities has been analysed. The velocity, magnetic field and temperature distributions have been obtained and their numerical results are shown graphically.Symbols u velocity - H _o applied magnetic field - H _x induced magnetic field - T temperature - T ₁ ^* ,T ₂ ^* temperatures of the upper and lower planes - density - p pressure - kinematic viscosity - magnetic diffusivity - electrical conductivity of the fluid - A ^* characteristic velocity - L characteristic length - _e magnetic permeability of the fluid - C _p specific heat - coefficient of viscosity - k thermal conductivity - ₁, ₂ permeabilities of the planes - ₁, ₂ conductivities of the planes - ₁, ₂ conductance ratios of the planes - Pr Prandtl number (=C _p /k) - E Eckert number - M Hartmann number (= _e H _o L/) - R _e Reynolds number (=LA ^*/) - R _m magnetic Reynolds number (= _e LA ^*) - S Pr.E(=S)     

On the equivalence of boundary conditions

We show that ifb andb are two boundary conditions (b.c.) for general spin systems on ^d such that the difference in the energies of a spin configuration in ^d is uniformly bounded, |H _,b ()–H _,b()|C < , then any infinite-volume Gibbs states and obtained with these b.c. have the same measure-zero sets. This implies that the decompositions of and into extremal Gibbs states are equivalent (mutually absolutely continuous). In particular, if is extremal,=. Application of this observation yields in an easy way (among other things) (a) the uniqueness of the Gibbs states for one-dimensional systems with forces that are not too long-range; (b) the fact that various b.c. that are natural candidates for producing non-translation-invariant Gibbs states cannot lead to such an extremal Gibbs state in two dimensions.Supported in part by NSF Grant PHY 78–15920 and by the Swiss National Foundation For Scientific Research.     

Some twisted self-dual solutions for the Yang-Mills equations on a hypertorus

TheSU(N) Yang-Mills equations are considered in a four-dimensional Euclidean box with periodic boundary conditions (hypertorus). Gauge-invariant twists can be introduced in these boundary conditions, to be labeled with integersn (= –n ), defined moduloN. The Pontryagin number in this space is often fractional. Whenever this number is zero there are solutions to the equationsG =0 HereG is the covariant curl. When this number is not zero we find a set of solutions to the equations , provided that the periodsa of the box satisfy certain relations.Work supported in part by the US Department of Energy under Contract No. DE-AC-03-76ER 00068 and by the Fairchild FoundationOn leave from the Institute for Theoretical Physics, University of Utrecht, P.O. Box 80.006, NL-3508 TA Utrecht, The Netherlands     

Semimodularity and the logic of quantum mechanics

If (, ,P, ) is an event-state-operation structure, then the events form an orthomodular ortholattice (, , ) and the operations, mappings from the set of states into , form a Baer *-semigroup (S, , *, ). Additional axioms are adopted which yield the existence of a homomorphism from (S, , *, ) into the Baer *-semigroup (S(), , *, ) of residuated mappings of (, , ) such thatx S maps states while _x S () maps supports of states. If (, , ) is atomic and there exists a correspondence between atoms and pure states, then the existence of provides the result: (, , ) is semimodular if and only if every operationx S is a pure operation (maps pure states into pure states).Supported in part by the United States Atomic Energy Commission and in part by the Fonds National Suisse.     

Microscopic selection principle for a diffusion-reaction equation

We consider a model of stochastically interacting particles on , where each site is assumed to be empty or occupied by at most one particle. Particles jump to each empty neighboring site with rate/2 and also create new particles with rate 1/2 at these sites. We show that as seen from the rightmost particle, this process has precisely one invariant distribution. The average velocity of this particle V() then satisfies ^–1/2V() as. This limit corresponds to that of the macroscopic density obtained by rescaling lengths by a factor ^1/2 and letting. This density solves the reaction-diffusion equation , and under Heaviside initial data converges to a traveling wave moving at the same rate .