Matter and light wave interferometry in gravitational fields

We consider the problem of finding the quantum mechanical phase associated with the propagation of a particle in a given external gravitational field, and conclude that it ism ds. In weak fieldsh this allows us to calculate the gravitationally induced phase on a freely traveling particle as 1/2 h P dx whereP is the ordinary momentum. This formula has the expected Newtonian limit and is then used to calculate effects in matter wave interferometry such as those due to gravity waves and the dragging of the ether frame by rotating bodies. Light wave interferometry is then considered and is shown to be also described by 1/2 h K dx , whereK is the wave vector of the light, and the integral is along the path of the ray. Matter and light wave interferometry are compared in various cases.A preliminary version of this work was presented at the Grenoble Workshop on Neutron Interferometry, June 1978.     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Far-Infrared Laser Stark Spectroscopy of CH3OD

The high resolution Stark spectra of the singly deuterated methanol isotope, CH₃OD, have been studied using the HCN laser with Stark fields up to approximately 60 000 V/cm. Numerous families of absorption lines have been observed in both parallel and perpendicular polarizations, resulting in the following assignments: with the 311 m line – J _K = 18₁ 18₀ E ₂, _t = 1; and with the 337 m line – J _k = 6₄ 5₃ E ₂, _t = 0 and J _K = 14₆ 13₅ A, _t = 1. Zero-field frequencies for the assigned transitions are in agreement with Fourier transform measurements and those calculated from the available molecular constants.     

Parity operator and quantization of δ-functions

In the Weyl quantization scheme, the -function at the origin of phase space corresponds to the parity operator. The quantization of a functionf() on phase space is the operator f(/2)W()dM, whereM is the parity andW() the Weyl operator.     

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.     

On the question of the existence of a canonically defined distance function for metrics with indefinite signature on a given manifold

Let be the set of all inner products with a given indefinite signature on a finite-dimensional vector spaceV. It is shown that any continuous pseudometricd on which is canonical, i.e., invariant with respect to all automorphisms ofV, is of the formd(g, h)=f( _g / _h ), where _g , _h denote the volume elements associated withg andh, respectively, andf is a real-valued function; i.e., there are no nontrivial distance functions. This result shows that a reasonable distance function between metric fields on a manifoldM cannot be obtained in terms of canonical distances of the inner products induced in the tangent spaces. A similar result is proved even for uniform structures instead of pseudometrics.     

The mass formula of the spherically symmetric solution of the five-dimensional vacuum equationsR μυ=0

Within the concept of extended elementary particles proposed by the author in some previous papers the mass formula of the general stationary spherically symmetric and purely electrical solution of the 5-dimensional vacuum equationsR =0 is calculated. The problem of how to establish a discrete mass spectrum is discussed in detail.     

Directed compact lattice animals: Exact results

The partially directed compact lattice animal model on the square lattice is solved exactly for the cluster number and average cluster radius along the directed axis in terms of the appropriate generating functions. For the critical exponents we find=0 and =1. Caliper size distribution along the directed axis is also calculated analytically. It is used to confirm =1 and to study some finite-size scaling properties for this model. For the perpendicular cluster radius distribution, a combination of analytic arguments and computer results leads to a conjecture on the exact form of the appropriate generating function and to the result =1/2. Some calculations are reported for the triangular lattice and for hypercubic lattices ind>2.     

Long-time tails in lattice Lorentz gases

We consider a Lorentz gas on a square lattice with a fraction c of scattering sites. The collision laws are deterministic (fixed mirror model) or stochastic (with transmission, reflection, and deflection probabilities ,, and respectively). If all mirrors are parallel, the mirror model is exactly solvable. For the general case a self-consistent ring kinetic equation is used to calculate the longtime tails of the velocity correlation function (0) (t) and the tensor correlation Q(0)Q(t) withQ= _{x y} . Both functions showt ^–2 tails, as opposed to the continuous Lorentz gas, where the tails are respectivelyt ^–2 andt ^–3. Inclusion of the self-consistent ring collisions increases the low-density coefficient of the tail in (0)(t) by 30–100% as compared to the simple ring collisions, depending on the model parameters.     

Kinetic studies of laser-induced synthesis of thin vanadium pentoxide films

The kinetics of Ar⁺ laser-induced oxidation of 100 nm thick vanadium films on glass substrates is followed by measuring time-dependent changes in reflected and transmitted intensity of a He-Ne probe beam. The growth rate of the vanadium pentoxide layer increases with increasing laser powerP as = ₀ exp(-a/P). At power densities above kW/cm² vanadium pentoxide crystallizes from the melt.     

An investigation of finite-size scaling for systems with long-range interaction: The spherical model

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr ^{–d –} , whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL ^d–d× ^d subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.     

On a Static Solution of the Einstein Equation with Incoming and Outgoing Radiation

The Einstein equation with T = k k + where k, l are null is considered with spherical symmetry and staticity. The solution has a naked singularity and is not asymptotically flat. However, it may be interpreted as an envelope for any static spherical body making it more massive. Such an interpretation and some of its implications are detailed.     

Direct observation of the second-order Stark effect of theX-B transition in molecular iodine

The second-order Stark shift of the components of the hyperfine structure of the transition¹ _g ⁺ ( = 0,j = 13, 15) ³ _ou ⁺ ( = 43,j = 12, 16) (of molecular iodine have been studied by means of saturated absorption spectroscopy in an external cell with the I₂ vapour located in an electric field. The anisotropic polarizabilities of the upper and lower levels together with the difference between the isotropic polarizabilities of the levels of the transition have been obtained.     

Weinberg Angle and Pion Beta Decay in the Spinor Strong Interaction Theory

From an isospin SU(2) × hypercharge U(1)gauge-invariant meson action for K⁺,^{+ +}, a prediction ofthe Cabbibo angle was obtained earlier. Using anotherresult of the spinor strong interaction theory that the s quark is only a littleheavier than the d quark, the above action can beextended to a weakly broken SU(3) one. The Weinbergangle is found to be 30° in the limit of this SU(3)symmetry. In the approximation and context entailing thislimit, the Weinberg angle can be removed from the listof undetermined fundamental parameters in electroweaktheory. The spinor strong interaction Lagrangian used above and applied to the decay⁺ e⁺ is shown tohold for ^{+ 0}e⁺ as well, renderingthe conserved vector current hypothesis hithertorequired to account for the latter decaysuperfluous.     

The pivot algorithm: A highly efficient Monte Carlo method for the self-avoiding walk

The pivot algorithm is a dynamic Monte Carlo algorithm, first invented by Lal, which generates self-avoiding walks (SAWs) in a canonical (fixed-N) ensemble with free endpoints (hereN is the number of steps in the walk). We find that the pivot algorithm is extraordinarily efficient: one effectively independent sample can be produced in a computer time of orderN. This paper is a comprehensive study of the pivot algorithm, including: a heuristic and numerical analysis of the acceptance fraction and autocorrelation time; an exact analysis of the pivot algorithm for ordinary random walk; a discussion of data structures and computational complexity; a rigorous proof of ergodicity; and numerical results on self-avoiding walks in two and three dimensions. Our estimates for critical exponents are=0.7496±0.0007 ind=2 and= 0.592±0.003 ind=3 (95% confidence limits), based on SAWs of lengths 200N10000 and 200N 3000, respectively.     

The S-matrix for abstract scattering systems

Let S() be the S-matrix at energy for an abstract scattering system. We derive a bound, in terms of the interaction, on integrals of the form h () S()- _HS ² d, where denotes the Hilbert-Schmidt norm.Supported by the Swiss National Science Foundation.     

High-frequency expansion of relativistic classical plasma dielectric tensor

A high-frequency sum-rule expansion is derived for the transverse elements of the relativistic classical plasma dielectric tensor in an isotropic system. The relativistic results are different from the nonrelativistic ones by a factor of ^–1(1 – ²/3c ²) for ₂ (k) and longitudinal plasmon and transverse photon frequencies, and by ^–2(1–2 ²/3c ²) for ₂ (k).     

Fock representations of the affine Lie algebraA 1 (1)

The aim of this note is to show that the affine Lie algebraA ₁ ⁽¹⁾ has a natural family _, ,v of Fock representations on the spaceC[x _i,y _j;i andj ], parametrized by (,v) C ². By corresponding the highest weight _, of _, to each (,), the parameter spaceC ₂ forms a double cover of the weight spaceC₀C –₁ with singularities at linear forms of level –2; this number is (–1)-times the dual Coxeter number. Our results contain explicit realizations of irreducible non-integrable highest wieghtA ₁ ⁽¹⁾ -modules for generic (,v).     

Measurement of the2H(d, γ)4He reaction at intermediate excitation energies

The²H(d, )⁴He differential cross section was measured at deuteron laboratory energies of 20, 24, and 28 MeV between _cm=45° and _cm=135°. AtE _d =28 MeV a complete angular distribution was determined and fitted with Legendre polynomials. The ratioR=d/d (_cm=90°)/d/d (_cm=135°) was measured for each deuteron energy.     

Interface formation and a structural phase transition for the spherical model of ferromagnetism

A detailed analysis is reported examining the local magnetic susceptibility (r), in relation to the correlation functionG(R) and correlation length , of a spherical model ferromagnet confined to geometry =L ^{d –d} × ^d ( ^d 2,d>2) under a continuous set oftwisted boundary conditions. The twist parameter in this problem may be interpreted as a measure of the geometry-dependent doping level of interfacial impurities (or antiferromagnetic seams) in theextended system at various temperatures. For _j 0, jd-d, no seams are present except at infinity, whereas if _j = 1/2, impurity saturation occurs. For 0 < _j < 1/2 the physical domain _phys =D ^{d –d} × ^d (D>L), defining the region between seams containing the origin, depends on temperature above a certain threshold (T>T ₀). Below that temperature (T>T ₀), seams are frozen at the same position (DL/2,d-d'=1), revealing a smoothly varying largescale structural phase transition.