The hierarchicalφ 4-trajectory by perturbation theory in a running coupling and its logarithmby perturbation theory in a running coupling and its logarithm

We compute the hierarchical ⁴- in terms of perturbation theory in a running coupling. In the three-dimensional case we resolve a singularity due to resonance of power counting factors in terms of logarithms of the running coupling. Numerical data are presented and the limits of validity explored. We also compute moving eigenvalues and eigenvectors on the trajectory as well as their fusion rules.     

Angular Spectrum of Modified Cylindrical Wave-Functions

The plane-wave expansion of the modified cylindrical functions, i.e., the product of the mth-order modified Bessel function K _m and the angular factor exp(im), is given. This expansion, which is found to involve only evanescent plane waves, may be used in the study of coupling phenomena between circular and planar guiding structures.     

A nonequilibrium entropy for dynamical systems

It is proposed to define entropy for nonequilibrium ensembles using a method of coarse graining which partitions phase space into sets which typically have zero measure. These are chosen by considering the totality of future possibilities for observation on the system. It is shown that this entropy is necessarily a nondecreasing function of the timet. There is no contradiction with the reversibility of the laws of motion because this method of coarse graining is asymmetric under time reversal. Under suitable conditions (which are stated explicitly) this entropy approaches the equilibrium entropy ast+ and the fine-grained entropy ast–. In particular, the conditions can always be satisfied if the system is aK-system, as in the Sinai billiard models. Some theorems are given which give information about whether it is possible to generate the partition used here for coarse graining from time translates of a finite partition, and at the same time elucidate the connection between our concept of entropy and the entropy invariant of Kolmogorov and Sinai.Research supported in part by NSF grants PHY78-03816 and PHY78-15920.     

Anomalous fluctuations in random walk dynamics

The anomalous dispersion of noninteracting particles randomly walking in a network is considered. It is shown that the existence of large dangling branches attached to a backbone induces a l/f-like behavior in the current autocorrelation function at low frequencies. The waiting times associated with dangling loops scale liket ^–3/2. The size of the dangling branches provides a lower cutoff to the power law behavior. When the side branches are infinite, self-similar structures, the power law behavior persists up to a zero frequency. The currents we consider are created either by a bias on the random walk or by a current source. We consider both the total current, which is often referred to in the literature, and the current measured at endpoints of a specimen attached to a (model) battery. The differences and similarities between the two corresponding correlations are analyzed. In particular, we find that in the second case l/f noise exists only for large bias. When a statistical distribution of dangling branches is considered, we find that the largest power of frequency in the spectrum is 1.13. Much of our results are true when the dangling branches are replaced by traps having waiting time distributions that equal those of the branches. The waiting time associated with a power law distribution of dangling loops (m ^–x:m is the length of the loop) scales liket ^–1 –(x/2). However, it is shown that geometry alone can be responsible for the appearance of power laws in the spectra. Random geometry can be regarded as a model (or source) of random hopping times.     

“Free” Evolution of Multi-particle Excitations in the Glauber Dynamics at High Temperature

The paper is devoted to the spectral properties of the Glauber dynamics for the Ising model at high temperature 1/. It is proven that for sufficiently small || there is an invariant subspace, in which the dynamics can be described as a free multi-particle evolution, provided that the one-particle subspace is singled out. The proof is based upon the Haag–Ruelle scattering theory.     

Lp-Spectral Theory of Locally Symmetric Spaces with $\mathbb{Q}$-Rank One

We study the L ^p -spectrum of the Laplace–Beltrami operator on certain complete locally symmetric spaces with finite volume and arithmetic fundamental group Γ whose universal covering X is a symmetric space of non-compact type. We also show, how the obtained results for locally symmetric spaces can be generalized to manifolds with cusps of rank one.      

A Generally Covariant Field Equation for Gravitation and Electromagnetism

A generally covariant field equation is developed for gravitation and electromagnetism by considering the metric vector q in curvilinear, non-Euclidean spacetime. The field equation is

Absence of continuous symmetry breaking in a one-dimensional n−2 model

For a one-dimensional array ofS ^N–1 spins (N 2) with isotropic pair interactions (and more general systems) with J(j–i) obeying sup_n[n^–1 ₁ ⁿ j ²|J(j)|]<, we prove that every equilibrium state is invariant under the natural action ofSO(N). In particular, there is no long-range order of the conventional type. Included is the caseJ(n)=n ^–2.Research partially supported by U.S.N.S.F. Grant No. MCS-78-01885.S. Fairchild Scholar at Caltech. On leave from Departments of Mathematics and Physics, Princeton University, Princeton, New Jersey 08544.     

Infrared asymptotic freedom of a hierarchical φ 3 6 lattice theory

For the weakly coupled lattice ₃ ⁶ theory in a hierarchical model approximation a nonperturbative renormalization group analysis in the spirit of Gawedzki and Kupiainen is performed to study the flow of the effective actions. We deduce a domain of attraction to the tricritical (Gaussian) fixed point. The two relevant coupling constants of the problem are controlled by analytic continuation to complex domains, tracing their images under the renormalization group iterations.     

The Biot-Savart-Ampère law and the vacuum fieldB (3)

It is shown that the longitudinal vacuum fieldB ⁽³⁾ emerges from the Biot-Savart-Ampère law governing the motion of an electron with intrinsic spin moving at the speed of light, in which case the expression forB ⁽³⁾ is identical with that obtained from the Dirac equation of one electron accelerated to the speed of light by an electromagnetic field. Use of an O(3), non-Abelian, gauge geometry forB ⁽³⁾ identifies the quantized photon momentum appearing in the Dirac equation witheA ⁽⁰⁾, wheree is the charge on the electron andA ⁽⁰⁾ the amplitude of the vector potential. The condition =eA ⁽⁰⁾ can be obtained in turn from the relativistic Hamilton-Jacobi equation of an electron accelerated to the speed of light by an electromagnetic field.     

Effect of Nd on the Superconductivity of Nd1+x Ba2-x Cu3O y with 0.1 ≤ x ≤ 0.35

The effect of Nd substitution at the Ba sites has been studied in Nd_1+x Ba_2-x Cu₃O _y system for 0.1 x 0.35. Orthorhombic to tetragonal structural phase transition occurs at about x = 0.17. With the increase of Nd, the T _c value decreases and T increases, where T is the difference between the onset and critical temperatures and indicates the sharpness of the transition. These changes are explained by ac-susceptibility measurements on Nd_1.1Ba_1.9Cu₃O_7.12 at 0.10 Oe. The susceptibility curves show the presence of about four phases, which are not detectable by X-ray diffraction technique.     

On the direct observation of the gas-dynamics of laser-pulse sputtering of polymers

We bring together a wide range of ideas relating to the gas-dynamic effects that are now recognized to play a leading role in laser-pulse sputtering. The ideas are grouped according to three basic models. (a) In the effusion model one deals with particles which are released from a target surface, form a Knudsen layer (KL), and then enter an unsteady adiabatic expansion (UAE). When the release terminates at time t=_r there is an abrupt change at the surface from positive to zero flow velocity, which means that particles moving towards the surface are reflected. The flow breaks up into three regions and analytical solutions exist for all aspects of this flow. (b) In the recondensation model the comportment of the target is initially like that of the effusion model but when the release terminates at t=_r the change at the surface is from positive to negative flow velocity, meaning that particles which move towards the surface recondense. Only numerical solutions presently exist (due to Sibold and Urbassek) but they are sufficient to show that the flow breaks up into two (not three) regions. (c) The outflow model could be described as the escape of gas from a finite reservoir, a well-known problem since it describes some aspects of guns. In its application to laser sputtering it is assumed that bond-breakage occurs rapidly over a characteristic depth and the resulting gas-like particles then flow out in a UAE; there is no formal KL.For part II, in which explicit photographs of laser-sputtered particles are analyzed, see [1]     

Optically pumped submillimeter laser lines from CH2F2 and CD2Cl2 using a12C18O2 CW laser

Thirty-nine new submillimetre laser lines in CH₂F₂ and twelve in CD₂Cl₂ have been obtained in a Fabry-Perot FIR resonator by optically pumping with a CW¹²C¹⁸O₂ laser. The wavelength range obtained for CH₂F₂ is 126m to 1091m and for CD₂Cl₂ 212m to 774m. The wavelength measurements are accurate to within 5.10^–3. The relative polarisations of the pump laser and the FIR laser output were also determined. Tentative assignments of the IR and FIR transitions were made using existing microwave data.     

In Situ Detection of the Pathogen Indicator E. coli Using Active Laser-Induced Fluorescence Imaging and Defined Substrate Conversion

To remotely sense the pathogen indicator E. coli in aquatic systems, we used laser-induced fluorescence imaging to detect the signature produced by the in situ conversion of the defined substrate medium ECMUG. The presence of the enzyme -glucuronidase, indicated by the activity of the fluorogenic 4-methylumbelliferyl (4MU)--D-glucuronide (MUG), is specific to the presence of this organism. Substrate conversion was accomplished in a small stream impacted by non-point source wastewater inputs. Sample chambers slowly inoculated source water with 100 ml of ECMUG media in direct sunlight. Luminescence spectroscopy monitored conversion activity and detected liberation of the 4 MU fluorochrome in 2.5 hours. Detection by laser-induced fluorescence imaging followed at dusk and indicated bright blue emissions typical for converted media. This technique lays the foundation for active remote sensing of source water contamination.     

Unification of electromagnetism and gravitation: The equations of electrodynamics derived from the Riemann tensor in general relativity

The equations of free-space electrodynamics are derived directly from the Riemann curvature tensor and the Bianchi identity of general relativity by contracting on two indices to give a novel antisymmetric Ricci tensor. Within a factore/h, this is the field-strength tensor G of free-space electrodynamics. The Bianchi identity for G describes free-space electrodynamics in a manner analogous to, but more general than, Maxwell's equations for electrodynamics, the critical difference being the existence in general and special relativity of the Evans-Vigier fieldB ⁽³⁾.     

OPTIS—An Einstein Mission for Improved Tests of Special and General Relativity

The mission OPTIS aims at improving tests of the foundations of Special and General Relativity by up to three orders of magnitude. The individual tests concern the isotropy and constancy of the speed of light, the time dilation (or Doppler effect), the universality of the gravitational redshift with various combinations of high precision clocks. Furthermore, laser tracking and a laser link allows a strongly improved measurement of the gravitomagnetic Lense–Thirring effect, of the gravitoelectric Einstein perigee advance, of the gravitational redshift, and a search for deviations from Newtonian gravity.For this mission, technologies are required which have been used recently to carry through the most precise tests of Special Relativity. The precision of these tests can be further increased under space conditions thanks to longer integration times, larger changes in the orbital velocity, and larger differences of the gravitational potential. Furthermore, very precise laser tracking and linking of satellites is a well established technique and will provide, in combination with the active drag–free control system, very accurate orbit data. The core technologies for OPTIS are optical cavities, highly stabilized lasers, capacitive gravitational reference sensors, drag–free control, ion clocks, frequency combs, and laser tracking systems. These technologies are also key technologies for other future missions.     

“Projective relativity” and magnetohydrodynamics

The geometrical structure of the Castelnuovo space-time and the Fantappié group are analyzed with the Inönj-Wigner method of contraction of a group with respect to the various subgroups. If we utilize the two vectorsposition andvelocity, we can study the structure of the magnetohydrodynamics tensor. It follows that from projective magnetohydrodynamics we can deduce as limiting cases four theories (two by two duals in the sense of the classical projective geometry).     

A comment on “critique of home and sengupta's derivation of a Bell inequality”

We clarify some aspects of our derivation of a Bell-type inequality, in response to a paper by Elby.The following comments refer to Andrew Elby's discussion note immediately following our present paper.(a) We wish to stress that physical distinction between NC and LC is particularly important in the case of local realist theories violating NC for any single system but satisfying LC for any correlated many-component system. Arguments given by Elby do not rule out a reasonable theory violating NC but obeying LC. Therefore, a physically meaningful possibility exists that while Bell's inequality derived from NC is violated for a single system, the inequality derived from LC is satisfied for correlated and spatially separated (non-interacting) systems. It is precisely this possibility which was explored by HS in deriving Bell's inequality from NC.(b) Since Elby's formulation of locality condition necessarily involves a relativistic constraint at the level of individual measurements, it is pointless to discuss its compatibility with predictions derived from non-relativistic quantum mechanics, which is well known to allow superluminal communication by mechanisms such as wavepacket travel or spread. Recently this aspect has been discussed in depth by P. Ghose and D. Home,Phys. Rev. A 43, 6382 (1991). It needs to be stressed that our formulation of LC is in line with the separability condition articulated by Einstein in different contexts; see, for example,J. Franklin Inst. 221, 349 (1936), reprinted inIdeas and Opinions (Crown, New York, 1954), pp. 290–323.On leave from: Department of Physics, Bose Institute, Calcutta 700009, India.     

Mechanisms of the generation of circular dichroism of singlet-triplet transitions

Possible mechanisms of the generation of circular dichroism of singlet-triplet transitions localized in achiral chromophores are investigated in this work. The estimates show that the spin-orbit interaction of the optical electrons in the field of the electrons and nuclei of the perturbing groups (the externall-s interaction) makes a contribution comparable in order of magnitude to the internal.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 7–10, July, 1981.     

Derivation of the Tully—Fisher Law: Doubts About the Necessity and Existence of Halo Dark Matter

For disk galaxies the fourth power of the circular velocity ⁴ _c of stars around thecore of the galaxy is proportional to the luminosity L, ⁴ _c L (Tully—Fisher law).Since L is proportional to the mass M of the galaxy, it follows that ⁴ _c M.Newtonian mechanics, however, yields ² _c = GM/r for a circular motion. In orderto rectify this big difference, astronomers assume the existence of dark matter.We derive the equation of motion of a star moving in the central field of a galaxyand show that, for a circular motion, it yields a term of the form ⁴ _c GMc/,where G is Newton's gravitational constant, c is the speed of light, and is theHubble time. This puts in doubt the existence of halo dark matter for galaxies.