Superluminal Signal Velocity and Causality

A superluminal signal velocity (i.e. faster than light) is said to violate causality. However, superluminal signal velocities have been measured in tunneling experiments recently. The classical dipole interaction approach by Sommerfeld and Brillouin results in a complex refractive index with a finite real part. For the tunneling process with its purely imaginary refractive index this model obtaines a zero-time traversing of tunneling barriers in agreement with wave meechanics. The information of a signal is proportional to the product of its frequency band width and its time duration. The reasons that superluminal signal velocities do not violate causality are: (i) physical signals are frequency band limited and (ii) signals have a finite time duration.     

Magnetization dynamics below of EuO and EuS

Between 4.2 K and the Curie temperatures of the cubic Heisenberg ferromagnets EuS and EuO, their homogeneous dynamic susceptibilities have been investigated by means of a broad-band reflectometer operating from 0.1 GHz to 40 GHz. For internal magnetic fields larger than the anisotropy fields H A ( T ) of both materials, their static susceptibilities exhibit a -divergence, which reveals quantitatively the dominance of dipolar-anisotropic spin-wave fluctuations. displays a Lorentzian shape the damping frequency of which obeys scaling in terms of .The scaling function agrees quantitatively with work by Frey and Schwabl [#!FS88!#] for dipolar Heisenberg ferromagnets at temperatures above T_c. Building upon their approach, the resonance frequency of the Lorentzian can be related to a memory effect in the damping determined by the large value of the relaxation rate of the longitudinal magnetization fluctuations . For EuS, this relation is substantiated directly by inelastic neutron scattering. All these features reveal the hitherto uncovered importance of the dipolar anisotropic fluctuations below T_c of ferromagnets. Received: 4 March 1998 / Accepted: 12 May 1998     

Astronomical implications of a cosmological theory of light propagation

It is shown that a simple Cosmological model of light propagation permits the existence and observation of recession velocities greater thanc, though the Einstein measure of these velocities remains less thanc in accordance with relativistic theory.The recent observation of quasars with red-shifts greater than unity is interpreted in terms of an exponential Doppler Law which is a consequence of the model. This law is further employed to provide an improved quantitative interpretation of the observed density of strong radio sources.     

Do electrons change their c-axis kinetic energy upon entering the superconducting state?

The interlayer tunneling mechanism of the cuprate high temperature superconductors involves a conversion of the confinement kinetic energy of the electrons perpendicular to the CuO-planes (c-axis) in the normal state to the pair binding energy in the superconducting state. This mechanism is discussed and the arguments are presented from the point of view of general principles. It is shown that recent measurements of the c-axis properties support the idea that the electrons substantially lower their c-axis kinetic energy upon entering the superconducting state, a change that is nearly impossible in any conventional mechanism. The proper use of a c-axis conductivity sum rule is shown to resolve puzzles involving the penetration depth and the optical measurements. Received: 5 January 1998 / Accepted: 17 March 1998     

Superluminality and parelectricity: The ammonia maser revisited

It is well known that the inversion of populations in the ammonia maser leads to stimulated emission, and hence amplification, of microwaves. However, it is not well known that an inverted medium also leads to the superluminal propagation of off-resonance, finite-band-width wave packets, whose phase, group, energy, and signal velocities, as defined by Sommerfeld and Brillouin, all exceed the vacuum speed of lightc. Einstein causality is not violated, since the front velocity isc. The inversion of populations also implies a parelectric medium with negative electric susceptibility. (Parelectric media should not be confused withparaelectric media, which are ferroelectrics just above their Curie points.) The existence of a parelectric medium implies the possibility of the levitation of an electrical charge in the vacuum above this medium, as well as stable electrostatic configurations of charges placed inside an evacuated cavity surrounded by this medium. The apparent violation of Earn-shaw's theorem will be discussed. Numerical estimates for a proposed experiment to observe parelectricity will be given.Dedicated to Walther on the ocassion of his 60 birthday     

The smooth structural change in mesoscopic Peierls chains

We investigate the Peierls transition in finite chains by exact (Lanczos) diagonalization and within a seminumerical method based on the factorization of the electron-phonon wave function (Adiabatic Ansatz, AA). AA can be applied for mesoscopic chains up to micrometer sizes and its reliability can be checked self-consistently. Our study demonstrates the important role played for finite systems by the tunneling in the double well potential. The chains are dimerized only if their size N exceeds a critical value N_c which increases with increasing phonon frequency. Quantum phonon fluctuations yield a broad transition region. This smooth Peierls transition contrasts not only to the sharp mean field transition, but also with the sharp RPA soft mode instability, although RPA partially accounts for quantum phonon fluctuations. For weak coupling the dimerization disappears below micrometer sizes; therefore, this effect could be detected experimentally in mesoscopic systems. Received: 3 January 1998 / Revised: 13 March 1998 / Accepted: 3 April 1998     

Heat,light and relativity

In this paper I argue that because we always observe nature through some spatial-temporal averaging operation we must interpret all observed statistical covariances of velocities and gradients as partial time derivatives. Systematic application of this result leads to a new interpretation of the radiation wave equation in whichc ² measures the statistical variance of velocity. The Galilean invariance ofc ² is then automatic. These results enable us to recast the Einstein-Minkowski space-time formalism within the framework of classical statistical mechanics. However, the Einstein work-energy relation and the constancy of the speed of light appear as equivalent approximations which become exact only in the adiabatic limit.     

Investigations on the soft-mode mechanism of the ferroelectric phase transition in

Dielectric and Raman spectroscopic measurements have been performed to investigate the ferroelectric phase transition in . Single crystals were grown by the zone melting method. The frequency dependence of the dielectric permittivity from 1 MHz to 1 GHz has been studied in a temperature range between 265 and 285 K. A Debye like dielectric dispersion was found, showing a critical slowing down around K. Polarized Raman spectra have been taken between 220 and 310 K. Two softening modes have been found, one of A- and another one of B / B g-symmetry. The phase transition mechanism in can be classified as partially order-disorder and partially displacive, confirming former structural results. It resembles strongly that of monoclinic . Received: 7 April 1998 / Revised: 5 June 1998 / Accepted: 16 June 1998     

Ladders in a magnetic field: a strong coupling approach

We show that non-frustrated and frustrated ladders in a magnetic field can be systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic field in the limit where the rung coupling is the dominant one. This mapping is valid in the critical region where the magnetization goes from zero to saturation. It allows one to relate the properties of the critical phase (H _c ¹, H _c ², the critical exponents) to the exchange integrals and provide quantitative estimates of the frustration needed to create a plateau at half the saturation value for different models of frustration. Received: 7 May 1998 / Revised and Accepted: 10 July 1998     

Effect of topological thresholds on thermal behaviour of germanium telluride glasses containing metallic additive

Differential Scanning Calorimetric (DSC) studies on Ag_xGe₁₅Te_85-x glasses have been undertaken over a wide range of compositions, to understand the effect of topological thresholds on thermal properties. It is found that the compositional dependence of glass transition temperature (T _g ), crystallization temperature (T _c ), activation energy for crystallization and thermal stability show anomalies at the rigidity percolation threshold. Unusual variations also observed in different thermal properties at the composition x = 20, clearly establishes the occurrence of chemical threshold in these glasses. Received: 27 January 1998 / Revised: 12 June 1998 / Accepted: 3 July 1998     

Effective interactions and superconductivity in the t-J model in the large-N limit

The feasibility of a perturbation expansion for Green's functions of the t-J model directly in terms of X-operators is demonstrated using the Baym-Kadanoff functional method. As an application we derive explicit expressions for the kernel of the linearized equation for the superconducting order parameter in leading order of a 1/N expansion. The linearized equation is solved numerically on a square lattice taking instantaneous and retarded contributions into account. Classifying the order parameter according to irreducible representations of the point group C_4v of the square lattice and according to even or odd parity in frequency we find that a reasonably strong instability occurs only for even frequency pairing with d-wavelike symmetry. The corresponding transition temperature T_c is where t is the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term and a retarded term due to charge and spin fluctuations. The latter is weakly attractive at low frequencies below ,strongly repulsive up to and attractive towards even higher energies. T_c increases with decreasing doping until a d-wavelike bond-order wave instability is encountered near optimal doping at for J=0.3. T_c is essentially linear in J and rather insensitive to an additional second-nearest neighbor hopping integral t'. A rather striking property of T_c is that it is hardly affected by the soft mode associated with the bond-order wave instability or by the Van Hove singularity in the case with second-nearest neighbor hopping. This unique feature reflects the fact that the solution of the gap equation involves momenta far away from the Fermi surface (due to the instantaneous term) and many frequencies (due to the retarded term) so that singular properties in momentum or frequency are averaged out very effectively. Received: 16 June 1998 / Accepted: 14 July 1998     

Magnetothermal instabilities in an organic superconductor

We have studied the occurrence of magnetothermal instabilities in a single crystal during field sweep magnetization experiments, equivalent to short time relaxation studies. We find instability behaviour in good agreement with a recent model by Mints, for a non-linear E(J) characteristic. In particular, we find that a decrease of the dynamic relaxation rate, characterizing the effective activation energy, precedes the unstable regime. We point out formal analogies between such instabilities and the general predictions for flux avalanches. Received: 11 December 1997 / Revised: 15 January 1998 / Accepted: 31 March 1998     

On charged mesoscopic metallic bubbles

We investigate the existence of stable charged metallic bubbles using the shell correction method. We find that for a given mesoscopic system of n atoms of a given metal and (positive) elementary charges, a metallic bubble turns out to have a lower total energy than a compact spherical cluster, whenever the charge number q is larger than a critical charge number q_c. For a magic number (n-q) of free electrons, the spherical metallic bubble may become stable against fission. Received: 17 November 1997 / Revised: 28 May 1998 / Accepted: 20 July 1998     

Nuclear fusion in charge-asymmetric muonic molecules

Nuclear fusion reactions in hydrogen-lithium muonic molecules, (where h=p,d,t) are considered and fusion rates from rotational states J=0 of the molecules are presented. Results obtained depend on the isotopic composition of the molecules and range between and . The upper limit for fusion rates from rotational states J=0 of hydrogen-helium muonic molecules, and , equal , is also found. Received: 4 December 1997 / Revised: 30 April 1998 / Accepted: 7 May 1998     

Asymptotic analysis of wall modes in a flexible tube

The stability of wall modes in a flexible tube of radius R surrounded by a viscoelastic material in the region R < r < H R in the high Reynolds number limit is studied using asymptotic techniques. The fluid is a Newtonian fluid, while the wall material is modeled as an incompressible visco-elastic solid. In the limit of high Reynolds number, the vorticity of the wall modes is confined to a region of thickness in the fluid near the wall of the tube, where the small parameter , and the Reynolds number is , and are the fluid density and viscosity, and V is the maximum fluid velocity. The regime is considered in the asymptotic analysis, where G is the shear modulus of the wall material. In this limit, the ratio of the normal stress and normal displacement in the wall, , is only a function of H and scaled wave number . There are multiple solutions for the growth rate which depend on the parameter .In the limit , which is equivalent to using a zero normal stress boundary condition for the fluid, all the roots have negative real parts, indicating that the wall modes are stable. In the limit , which corresponds to the flow in a rigid tube, the stable roots of previous studies on the flow in a rigid tube are recovered. In addition, there is one root in the limit which does not reduce to any of the rigid tube solutions determined previously. The decay rate of this solution decreases proportional to in the limit , and the frequency increases proportional to . Received: 5 November 1997 / Revised: 10 March 1998 / Accepted: 29 April 1998     

An universal relation between fractal and Euclidean (topological) dimensions of random systems

It is shown that a dimension-invariant form for fractal dimension D of random systems (where d is Euclidean dimension of the embedding space) is in good agreement with results of numerical simulations performed by different authors for critical (p=p _c ) and subcritical (p<p _c ) percolation, for lattice animals, and for different aggregation processes. Received: 9 July 1998 / Revised and Accepted: 12 July 1998     

Elliptic curves from finite order recursions or non-involutive permutations for discrete dynamical systems and lattice statistical mechanics

We study birational mappings generated by matrix inversion and permutations of the entries of matrices. For q=3 we have performed a systematic examination of all the birational mappings associated with permutations of matrices in order to find integrable mappings and some finite order recursions. This exhaustive analysis gives, among 30 462 classes of mappings, 20 classes of integrable birational mappings, 8 classes associated with integrable recursions and 44 classes yielding finite order recursions. An exhaustive analysis (with a constraint on the diagonal entries) has also been performed for matrices: we have found 880 new classes of mappings associated with integrable recursions. We have visualized the orbits of the birational mappings corresponding to these 880 classes. Most correspond to elliptic curves and very few to surfaces or higher dimensional algebraic varieties. All these new examples show that integrability can actually correspond to non-involutive permutations. The analysis of the integrable cases specific of a particular size of the matrix and a careful examination of the non-involutive permutations, shed some light on the integrability of such birational mappings. Received: 9 February 1998 / Revised: 13 March 1998 / Accepted: 17 March 1998     

Characterization of photorefractive materials by spontaneous noncolinear frequency doubling

‘Spontaneous’ noncolinear frequency doubling (SNCFD) is a type of optical second-harmonic generation (SHG) that uses scattered light to provide additional fundamental beams in order to accomplish noncolinear phase matching. Based on a novel algorithm for the automated evaluation of the resulting ring patterns, we present an easy-to-apply, sensitive, and non-destructive method for the characterization of photorefractive materials, yielding two-dimensional spatial resolution. As applications of the technique, examples for the characterization of lithium niobate crystals are presented. Received: 30 October 1998 / Revised version: 17 December 1998 / Published online: 7 April 1999