First order phase transitions studied in the dynamical ensemble

A knowledge of the density of states () of a many particle system ( is the energy per particle) contains the complete information about its thermal behaviour. In this paper it will be demonstrated that () can very efficiently and precisely be determined by a Monte Carlo calculation in an ensemble where the system of interest is coupled to another system of comparable size. This is in contrast to the canonical approach where the system of interest is coupled to an infinite bath at a temperatureT. The usefulness of the approach will be demonstrated for theq-states Potts model withq=4, 5, and 8 where the numerical data can be compared with exact results. In our numerical data we can clearly identify a first order phase transition forq5 and a second order transition forq=4.     

Second-harmonic generated by self-squeezed light in isotropic medium. The role of light intensity-dependent effects and molecular-statistical structure

An isotropic medium with electrically removed centre of symmetry in which a fundamental wave at frequency generates the second harmonic at 2 is considered. The two waves give rise to self-acting effects modifying the refractive indices at and/or 2 (selfinduced ellipse rotation, optical Kerr effect). For this physical situation, an effective interaction Hamiltonian is introduced involving nonlinear coupling parameters, discussed versus the dc electric field and temperature as well as the density, concentration and molecular structure of the medium. The solutions of the respective quantum equations for the field operators at and 2 permit, in particular, the calculation of the variances for a novel process of second-harmonic generation by light, self-squeezed in an isotropic medium. It is shown that squeezing in the out-of-phase component of the second harmonic beam follows, with some delay, after self-squeezing in the in-phase component of the fundamental beam.Sponsored by the Polish Academy of Sciences, Project CPBP 01.12     

Note: An Unusual Route to General Relativity Equation in Presence of Dust in Irrotational Motion

We show that the general relativity theory equation, in presence of pressureless matter (dust) in irrotational motion, can be recovered from a scalar-tensor like variational approach. In this approach, the kinetic energy, , of a dynamical scalar field , couples directly to gravity. The lagrangian, exempt of explicit matter term, is varied in the framework of the first order formalism, and a conformal transformation, restoring riemannian geometry, is made. In this approach, it turns out that a non-empty spacetime is necessarily four-dimensional.     

Screw dislocation dipole in non-linear continuum

The elastic field of a screw dislocation dipole, i.e., of two parallel screw dislocations of opposite signs is found within the non-linear isotropic theory of elasticity of second order. The linear solution for a screw dislocation dipole with hollow cores is taken for the first approximation and the second order terms are calculated using the method of stress functions developed and applied previously on one screw dislocation by Kröner and Seeger. The stress field and the volume dilatation is discussed in detail for a dipole with singular dislocation lines taken as limiting case of a dipole with hollow cores.ikova 22, Brno, Czechoslovakia.Na Slovance 2, Praha 8, Czechoslovakia.     

Three-surface twistors and conformal embedding

The three-surface twistor equation is defined for an arbitrary three-surface in an arbitrary curved spaceM. It is proved that three-surface twistors exist on 2 if and only if can be embedded in a conformally flat space-time with the same first and second fundamental forms.     

Dual-mode optical fibres with zero intermodal dispersion

An exact analytical approach to the synthesis of the refractive-index profile of dual-mode optical fibres with zero intermodal dispersion is presented, and the computer-aided, trial-and-error synthesis of the optimal profile is described. The synthesis is based on inverse scattering theory. Self-consistency of free potentials corresponding to individual modes was attained by numerical methods. The characteristics of the optical fibres with synthetized profiles were analysed, the optimization constraints were specified, and an optimum profile was found. The results can be used for the design of broadband optical fibres.Notation (r), (r) Single and double derivatives - C _l(r) Determinant of a matrix det - k _l (r) Vector - k _l (r) _l (r) The scalar products of the vectors - K _l(wr) The modified Bessel function of the second kind - _l(wr) The modified Bessel function of the first kind - J _l(uaR) The Bessel function of the first kind     

On the activity of carbon in ferrite

Two different deviations from the Henry's law were found for carbon in ferrite. The first deviation follows from the concentration dependence of the excess change in entropy accompanying the solution of carbon in ferrite as found by Schürmann et al. and the second one was found by evaluating the isothermal plots of the activity of carbon as a function of its concentration from other experimental data found in the literature. It has been pointed out that the first deviation is improbable and a simple hypothesis was proposed for explaining the second one. Our magnetic relaxation measurements performed for the special decisive case confirmed the second deviation, but they also excluded the proposed hypothesis. The second deviation was therefore explained by more complicated model whereas the first one by inadequate treatment of experimental data.The author would like to thank Dr. J. ermák and Dr. J. Laek for helpful discussions. He is also grateful to Dr. B. esták for his standing interest in this work.     

Properties of a weak link with tunable strength in a quasi-one-dimensional superconductor

In a superconducting whisker a region of weakened superconductivity (weak link) has been induced by a second crystal carrying a control current and crossing the first one. By varying the control current the grade of weakness could be continuously adjusted and its influence on the voltage-current characteristics of the weak link could be investigated.     

Two-Time-Scale Relaxation Towards Thermal Equilibrium of the Enigmatic Piston

We investigate the evolution of a system composed of N non-interacting point particles of mass m in a container divided into two chambers by a movable adiabatic piston of mass Mm. Using a two-time-scale perturbation approach in terms of the small parameter =2m/(M+m), we show that the evolution towards thermal equilibrium proceeds in two stages. The first stage is a fast, deterministic, adiabatic relaxation towards mechanical equilibrium. The second stage, which takes place at times (M), is a slow fluctuation-driven, diathermic relaxation towards thermal equilibrium. A very simple equation is derived which shows that in the second stage, the position of the piston is given by X _M (t)= L[1/2–(t)] where the function is independent of M. Numerical simulations support the assumptions underlying our analytical derivations and illustrate the large mass range in which the picture holds.     

Diffusion in a bistable potential: A systematic WKB treatment

We study the distributionP of a single stochastic variable, the evolution of which is described by a Fokker-Planck equation with a first moment deriving from a bistable potential, in the limit of constant and small diffusion coefficient. A systematic WKB analysis of the lowest eigenmodes of the equivalent Schrödinger-like equation yields the following results: the final approach to equilibrium is governed by the Kramers high-viscosity rate, which is shown to be exact in this limit; for intermediate times, we show that Suzuki's scaling statement does give the correct behavior for the transition between the one-peak and the two-peak structure forP. However, the intermediate time domain also contains a second half, whereP enters the diffusive equilibrium regions, characterized by a time scale of the same order as Suzuki's time.     

Electromagnetic-gravitational energy systems

Two methods axe considered to tap the earths' rotational energy. This ancient collapsed gravitational energy exceeds the earth-lunar binding energy. One involves an orbiting electromagnetic-gravitational coupling system whereby the earth's rotation, with its nonuniform mass distribution, first uses gravity to add orbital energy to a satellite, similar to a planetary flyby.rd The second stage involves enhanced satellite drag as current-carrying coils withdraw the added orbital energy as they pass through the earth's nonuniform magnetic field. A second more direct method couples the earth's rotational motion using conducting wires moving through the noncorotating part (ionospheric current systems) of the geomagnetic field. These methods, although not immediately feasible, are considerably more efficient than using pure gravitational coupling to earth-moon tides.     

Correlation inequalities for multicomponent rotators

A recent approach to G.H.S. and Lebowitz inequalities is used to prove Griffiths' second inequality for 3 and 4 component models (e.g. Classical Heisenberg model, ||⁴ Euclidean fields). Applications include monotonicity of the mass gap in the external field, and two-sided inequalities between parallel and transverse correlations.     

Effect of neon mixing on vibrational temperature of molecular nitrogen plasma generated at 13.56 MHz

Optical emission spectroscopy is used to investigate the effect of neon mixing on the electron temperature and vibrational temperature of second positive and first negative system of nitrogen plasma generated by 13.56 MHZ RF generator. The electron temperature is determined from NeI lines intensities, using Boltzman's plot. The relative changes in vibrational population of N₂(C³Πu) and states with neon mixing are monitored by measuring the emission intensities of second positive and first negative system of nitrogen molecules. Vibrational temperature is calculated for the sequences Δν=0,1,−2, that follows the Boltzman's distribution. It is found that electron temperature as well as vibrational temperature of second positive and first negative system can be raised significantly by mixing neon in nitrogen plasma. Vibrational temperature at 250 watt RF power, of second positive system is raised up to 0.67 eV at 90% neon where as for first negative system it is raised up to 0.78 eV. It is found that vibrational temperature increases with the gas pressure.     

Low-frequency noise of Gunn-oscillator first and second harmonics

The low-frequency modulation noise of a Gunn oscillator is analyzed assuming that the diode ac voltage contains the first and second harmonics. The requirements for stable operation with allowance for the mutual effect of the harmonics are examined. It is shown that the procedure for determination of external Q according to frequency pulling is not applicable to such an oscillator. The fluctuational characteristics of a Gunn oscillator with outputs at the first and second harmonics are investigated experimentally. The experimental data are in qualitative agreement with the analysis results.Presented at All-Union Coordinating Conference Low-Frequency Noise in Semiconductor Devices (Chernogolovka, Moscow Region, June, 1991).St. Petersburg State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 2, pp. 226–241, February, 1994.     

The blob algebra and the periodic Temperley-Lieb algebra

We determine the structure of two variations on the Temperley-Lieb algebra, both used for dealing with special kinds of boundary conditions in statistical mechanics models. The first is a new algebra, the blob algebra. We determine both the generic and all the exceptional structures for this two parameter algebra. The second is the periodic Temperley-Lieb algebra. The generic structure and part of the exceptional structure of this algebra have already been studied. We complete the analysis using results from the study of the blob algebra.     

Phase diagram of a simple model of Eu p Sr1−p S

A random site Ising model on the checkerboard square lattice with first neighbor interactionsJ in all first neighbor bonds and second neighbor interactionsJ in red squares is considered as a simple model of the dilute spin glass of Eu _p Sr_1–p S. The phase boundary between the paramagnetic and ferromagnetic phases, and that between the paramagnetic and spin glass phases are calculated. The obtained phase diagram is qualitatively similar to the experimental result by Maletta and Convert.     

Relativistic transformations of thermodynamic quantities

A unique solution is proposed to the problem of how thermodynamic processes between thermodynamic systems at relative rest appear to a moving observer. Assuming only transformations for entropy, pressure, and volume and the invariance of the fundamental thermodynamic equation, one can derive transformations for (thermodynamic) energy and temperature. The invariance of the first and second laws entails transformations for work and heat. All thermodynamic relations become Lorentz-invariant. The transformations thus derived are in principle equivalent to those of Einstein and Planck, except that our expressions for energy and work do not include the mass motion energy. This results in a simpler formulation and endows our transformations (especially that of temperature) with a straightforward physical interpretation.     

Efficiency of the microcanonical over-relaxation algorithm for vector spins analyzing first and second order transitions

We simulate vectorial spin systems solely with the microcanonical over-relaxation algorithm where the temperature is calculated by a formula of Nurdin and Schotte. We show that this procedure is the most efficient local algorithm besides the nonlocal cluster algorithm not only for first order transitions but also for second order ones. A comparison is made with the Metropolis, heat bath, multicanonical and the Creutzs demon algorithms. We study, using these algorithms, the frustrated J1-J2 model on a cubic lattice for XY, Heisenberg and O(4) spins. These models have a breakdown of symmetry Z3 SO(N)/SO(N-1) for the number N = 2,3,4 of spin components leading to transitions of first order. We show that they are strongly first order. Then, to test the over-relaxation update for second order transitions, we study a ferromagnet on a cubic lattice and a frustrated antiferromagnet on a stacked triangular lattice. We finally point out the advantages and the flaws of the over-relaxation procedure.     

Proof of a quantum mechanical nonlocal influence

First it is proved that, in a deterministic theory, Malus' law requires that, if a photon is successively transmitted by two polarizers with appropriately chosen settings, the first transmission influences a hidden variable (co-) determining the second one. We derive from this that in an ideal EPR experiment (giving the result predicted by quantum mechanics for two correlated photons transmitted by two polarizers with suitably chosen settings) there has to be a nonlocal influence from the first transmission interaction to the second. Subsequently we argue that we can abandon determinism as an assumption so that the locality hypothesis is in any case untenable if the predictions of quantum mechanics are all correct.     

The Polyakov path integral over bordered surfaces (the open string amplitudes)

We use the Feynman functional quantization scheme adapted to the gauge theories with reparametrization invariance to the functional covariant first quantization of the open bosonic BDHP string in a position representation. The consistent functional integral representation of the open string propagator is derived and evaluated. This result is used as a starting point for two kinds of constructions of the off-shell multiloop open string amplitudes. The general idea of the presented approach is to consider the off-shell amplitudes as functionals on the space of contours endowed with an intrinsic metric or on the space /₊.