Table of contents

An attempt to construct a cosmological scenario directly from string theory is made. Cosmological string theory was presented by Antoniadis, Bachas, Ellis and Nanopoulos. They also expect loop effects on cosmological string theory. In this paper, we point out the other importance of the one-loop effect, the finite temperature effect. The equations of motion for background geometry at finite temperature are given. We address a problem on derivation of the effective action at nonzero temperature.

The one-loop effective action (EA) in conformal (super) gravity on a background which is described by a homogeneous isotropic spatially flat metric with nontrivial topology is calculated. Nonsingular cosmologies with nontrivial topology are constructed on the basis of this EA. A cosmological model with a metric corresponding to an inflationary universe and reducing torsion is obtained in the framework of quantum conformal gravity with torsion.

We investigate the damage or Hamming distance between two configurations of Ising spins. We find an exact relation between the difference of the two possible types of damage and the spin-spin correlation function, which is generally valid. For the specific case of ferromagnetic interactions, heat bath dynamics and same sequence of random numbers, this relation involves only one type of damage. The susceptibility and the magnetization can also be expressed in terms of the damage. Numerical determination of the damage for the 2d Ising model is not only an efficient way to calculate correlation functions but also gives access to spin fluctuations visualized as clusters of damaged sites which have a fractal dimension d−β/ν at T_c and whose size distribution is also related to static exponents.

A quantum Ising spin chain with two-valued nearest-neighbour couplings arranged in a quasi-periodic sequence is considered, in the presence of a uniform transverse field. The scaling properties of the energy spectrum of the model are analytically determined. The system can undergo a phase transition both when the two couplings have equal sign (ferro- or antiferromagnetic couplings) and when they have opposite sign (frustrated system). The critical point is explicitly obtained; the critical behaviour is shown to be the same as in the periodic case.

Configurational statistics of heteropolymer with quenched disordered sequence of links is investigated with the aid of replica approach. It is shown that frozen states with broken ergodicity exist in this system. The features of nonergodic state as well as the freezing transition depend drastically on the dimensionality of space d. For d > 2 the model is analogous to Potts glass and there exists the first-order phase transition with discontinuous behaviour of the order parameter–replica overlaps–but without specific heat. The set of states in the frozen phase is not ultrametric and the number of states decreases when the heterogeneity of the chain increases. For d < 2 the transition is of the second order, the set of states is ultrametric and the number of states does not depend on heterogeneity of the polymer.

The first direct spectroscopic determination of the frequency of the ν₁ vibration of H₃⁺ is reported: ω₁ = (3178.29 ± 0.1) cm⁻¹. This value was derived from the limits of Rydberg series of H₃. Rydberg states of H₃ were prepared by using laser excitation of a fast molecular beam and detected by means of H₃⁺ ions formed by autoionization. Vibrational frequencies of H₃ were accurately determined for the first time. Perturbations in the Rydberg series and Fano profiles were observed.

Pionium (Pi), the Coulomb bound state of a positive pion π⁺ and an electron e⁻, has been formed with the beam-foil technique in vacuum with a total yield of 4.4(4) · 10⁻⁵ per incoming pion. Neutral Pi was selected by a combined technique of magnetic sweeping and time-of-flight separation from the charged π⁺ beam. Pi was identified by the characteristic decay chain π⁺ → μ⁺ν_μ plus μ⁺ → e⁺ν_eμ and the velocity distribution of the slow pions and neutral Pi. This distribution was calculated with a Monte Carlo simulation and is in good agreement with the measurements.

The amplitude noise of a laser diode submitted to electronic feedback is evaluated using a new circuit theory. It is postulated that the electron-hole injection rate equals the photon generation rate at any time, and Nyquist-like noise sources are introduced. Previous results based on quantum mechanics are recovered. It is found that the amplitude fluctuations of an optical beam in the coherent state can be squeezed below shot noise by feeding back the driving current of a laser amplifier.

Kramers theory is applied to the expulsion of polymeric surfactants out of aggregates. For saturated monolayers of A-B diblock copolymers at a flat interface between a B melt and a good solvent the rate constant scales as b ≈ exp[−γa²N_B^2/3/kT]N_A^−21/11, where N_A and N_B are the polymerization indices of the two blocks, γ is the surface tension of the interface and a is a typical monomer size. For starlike micelles b scales as b ≈ exp[−γa²N_B^2/3/kT] · N_A^−9/5N_B^−2/25. The polymeric nature of these surfactants imposes special modifications on the theory: i) in certain stages the displacement along the reaction coordinate is not the relevant length scale. ii) The exterior potential tail may replace the saddle point region in determining the rate.

An expression for the contribution of trapped entanglements to stress in a cross-linked polymer network is obtained using a slip-link model. This is intended as a simplified alternative to the replica calculation (Ball et al.), and is a more exact treatment of the "hoop" model (Adolf) and a generalization of the "belt-loop" model (Kosc). We discuss the relationship between slip-link and tube models and consider under what circumstances the two ideas are equivalent.

We present the first ¹⁷O NMR data obtained in YBa₂Cu₃O_7-δ powder with T_c = 90 K in which oxygen sites on Cu-O chains had been selectively populated by a gas exchange process performed at low temperature. A comparison between fully exchanged and chain only exchanged samples suggests that magnetic-field-swept spectra cannot discriminate between both kinds of samples. Fourier-transformed spectra do however provide a very clear assignment between plane and chain-bridge sites. The spin-lattice relaxation of chain sites measured between 4.2 and 300 K is dramatically nonexponential, as expected for nuclei in the presence of an important quadrupolar interaction. Our data show the existence of a shortening of the chain relaxation in a limited temperature domain slightly below T_c. This hump of relaxation supports the absence of zeros of the superconducting order parameter over the Fermi surface and the s-symmetry for the pair wave function.

Using nonresonant microwave absorption, flux creep in zero external field can conveniently be measured in single crystals of Y₁Ba₂Cu₃O_7-x. The flux decay follows a logarithmic decay law over at least 4 time decades, without any deviation even in the sub-second time regime. The measurements are performed with a preparation field B_ext ≪ H_c1, i.e. deep in the Meissner phase. The observed scaling of the logarithmic decay rate R ∼ B_ext^3±0.5 is not consistent with the model of thermally activated flux creep, which might only be applicable for B_ext > H_c1. The new experimental method has the potential to prepare and probe the transient sample magnetization in up-to-now unaccessible time regimes.

We present the results of our measurements of the lattice constants and magnetic susceptibility of the pseudo-ternary system CeRh₂Si_2-xGe_x which crystallizes in the tetragonal ThCr₂Si₂ structure. Both of the cell constants a and c increase linearly with x. The magnetic ordering temperature T_N exhibits initially an enhancement with the increase in x (T_N = 36.9 K for x = 0 and 38.3 K for x = 0.125) and then decreases as x continues to increase further. These results, along with those on the pressure dependence of T_N in CeRh₂Si₂, can be understood on the basis of the Doniach's model of a Kondo necklace. We discuss also the applicability of this model to describe the strong correlation between the structural aspects and the ground-state properties of the whole series of Ce-based ternaries CeM₂X₂ (M = 3d, 4d and 5d elements; X = Si, Ge) of the ThCr₂Si₂ structure.

We show that Fe_xZn_1-xF₂ with x = 0.25 displays spin glass characteristics, in contrast to the random-field behaviour this system exhibits at larger concentrations (x > 0.4). A scaling analysis of the nonlinear susceptibility data above the freezing temperature gives critical exponents in excellent agreement with those found in metallic systems and also compatible with theoretical predictions for short-range Ising spin glasses. These results provide strong evidence of universality of the Ising critical behaviour in spin glasses regardless of their insulating or metallic nature.

The performance of an iterative learning rule for neural networks of spin-glass-type is studied. The algorithm minimizes a cost function quadratic in the synaptic couplings. An exact expression for the time development of the cost function is derived for the case of extensively many random patterns in large networks. A learning time as a function of the storage ratio α (number of patterns/number of spins) is calculated. It diverges as (1 − α)⁻² as the storage ratio approaches 1.

The retrieval properties of a Hopfield model of associative memory as a function of external fields correlated with the input pattern are studied. We show by analytical calculations within replica symmetric theory and by numerical simulations that the system successfully retrieves information even if the number of stored patterns exceeds the critical value of the pure Hopfield model.