Table of contents

Lee has recently described a rejection-free' microcanonical Monte Carlo technique in which data is only collected near the centre of a microcanonical window. It is shown here that data can be efficiently collected from other energy levels in the window and that a rejection-free' technique can also be established for these levels. This leads to a significant improvement in efficiency over the method of Lee.

The superconformal algebras of Ademollo et al are generalized to a multi-index form. The structure obtained is similar to the Moyal bracket analogue of the Neveu - Schwarz algebra.

We develop an asymptotic method that yields analytic results for the upper bounds for the ensemble averaged reaction front position and speed in a d-dimensional high Reynolds number turbulent flow. The chemical reaction is assumed to be of Kolmogorov - Petrovskii - Piskunov type and the velocity is an incompressible Gaussian random field. In addition to the general formalism, some examples are worked out in detail.

The existence of a denaturation temperature, , in the folding of random heteropolymers allows us to determine the distribution of enthalpy levels within the space of contact patterns. The resulting statistics yield a metastable ensemble of foldings dynamically dominant below , and reproduce the relaxation dynamics of a disordered glassy material, in accord with previous findings.

We simulate a kinetic growth model on the square lattice using a Monte Carlo approach in order to study ramified polymerization with short-distance attractive interactions between monomers. The phase boundary separating finite from infinite growth regimes is obtained in the (T,b) space, where T is the reduced temperature and b is the branching probability. In the thermodynamic limit, we extrapolate the temperature below which the phase is found to be always infinite. We also observe the occurrence of a roughening transition at the polymer surface.

In this paper we continue the investigation of an anisotropic integrable spin chain, consisting of spins s = 1 and , started in our paper (Meiß ner St and Dörfel B-D 1996 J. Phys. A: Math. Gen. 29 1949) . The thermodynamic Bethe ansatz is analysed especially for the case, when the signs of the two couplings and differ. For the conformally invariant model we have calculated heat capacity and magnetic susceptibility at low temperature. In the isotropic limit our analysis is carried out further and susceptibilities are calculated near phase transition lines (at T = 0).

We develop a Coulomb-gas description of the critical fluctuations in the fully packed loop model on the honeycomb lattice. We identify the complete operator spectrum of this model in terms of electric and magnetic vector charges, and we calculate the scaling dimensions of these operators exactly. We also study the geometrical properties of loops in this model, and we derive exact results for the fractal dimension and the loop-size distribution function. A review of the many different representations of this model that have recently appeared in the literature, is given.

The Hamiltonian equation of motion is studied for a vortex occurring in a two-dimensional Heisenberg ferromagnet of anisotropic type by starting with the effective action for the spin field formulated by the Bloch (or spin) coherent state. The resultant equation shows the existence of a geometric force that is analogous to the so-called Magnus force in superfluids. This specific force plays a significant role in the quantum dynamics of a single vortex, for example the determination of the bound state of the vortex trapped by a pinning force arising from the interaction of the vortex with an impurity.

In this paper we propose a method aiming at a quantitative study of the glass transition in a system of interacting particles. In spite of the absence of any quenched disorder, we introduce a replicated version of the hypernetted chain equations. The solution of these equations, for hard or soft spheres, signals a transition to the glass phase at reasonable values of the density, and finds a nice form for the correlations in the glass phase. However, the predicted value of the energy and specific heat in the glass phase are wrong, calling for an improvement of this method.

We have obtained the mean square displacement for Brownian motion of particles in a fluid under a square-well potential. It is shown that for a deep well, there are short- and long-time regimes where the mean square displacement is proportional to time as well as a long intermediate transition stage. Even for a very mild case where the ratio A of the potential height to the thermal energy is 3 and its width is 5, we need time t of to recover Einstein's relation, which is unpractically too long where D is diffusion coefficient. In the short time regime where an escape process from the well dominates the considerably slow dynamics, the mean square displacement is approximately given by with the exponential factor appearing in theory of chemical reactions.

A particle-hopping model is presented to simulate the segregation of cars on a two-lane highway which consists of a slow lane and a fast lane. The changing of cars between the slow and fast lanes is taken into account. When a fast (slow) car overtakes (is overtaken by) a slow (fast) car on the slow (fast) lane, the fast (slow) car shifts to the fast (slow) lane. By satisfying the demand for faster movement, a segregation of cars occurs. The car densities, velocities and currents on the slow and fast lanes are calculated by computer simulation. The velocity distributions on the two lanes are also shown. It is found that the traffic current is enhanced by the changing of cars between two lanes. The kinetics of segregation between the slow and fast lanes is described in terms of a Boltzmann-like kinetic equation. The kinetic equation is solved by a numerical method. The velocity distributions, car densities, velocities and currents obtained from the kinetic equation are compared with the simulation results.

A three-state model is formulated in terms of raising and lowering operators. As an application, cyclic chemical reactions with three different species in the solid state are studied. The evolution equations for the densities and for the correlation functions can be derived starting from a master equation in a generalized Fock space representation on a lattice. Such a description guarantees the consideration of the excluded volume effect. In contrast to the classical kinetic behaviour, the system offers stable and unstable regimes depending on the averaged composition ratio.

This paper studies the function built from the zeros of the Bessel function . The known first eight terms of the McMahon expansion with are used to construct an accurate approximation to . The quality of this approximation is investigated numerically by comparison with a known but (at least numerically) little-studied integral formula for . Excellent numerical agreement is found for fixed and variable (real) s, and for fixed s and variable . Both formulae for therefore seem to work well. Our approximation also accurately reproduces known special values of . Important properties of are investigated for the first time, including several of its zeros. In addition, some general theory is presented in two areas: (i) perturbed spectra and (ii) the interrelationship between functions like representable as infinite products, and the functions constructed from their infinite spectrum of zeros.

The spectral theory for the Schrödinger equation on the half-line is treated through an analysis of the asymptotics of quadratic forms in a pair of solutions. Solutions of the second- and third-order differential equations for these forms are derived. In the case of the second-order DE (Milne's equation), it is shown that a single solution leads to the determination of the singular spectrum; this generalizes previous results which applied only to isolated points of the discrete spectrum. For the absolutely continuous spectrum, it is shown that a single solution allows one not only to locate the spectrum, but also to determine the spectral density function explicitly.

We present a free boson realization of the vertex operators and their duals for the solvable SOS lattice model of type. We discuss a possible connection with the calculation of correlation functions.

A quantum wave with probability density , confined by Dirichlet boundary conditions in a D-dimensional box of arbitrary shape and finite surface area, evolves from the uniform state . For almost all positions , the graph of the evolution of P is a fractal curve with dimension . For almost all times t, the graph of the spatial probability density P is a fractal hypersurface with dimension . When D = 1, there are, in addition to these generic time and space fractals, infinitely many special `quantum revival' times when P is piecewise constant, and infinitely many special spacetime slices for which the dimension of P is 5/4. If the surface of the box is a fractal with dimension , simple arguments suggest that the dimension of the time fractal is , and that of the space fractal is .

Methods of computing plethysms of the fundamental unitary irreducible representations of the non-compact symplectic group Sp(2n,R) are considered. Complete results are given for the symmetrized second powers. A number of new S-function identities are reported. The stability properties of the Sp(2n,R) plethysms are noted as well as a remarkable conjugacy relation. The application of the plethysms to N-particles in an isotropic harmonic oscillator is briefly outlined.

The general solution of the graded contraction equations for a grading of the real compact simple Lie algebra so(N+1) is presented in an explicit way. It turns out to depend on independent real parameters. The structure of the general graded contractions is displayed for the low-dimensional cases, and kinematical algebras are shown to appear straightforwardly. The geometrical (or physical) meaning of the contraction parameters as curvatures is also analysed; in particular, for kinematical algebras these curvatures are directly linked to geometrical properties of possible homogeneous spacetimes.

The new method for computation of the physical characteristics of quantum systems with many degrees of freedom is described. This method is based on the representation of the matrix element of the evolution operator in Euclidean metrics in a form of the functional integral with a certain measure in the corresponding space and on the use of approximation formulae which we constructed for this kind of integral. The method does not require preliminary discretization of space and time and allows us to use the deterministic algorithms. This approach proved to have important advantages over the other known methods, including the higher efficiency of computations. Examples of application of the method to the numerical study of some potential nuclear models as well as comparison of results with the experimental data and with the values obtained by the other authors are presented.

We find the eigenfunctions of the Peres spin-zero lightcone energy - momentum operators. These are compared with the usual Klein - Gordon basis states. A continuity equation is found with a positive definite probability density.

Due to a publishing error the following note in proof was omitted from this paper:

Since completing this work, we have learned of related calculations by Beenakker et al (Beenakker C W J, Paasschens J C J and Brouwer P W 1996 Phys. Rev. Lett. 76 1368).