Table of contents

A discrete stochastic process with stationary power law distribution is obtained from a death-multiple immigration population model. Emigrations from the population form a random series of events which are monitored by a counting process with finite-dynamic range and response time. It is shown that the power law behaviour of the population is manifested in the intermittent behaviour of the series of events.

Using its multiple integral representation, we compute the large distance asymptotic behaviour of the emptiness formation probability of the XXZ spin-1/2 Heisenberg chain in the massless regime.

We consider the survival probability of a particle in the presence of a finite number of diffusing traps in one dimension. Since the general solution for this quantity is not known when the number of traps is greater than two, we devise a perturbation series expansion in the diffusion constant of the particle. We calculate the persistence exponent associated with the particle's survival probability to second order and find that it is characterized by the asymmetry in the number of traps initially positioned on each side of the particle.

We analyse the influence of an impurity in the evolution of moving discrete breathers in a Klein–Gordon chain with non-weak nonlinearity. Three different types of behaviour can be observed when moving breathers interact with the impurity: they pass through the impurity continuing their direction of movement; they are reflected by the impurity; they are trapped by the impurity, giving rise to chaotic breathers, as their Fourier power spectra show. Resonance with a breather centred at the impurity site is conjectured to be a necessary condition for the appearance of the trapping phenomenon. This paper establishes a difference between the resonance condition of the non-weak nonlinearity approach and the resonance condition with the linear impurity mode in the case of weak nonlinearity.

Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the parameters. However, some systems do not obey power-law scaling, instead there is numerical evidence for a logarithmic scaling form, in which the scaling function depends on ratios of the logarithms of the parameters. Based on previous ideas by Tang we propose that this type of logarithmic scaling can be explained by a concept of local scaling invariance with continuously varying exponents. The functional dependence of the exponents is constrained by a homomorphism which can be expressed as a set of partial differential equations. Solving these equations we obtain logarithmic scaling as a special case. The other solutions lead to scaling forms where logarithmic and power-law scaling are mixed.

The product of traffic flow and the fraction of stopped cars is proposed to determine the probability P_ac for car accidents in the Fukui–Ishibashi model by analysing the necessary conditions of the occurrence of car accidents. Qualitative and quantitative characteristics of the probability P_ac can well be explained. A strategy for avoiding car accidents is suggested.

Nonequilibrium short-time dynamics of first-order phase transition in a driven-disordered system at zero temperature is investigated. In a random-bond Ising model under external field, the largest discontinuous jump of order parameter shows a power-law evolution in short times: ΔM(t) ∼ t^θ. The scaling exponent θ is equal to (d − β/ν)/z, where d is the dimensionality; β, ν and z are the critical exponents of the system. θ is found to be a universal exponent for any metastable relaxation in the short-time regime. This investigation suggests that the short-time dynamics is valid for the first-order phase transition in the driven disordered system and the critical phenomenon of the disordered system can be understood in the framework of nonequilibrium dynamics.

We propose a possible answer to one of the most exciting open questions in physics and cosmology, that is, the question why we seem to experience four-dimensional spacetime with three ordinary and one time dimensions. Making assumptions (such as particles being in first approximation massless) about the equations of motion, we argue for restrictions on the number of space and time dimensions. Accepting our explanation of the spacetime signature and the number of dimensions would be a point supporting (further) the importance of the 'internal space'.

The temporal motion of observables of a quantum mechanical N-level system is studied. In particular, I investigate the mapping, in its dependence on the matrix V parametrizing the Lindblad generator, of given initial configurations into the resulting configurations at large times t(t → ∞). Explicit solutions are given for a large class of V.

In the first section of this paper, we show that the functions in involution of the Gelfand–Cetlin system can be obtained from a λ-parametric Lax equation. In the second section, we observe that the Gelfand–Cetlin system has no obstructions to global action–angle coordinates, and we give an explicit expression of global (action) angle coordinates. In the third section, we remark the fact that the Gelfand–Cetlin system is obtained via a nesting of superintegrable systems, and show they all present a non-vanishing Chern class.

We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for the existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model and the Belousov–Zhabotinskii system. To achieve this, we solve over an arbitrary field the matrix equations SA = A^tS and SA = −A^tS for a quadratic matrix A and its transpose A^t, which may be of independent interest.

Taking the (2 + 1)-dimensional Broer–Kaup–Kupershmidt system as a simple example, some special types of (2 + 1)-dimensional compacton solutions are constructed. It is shown that there is quite rich interaction behaviour between two travelling compactons. For some types of compactons, the interactions among them may not be completely elastic. For some others, the interactions are completely elastic. There is no phase shift for the interactions of the (2 + 1)-dimensional compactons discussed in this paper.

Spectral determinants have proved to be valuable tools for resumming the periodic orbits in the Gutzwiller trace formula of chaotic systems. We investigate these tools in the context of integrable systems to which these techniques have not been previously applied. Our specific model is a stroboscopic map of an integrable Hamiltonian system with quadratic action dependence, for which each stage of the semiclassical approximation can be controlled. It is found that large errors occur in the semiclassical traces due to edge corrections which may be neglected if the eigenvalues are obtained by Fourier transformation over the long time dynamics. However, these errors cause serious harm to the spectral approximations of an integrable system obtained via the spectral determinants. The symmetry property of the spectral determinant does not generally alleviate the error, since it sometimes sheds a pair of eigenvalues from the unit circle. By taking into account the leading-order asymptotics of the edge corrections, the spectral determinant method makes a significant recovery.

Robertson and Hadamard–Robertson theorems on non-negative definite Hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg–Robertson, Robertson–Schrödinger and trace uncertainty relations in deformation quantization are found. Some conditions under which the uncertainty relations are minimized are also given.

We show that a recently proposed shifted large-l expansion is exactly the well-known shifted large-N expansion. Results for truncated Coulomb potentials cast doubts on previous conclusions drawn from shifted large-l calculations.

Comment on the letter by (A V Tsiganov 2002 J. Phys. A: Math. Gen.35 L309 .

Fernandez comments [1] on our pseudo-perturbative shifted-ℓ expansion technique [2, 3] is either unfounded or ambiguous.

With effect from 1 January 2003 (volume 36), the following classification scheme will be introduced for research papers published in Journal of Physics A: Mathematical and General. We believe that this new scheme will help to clarify the journal's scope and enable authors and readers to more easily locate the appropriate section for their work.

We also list below some more detailed subject areas which should help define each section heading. These lists are by no means exhaustive and are intended only as a guide to the type of papers we envisage appearing in each section. We acknowledge that no classification scheme can be perfect and that there are some papers which might be placed in more than one section. Whenever possible, we will respect the author's wishes on placement and undertake to inform authors when we feel that a different classification is more appropriate.

We are happy to provide further advice on paper classification to authors upon request (please email jphysa@iop.org).

1. Statistical physics May include papers on

• statistical mechanics, lattice theory and thermodynamics

• quantum statistical mechanics and Bose-Einstein condensation

• phase transitions and critical phenomena

• numerical and computational methods

• theories of interacting particles (many-body theories)

• theoretical condensed matter and mesoscopic systems

• disordered systems, spin glasses and neural networks

• nonequilibrium processes

• nonlinear dynamics and classical chaos

• quantum chaos

• cellular automata

• biophysics

• integrable systems

• random matrix theory

• special functions

• Lie algebras and quantum groups

• classical mechanics

• inverse problems

• foundations of quantum mechanics

• quantum information, computation and cryptography

• theoretical quantum optics

• open quantum systems

• gauge and conformal field theory

• quantum electrodynamics and quantum chromodynamics

• string theory and its developments

• classical electromagnetism

• fluid dynamics and turbulence

• plasma physics