Table of contents

This scheme is used to clarify the journal's scope and enable authors and readers to more easily locate the appropriate section for their work. For each of the sections listed in the scope statement we suggest some more detailed subject areas which help define that subject area. 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. We are happy to provide further advice on paper classification to authors upon request (please email jphysa@iop.org).

1. Statistical physics

• numerical and computational methods

• statistical mechanics, phase transitions and critical phenomena

• quantum condensed matter theory

• Bose–Einstein condensation

• strongly correlated electron systems

• exactly solvable models in statistical mechanics

• lattice models, random walks and combinatorics

• field-theoretical models in statistical mechanics

• disordered systems, spin glasses and neural networks

• nonequilibrium systems

• network theory

• nonlinear dynamics and classical chaos

• fractals and multifractals

• quantum chaos

• classical and quantum transport

• cellular automata

• granular systems and self-organization

• pattern formation

• biophysical models

• combinatorics

• algebraic structures and number theory

• matrix theory

• classical and quantum groups, symmetry and representation theory

• Lie algebras, special functions and orthogonal polynomials

• ordinary and partial differential equations

• difference and functional equations

• integrable systems

• soliton theory

• functional analysis and operator theory

• inverse problems

• geometry, differential geometry and topology

• numerical approximation and analysis

• geometric integration

• computational methods

• coherent states

• eigenvalue problems

• supersymmetric quantum mechanics

• scattering theory

• relativistic quantum mechanics

• semiclassical approximations

• foundations of quantum mechanics and measurement theory

• entanglement and quantum nonlocality

• geometric phases and quantum tomography

• quantum tunnelling

• decoherence and open systems

• quantum cryptography, communication and computation

• theoretical quantum optics

• quantum field theory

• gauge and conformal field theory

• quantum electrodynamics and quantum chromodynamics

• Casimir effect

• integrable field theory

• random matrix theory applications in field theory

• string theory and its developments

• classical field theory and electromagnetism

• metamaterials

• turbulence

• fundamental plasma physics

• fundamental fluid mechanics

• kinetic theory

• magnetohydrodynamics and multifluid descriptions

• strongly coupled plasmas

• one-component plasmas

• non-neutral plasmas

• astrophysical and dusty plasmas

We study mean-field percolation with freezing. Specifically, we consider cluster formation via two competing processes: irreversible aggregation and freezing. We find that when the freezing rate exceeds a certain threshold, the percolation transition is suppressed. Below this threshold, the system undergoes a series of percolation transitions with multiple giant clusters ('gels') formed. Giant clusters are not self-averaging as their total number and their sizes fluctuate from realization to realization. The size distribution F_k, of frozen clusters of size k, has a universal tail, F_k ∼ k⁻³. We propose freezing as a practical mechanism for controlling the gel size.

The dynamics of the full, dissipative, Fermi accelerator model is shown to exhibit crisis events as the damping coefficient is varied. The investigation, based on analysis of a two-dimensional nonlinear map, has also led to a numerical determination of the basin of attraction for its chaotic attractor.

We present a novel class of real symmetric matrices in arbitrary dimension d, linearly dependent on a parameter x. The matrix elements satisfy a set of nontrivial constraints that arise from asking for commutation of pairs of such matrices for all x, and an intuitive sufficiency condition for the solvability of certain linear equations that arise therefrom. This class of matrices generically violates the Wigner von Neumann non-crossing rule, and is argued to be intimately connected with finite-dimensional Hamiltonians of quantum integrable systems.

A new method for computing the conductivity of random irregular resistor networks is developed. This method is a generalization of the transfer-matrix technique, proposed by Derrida and Vannimenus for regular 2D and 3D lattices. At the same time for large systems the method presented in this paper is more efficient than the transfer-matrix technique. To demonstrate the method it is applied to a cubic lattice at the percolation threshold and away from it. The conductivity has been found for lattices with size up to 324³. The ratio between the conductivity exponent t and the correlation length exponent η was estimated to be t/η = 2.315, in good agreement with the literature data.

We study an asymptotic behaviour of a special correlator known as the emptiness formation probability (EFP) for the one-dimensional anisotropic XY spin-1/2 chain in a transverse magnetic field. This correlator is essentially the probability of formation of a ferromagnetic string of length n in the antiferromagnetic ground state of the chain and plays an important role in the theory of integrable models. For the XY spin chain, the correlator can be expressed as the determinant of a Toeplitz matrix and its asymptotical behaviours for n → ∞ throughout the phase diagram are obtained using known theorems and conjectures on Toeplitz determinants. We find that the decay is exponential everywhere in the phase diagram of the XY model except on the critical lines, i.e. where the spectrum is gapless. In these cases, a power-law prefactor with a universal exponent arises in addition to an exponential or Gaussian decay. The latter Gaussian behaviour holds on the critical line corresponding to the isotropic XY model, while at the critical value of the magnetic field the EFP decays exponentially. At small anisotropy one has a crossover from the Gaussian to the exponential behaviour. We study this crossover using the bosonization approach.

We evaluate by analytical means the Ruelle ζ-function for a spin model with global coupling. The implications of the ferromagnetic phase transitions for the analytical properties of the ζ-function are discussed in detail. In the paramagnetic phase the ζ-function develops a single branch point. In the low-temperature regime two branch points appear which correspond to the ferromagnetic state and the metastable state. The results are typical for any Ginsburg–Landau-type phase transition.

The general binary breakage problem with power-law breakage functions and two families of symmetric and asymmetric breakage kernels is studied in this work. A useful transformation leads to an equation that predicts self-similar solutions in its asymptotic limit and offers explicit knowledge of the mean size and particle density at each point in dimensionless time. A novel moving boundary algorithm in the transformed coordinate system is developed, allowing the accurate prediction of the full transient behaviour of the system from the initial condition up to the point where self-similarity is achieved, and beyond if necessary. The numerical algorithm is very rapid and its results are in excellent agreement with known analytical solutions. In the case of the symmetric breakage kernels only unimodal, self-similar number density functions are obtained asymptotically for all parameter values and independent of the initial conditions, while in the case of asymmetric breakage kernels, bimodality appears for high degrees of asymmetry and sharp breakage functions. For symmetric and discrete breakage kernels, self-similarity is not achieved. The solution exhibits sustained oscillations with amplitude that depends on the initial condition and the sharpness of the breakage mechanism, while the period is always fixed and equal to ln 2 with respect to dimensionless time.

We develop a systematic algorithm for constructing an -fold supersymmetric system from a given vector space invariant under one of the supercharges. Applying this algorithm to spaces of monomials, we construct a new multi-parameter family of -fold supersymmetric models, which shall be referred to as 'type C'. We investigate various aspects of these type C models in detail. It turns out that in certain cases these systems exhibit a novel phenomenon, namely, partial breaking of -fold supersymmetry.

Dispersive effects due to microstructure of materials combined with nonlinearities give rise to solitary waves. In this paper the existence of solitary wave solutions is proved for a rather general hierarchical governing equation which accounts for nonlinearities on both macro- and microscales. Properties of the waves are established. Waves are asymmetric in the case of the nonlinearity in the microscale. Dispersive effects are due to the scale dependence.

In this paper, we consider two models which exhibit equilibrium BEC superradiance. They are related to two different types of superradiant scattering observed in recent experiments. The first one corresponds to the amplification of matter waves due to Raman superradiant scattering from a BE condensate, when the recoiled and the condensed atoms are in different internal states. The main mechanism is stimulated Raman scattering in two-level atoms, which occurs in a superradiant way. Our second model is related to the superradiant Rayleigh scattering from a BE condensate. This again leads to a matter-wave amplification but now with the recoiled atoms in the same state as the atoms in the condensate. Here the recoiling atoms are able to interfere with the condensate at rest to form a matter-wave grating (interference fringes) which is observed experimentally.

The construction of an infinite-dimensional differentiable manifold not modelled on any Banach space is proposed. Definition, metric and differential structures of a Weyl algebra (P*_pM[[ℏ]], ○) and a Weyl algebra bundle are presented. Continuity of the ○-product in the Tichonov topology is proved. Construction of the ∗-product of the Fedosov type in terms of theory of connection in a fibre bundle is explained.

Starting from a spectral problem, we derive the well-known Heisenberg hierarchy. An explicit and universal Darboux transformation for the whole hierarchy is constructed. The soliton solutions for the Heisenberg hierarchy are obtained by applying the Darboux transformation.

We study a particular class of the mappings introduced by Quispel, Roberts and Thompson that come from a two-component system but can be naturally reduced to a one-component one. We classify all these mappings on the basis of the canonical forms of the QRT matrices. We also present the extension of these systems to nonautonomous forms, which are usually discrete Painlevé equations.

Canonical transformations are defined and discussed along with the coherent and the ultracoherent vectors. It is shown that the single-mode and the n-mode squeezing operators are elements of the group of canonical transformations. An application of canonical transformations is made, in the context of open quantum systems, by studying the effect of squeezing of the bath on the decoherence properties of the system. Two cases are analysed. In the first case, the bath consists of a massless bosonic field with the bath reference states being the squeezed vacuum states and squeezed thermal states while in the second case a system consisting of a harmonic oscillator interacting with a bath of harmonic oscillators is analysed with the bath being initially in a squeezed thermal state.

We investigate the problem of coexistence of position and momentum observables. We characterize those pairs of position and momentum observables which have a joint observable.

Mutually unbiased bases generalize the X, Y and Z qubit bases. They possess numerous applications in quantum information science. It is well known that in prime power dimensions N = p^m (with p prime and m a positive integer), there exists a maximal set of N + 1 mutually unbiased bases. In the present paper, we derive an explicit expression for those bases, in terms of the (operations of the) associated finite field (Galois division ring) of N elements. This expression is shown to be equivalent to the expressions previously obtained by Ivanovic (1981 J. Phys. A: Math. Gen.14 3241) in odd prime dimensions, and Wootters and Fields (1989 Ann. Phys.191 363) in odd prime power dimensions. In even prime power dimensions, we derive a new explicit expression for the mutually unbiased bases. The new ingredients of our approach are, basically, the following: we provide a simple expression of the generalized Pauli group in terms of the additive characters of the field, and we derive an exact groupal composition law between the elements of the commuting subsets of the generalized Pauli group, renormalized by a well-chosen phase-factor.

Off-diagonal long-range order (ODLRO) which is believed to be one characteristic of superconductivity is a quantum phenomenon not describable in classical mechanical terms. The quantum state constructed by η-pairing demonstrates ODLRO. Entanglement is a key concept of the quantum information processing and has no classical counterpart. We study the entanglement property of the η-pairing quantum state by concurrence and entropy which are two measures of the entanglement. We show that the concurrence of entanglement between one-site and the rest sites is exactly the correlation function of the ODLRO for the η-pairing state in the thermodynamic limit. So, when the η-pairing state is entangled, it demonstrates ODLRO and is thus in the superconducting phase, if it is a separable state, there is no ODLRO. In the thermodynamical limit, the entanglement between the M-site and other sites of the η-pairing state does not vanish. Other types of ODLRO of the η-pairing state are presented. We show that the behaviour of the ODLRO correlation functions is equivalent to that of the entanglement of the η-pairing state. The scaling of the entropy of the entanglement for the η-pairing state is studied.

Within the framework of Bohmian mechanics dwell times find a straightforward formulation. The computation of associated probabilities and distributions however needs the explicit knowledge of a relevant sample of trajectories and therefore implies formidable numerical effort. Here, a trajectory free formulation for the average transmission and reflection dwell times within static spatial intervals [a, b] is given for one-dimensional scattering problems. This formulation reduces the computation time to less than 5% of the computation time by means of trajectory sampling.

New amplitude-phase formulae for Regge-pole positions and residues are derived. The derivation makes use of certain invariants of the Ermakov–Lewis type. The formulas allow calculation to be made on the real r-axis, with an additional flexibility to optimize its numerical aspects.

The one-particle Schrödinger and Dirac equations are derived, without making any quantization hypothesis, from the postulate that an elementary particle is a physical wave packet of dynamically varying form and size, rather than a pointlike object located somewhere within the support of a wavefunction that serves only as a mathematical probability amplitude. An isolated multiparticle system can, similarly, be described in principle as a set of interacting wave packets governed by coupled one-particle equations, a picture from which, in the nonrelativistic limit, the multiparticle Schrödinger equation can be obtained as a sufficiency condition for the system to have a conserved total energy equal to a particular value E.

We prove Noether's direct and inverse second theorems for Lagrangian systems on fibre bundles in the case of gauge symmetries depending on derivatives of dynamic variables and parameters of an arbitrary order. The appropriate notions of a reducible gauge symmetry and Noether identity are formulated, and their equivalence by means of a certain intertwining operator is proved.

We propose nonlinear integral equations for the finite volume one-particle energies in the O(3) and O(4) nonlinear σ-models. The equations are written in terms of a finite number of components and are therefore easier to solve numerically than the infinite component excited-state TBA equations proposed earlier. Results of numerical calculations based on the nonlinear integral equations and the excited-state TBA equations agree within numerical precision.

The structure of the observable algebra of lattice QCD in the Hamiltonian approach is investigated. As was shown earlier, is isomorphic to the tensor product of a gluonic C*-subalgebra, built from gauge fields and a hadronic subalgebra constructed from gauge-invariant combinations of quark fields. The gluonic component is isomorphic to a standard CCR algebra over the group manifold SU(3). The structure of the hadronic part, as presented in terms of a number of generators and relations, is studied in detail. It is shown that its irreducible representations are classified by triality. Using this, it is proved that the hadronic algebra is isomorphic to the commutant of the triality operator in the enveloping algebra of the Lie superalgebra sl(1/n) (factorized by a certain ideal).

This book gives a clear exposition of quantum field theory at the graduate level and the contents could be covered in a two semester course or, with some effort, in a one semester course.

The book is well organized, and subtle issues are clearly explained. The margin notes are very useful, and the problems given at the end of each chapter are relevant and help the student gain an insight into the subject. The solutions to these problems are given in chapter 12. Care is taken to keep the numerical factors and notation very clear.

Chapter 1 gives a clear overview and typical scales in high energy physics. Chapter 2 presents an excellent account of the Lorentz group and its representation. The decomposition of Lorentz tensors underSO(3) and the subsequent spinorial representations are introduced with clarity. After giving the field representation for scalar, Weyl, Dirac, Majorana and vector fields, the Poincaré group is introduced. Representations of 1-particle states using m² and the Pauli–Lubanski vector, although standard, are treated lucidly.

Classical field theory is introduced in chapter 3 and a careful treatment of the Noether theorem and the energy momentum tensor are given. After covering real and complex scalar fields, the author impressively introduces the Dirac spinor via the Weyl spinor; Abelian gauge theory is also introduced. Chapter 4 contains the essentials of free field quantization of real and complex scalar fields, Dirac fields and massless Weyl fields. After a brief discussion of the CPT theorem, the quantization of electromagnetic field is carried out both in radiation gauge and Lorentz gauge. The presentation of the Gupta–Bleuler method is particularly impressive; the margin notes on pages 85, 100 and 101 invaluable.

Chapter 5 considers the essentials of perturbation theory. The derivation of the LSZ reduction formula for scalar field theory is clearly expressed. Feynman rules are obtained for the λϕ⁴ theory in detail and those of QED briefly. The basic idea of renormalization is explained using the λϕ⁴ theory as an example. There is a very lucid discussion on the `running coupling' constant in section 5.9. Chapter 6 explains the use of the matrix elements, formally given in the previous chapter, to compute decay rates and cross sections. The exposition is such that the reader will have no difficulty in following the steps. However, bearing in mind the continuity of the other chapters, this material could have been consigned to an appendix.

In the short chapter 7, the QED Lagrangian is shown to respect P, C and T invariance. One-loop divergences are described. Dimensional and Pauli–Villars regularization are introduced and explained, although there is no account of their use in evaluating a typical one-loop divergent integral.

Chapter 8 describes the low energy limit of the Weinberg–Salam theory. Examples for μ^-→ e^-barnu_eν _μ, π⁺→ l⁺ν_l and K⁰→ π^-l⁺ν_l are explicitly solved, although the serious reader should work them out independently. On page 197 the `V-A structure of the currents proposed by Feynman and Gell-Mann' is stated; the first such proposal was by E C G Sudarshan and R E Marshak.

In chapter 9 the path integral quantization method is developed. After deriving the transition amplitude as the sum over all paths, in quantum mechanics, a demonstration that the integration of functions in the path integral gives the expectation value of the time ordered product of the corresponding operators is given and applied to real scalar free field theory to get the Feynman propagator. Then the Euclidean formulation is introduced and its `tailor made' role in critical phenomena is illustrated with the 2-d Ising model as an example, including the RG equation.

Chapter 10 introduces Yang–Mills theory. After writing down the typical gauge invariant Lagrangian and outlining the ingredients of QCD, the adjoint representation for fields is given. It could have been made complete by giving the Feynman rules for the cubic and quartic vertices for non-Abelian gauge fields, although the reader can obtain them from the last term in equation 10.27. In chapter 11, spontaneous symmetry breaking in quantum field theory is described. The difference in quantum mechanics and QFT with respect to the degenerate vacua is clearly brought out by considering the tunnelling amplitude between degenerate vacua. This is very good, as this aspect is mostly overlooked in many textbooks. The Goldstone theorem is then illustrated by an example. The Higgs mechanism is explained in Abelian and non-Abelian (SU(2)) gauge theories and the situation in SU(2)xU(1) gauge theory is discussed.

This book certainly covers most of the modern developments in quantum field theory. The reader will be able to follow the content and apply it to specific problems. The bibliography is certainly useful. It will be an asset to libraries in teaching and research institutions.

This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on.

Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are:

• the failure of the traditional description of chaotic dynamics in terms of diffusion equations;

• he fractional kinematics, its foundation and renormalization group analysis;

• `pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents;

• directional complexity and entropy.

The purpose of this book is to provide reearchers and students in physics, mathematics and engeenering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and `further reading'.

Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject.

My one regret is that the book does not mention the famous `Shadowing Lemma' of Anosov and Bowen for hyperbolic systems.

By treating path integrals the author, in this book, places at the disposal of the reader a modern tool for the comprehension of standard quantum mechanics. Thus the most important applications, such as the tunnel effect, the diffusion matrix, etc, are presented from an original point of view on the action S of classical mechanics while having it play a central role in quantum mechanics.

What also emerges is that the path integral describes these applications more richly than are described traditionally by differential equations, and consequently explains them more fully.

The book is certainly of high quality in all aspects: original in presentation, rigorous in the demonstrations, judicious in the choice of exercises and, finally, modern, for example in the treatment of the tunnel effect by the method of instantons. Moreover, the correspondence that exists between classical and quantum mechanics is well underlined. I thus highly recommend this book (the French version being already available) to those who wish to familiarize themselves with formulation by path integrals. They will find, in addition, interesting topics suitable for exploring further.