We reply to comments by P.Markos, L.Schweitzer and M.Weyrauch [preceding paper] on our recent paper [J. Phys.: Condens. Matter 63, 13777 (2002)]. We demonstrate that our quite different viewpoints stem for the different physical assumptions made prior to the choice of the mathematical formalism. The authors of the Comment expect a priori to see a single thermodynamic phase while our approach is capable of detecting co-existence of distinct pure phases. The limitations of the transfer matrix techniques for the multi-dimensional Anderson localization problem are discussed.

Starting from the analysis of the hierarchy of equations for many-point reactant densities involved in three kinds of basic bimolecular reactions, A + A + B, A + B + C, A + B + B, in condensed media, a review is given of a new class of self-organisation phenomena. Unlike the usual synergetic effects, these phenomena are characterised by the appearance of microscopic dynamical clustering of similar reactants, which, however, does not violate the macroscopic homogeneity of the system. The many-particle effects are described in terms of the correlation length and critical exponents in much the same way as is done in the theory of critical phenomena (phase transitions) developed in statistical physics. It is shown that microscopic self-organisation results in asymptotic decay laws for reactant densities which are unusual for standard physical and chemical kinetics. The corresponding reduction of reaction rate with time is due to the emergence, in the course of biomolecular reaction, of a non-Poisson fluctuation spectrum of reactant densities governing the time development of average quantities. The universal character of the newly discovered self-organisation phenomena has been demonstrated to occur not only in numerous kinds of diffusion-controlled reactions, but also for static reactions at low temperatures, including reactant accumulation, when there is a source creating them (e.g. irradiation) and a long-range (tunnelling) recombination of immobile donors and acceptors in crystals. The mathematical formalism developed is applied to the two-stage bimolecular processes using the Lotka and Lotka-Volterra models as examples. Their analysis has revealed that in this case the generally accepted viewpoint on the self-organisation phenomena fails. This review was received in its present form in June 1988. 'Everything should be done as simply as possible but not simpler.' A Einstein 'Entia non sunt multiplicanda sine necesitate.

The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter 14 (2002) 13777] is generalized for higher spatial dimensions D. In this way the generalized Lyapunov exponents for diagonal correlators of the wave function, ψ 2 n,m , can be calculated analytically and exactly. This permits to determine the phase diagram of the system. For all dimensions D > 2 one finds intervals in the energy and the disorder where extended and localized states coexist: the metal-insulator transition should thus be interpreted as a first-order transition. The qualitative differences permit to group the systems into two classes: low-dimensional systems (2 ≤ D ≤ 3), where localized states are always exponentially localized and high-dimensional systems (D ≥ Dc = 4), where states with non-exponential localization are also formed. The value of the upper critical dimension is found to be D0 = 6 for the Anderson localization problem; this value is also characteristic of a related problem -percolation.

This review deals with the theoretical study of the kinetics of the A t €3 + 0 bimolecular reaction between point Frenkel defects in irradiated solids. Three different approaches are discussed: macroscopic, mesoscopic and microscopic, and their advantages and shortcomings are analysed. Special attention is paid to the formalism of many-point particle densities and its application in the study of the effects of defect-density fluctuations. The kinetics of all recombination regimes are considered in detail, including static reactions, correlated annealing, diffusion-and hoppingcontrolled reactions, and aggregation of immobile defects under the conditions of a permanent defect source (irradiation). Problems rarely discussed in the literature are emphasized: transient kinetics; effects of long-range hop lengths and of defect interaction; cooperative phenomena at high defect densities and for long reaction times; and accuracy of Kirkwood's superposition approximation. Theory is illustrated by relevant experimental data for ionic crystals.