### Article

## Entanglement entropy and particle number cumulants of disordered fermions

We study the entanglement entropy and particle number cumulants for a system of disordered noninteracting fermions in d dimensions. We show, both analytically and numerically, that for a weak disorder the entanglement entropy and the second cumulant (particle number variance) are proportional to each other with a universal coefficient. The corresponding expressions are analogous to those in the clean case but with a logarithmic factor regularized by the mean free path rather than by the system size. We also determine the scaling of higher cumulants by analytical (weak disorder) and numerical means. Finally, we predict that the particle number variance and the entanglement entropy are nonanalytic functions of disorder at the Anderson transition.

The round table rises important questions - the questions concerning developments of the conceptual apparatus which would provide constructive movement within the limits of a complexity paradigm. These problems concern the status of the such paradigm, how it is accepted or not accepted in natural-science and philosophical traditions, what influence it renders to express its specificity on description languages. Different aspects and ways of understanding of complexity are considered in a context of the conceptual strategy which is offered by the French philosopher Gilles Deleuze. During the discussion an attempt of rethinking the relation of methodology and ontology, parts and whole, a text and a context etc. is undertaken. Also the problem that draws attention of the participants of a round table is the conceptualization of the opposition “simple-complex”. Within the limits of the discussion on the dichotomy “simple-complex” possible approaches to complex thinking are considered to construct the concept “complex vision of the world”. In this aspect the construction ontology of nonclassical type, the ontology, which is based not on static vision of the world, not on identity, but on dynamics, on becoming, is discussed. The accent is done on dynamics and on removal of classical dichotomies, for example on removal of dichotomy “methodology-ontology”. This suggests a new postnonclassical ontology and special type of methodology. The special attention is given to the problem of observer, considering that the conceptual character “observer of complexity” is found almost in all later works of Deleuze. Thus the emphasis is made on a role of recursion and communications during such observation. In this context complexity is seen as a recursive process between integrity and partiality which basic premise is the idea of distinction. The observer of complexity is the observer creating distinctions, staying in the nonequilibrium, uncertain situation which is open for the future having in the past the set of causes and effects for retrospective explanations which however cannot serve as a support for the determined forecasts of the future events. Position, according to which it is necessary to refuse the position of the external observer, considering this or that state of affairs from outside, is put forward. Moreover, we have in mind postnonclassical complexity, but not difficult complex problems that we have to solve. And this fact can be grasped from a number of practices related primarily to innovation activities. Also the special attention is given to postnonclassical control strategy of complex systems which can be considered in terminology of Deleuze as movements from “virtual object” to “the virtual subject”. The considerable attention in performances is given to the status of truth in a paradigm of complexity (in perspective of philosophical strategy of Deleuze). At last, the considered theme is developed in a context of congruence of philosophies of Deleuze with philosophical and research strategy of Edgar Moraine (the author of the term “paradigm of complexity”) and also with the theory of autopoiesis offered by Francisco Varela and Humberto Maturana.

Some aspects of the phenomenon of complexity which are congruent to the conceptual constructions of Gilles Deleuze are considered in the presentation of Helena Knyazeva. Six such methodologically important aspects of the phenomenon of complexity are singled out by her. The round table rises important questions – the questions concerning developments of the conceptual apparatus which would provide constructive movement within the limits of a complexity paradigm. These problems concern the status of the such paradigm, how it is accepted or not accepted in natural-science and philosophical traditions, what influence it renders to express its specificity on description languages. Different aspects and ways of understanding of complexity are considered in a context of the conceptual strategy which is offered by the French philosopher Gilles Deleuze. During the discussion an attempt of rethinking the relation of methodology and ontology, parts and whole, a text and a context etc. is undertaken. Also the problem that draws attention of the participants of a round table is the conceptualization of the opposition “simple–complex”. Within the limits of the discussion on the dichotomy “simple–complex” possible approaches to complex thinking are considered to construct the concept “complex vision of the world”. In this aspect the construction ontology of nonclassical type, the ontology, which is based not on static vision of the world, not on identity, but on dynamics, on becoming, is discussed. The accent is done on dynamics and on removal of classical dichotomies, for example on removal of dichotomy “methodologyontology”. This suggests a new postnonclassical ontology and special type of methodology. The special attention is given to the problem of observer, considering that the conceptual character “observer of complexity” is found almost in all later works of Deleuze. Thus the emphasis is made on a role of recursion and communications during such observation. In this context, complexity is seen as a recursive process between integrity and partiality which basic premise is the idea of distinction. The observer of complexity is the observer creating distinctions, staying in the nonequilibrium, uncertain situation which is open for the future having in the past the set of causes and effects for retrospective explanations which however cannot serve as a support for the determined forecasts of the future events. Position, according to which it is necessary to refuse the position of the external observer, considering this or that state of affairs from outside, is put forward. Moreover, we have in mind postnonclassical complexity, but not difficult complex problems that we have to solve. And this fact can be grasped from a number of practices related primarily to innovation activities. Also the special attention is given to postnonclassical control strategy of complex systems which can be considered in terminology of Deleuze as movements from “virtual object” to “the virtual subject”. The considerable attention in performances is given to the status of truth in a paradigm of complexity (In perspective of philosophical strategy of Deleuze). At last, the considered theme is developed in a context of congruence of philosophies of Deleuze with philosophical and research strategy of Edgar Morin (the author of the term “paradigm of complexity”) and also with the theory of autopoiesis offered by Francisco Varela and Humberto Maturana.

A brief overview of entanglement characterization is given in the cases of biphoton and multiphoton polarization states. The importance of the approach is stressed based on the Schmidt decomposition. This method is applied to the characterization of the quadrature entanglement in two-mode multiphoton states. The fruitfulness of this approach is illustrated by a series of examples.

The subject of this book is theory of quantum system presented from information science perspective. The central role is played by the concept of quantum channel and its entropic and information characteristics. Quantum information theory gives a key to understanding elusive phenomena of quantum world and provides a background for development of experimental techniques that enable measuring and manipulation of individual quantum systems. This is important for the new efficient applications such as quantum computing, communication and cryptography. Research in the field of quantum informatics, including quantum information theory, is in progress in leading scientific centers throughout the world. This suggests a need for a text that not only introduces the basic concepts of quantum information theory, but also presents in detail some of its recent achievements. The book gives an accessible, albeit mathematically rigorous and self-contained introduction to the subject, starting from primary structures and leading to fundamental results and to exiting open problems.

One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of quantum channel which is a basic building block of any data-transmitting or data-processing system. This development resulted in an elaborated structural theory and was accompanied by the discovery of a whole spectrum of entropic quantities, notably the channel capacities, characterizing information-processing performance of the channels. This paper gives a survey of the main properties of quantum channels and of their entropic characterization, with a variety of examples for finite dimensional quantum systems. We also touch upon the ``continuous-variables'' case, which provides an arena for quantum Gaussian systems. Most of the practical realizations of quantum information processing were implemented in such systems, in particular based on principles of quantum optics. Several important entropic quantities are introduced and used to describe the basic channel capacity formulas. The remarkable role of the specific quantum correlations -- entanglement -- as a novel communication resource, is stressed.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.