In the present treatise progress in topological approach to Hall system physics is reported, including recent achievements in graphene. The new homotopy methods of cyclotron braid subgroups, originally introduced by the authors, turn out to be of particular convenience in order to grasp peculiarity of 2D charged systems upon magnetic field resulting in fractional Hall states. The identified cyclotron braids allow for natural recovery of Laughlin correlations from the first principles, without invoking any artificial constructions as composite fermions with flux tubes or vortices. Progress in understanding of the structure and role of composite fermions in Hall system is provided, which can also lead to some corrections of numerical results in energy minimization made within the traditional formulation of the composite fermion model. The crucial significance of carrier mobility, apart from interaction in creation of the fractional quantum Hall effect (FQHE), is described and supported by recent graphene experiments. Recent advancement in the FQHE field including topological insulators and optical lattices is reviewed and commented upon in terms of the braid group approach. The braid group methods are presented from a more general point of view including proposition of pure braid group application. Book jacket.

This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. The articles in this second volume discuss areas related to algebraic geometry, emphasizing the connections of this central subject to integrable systems, arithmetic geometry, Riemann surfaces, coding theory and lattice theory.

Graphene is, basically, a single atomic layer of graphite, an abundant mineral that is an allotrope of carbon that is made up of very tightly bonded carbon atoms organized into a hexagonal lattice. What makes graphene so special is its sp2 hybridization and very thin atomic thickness (of 0.345 Nm). These properties are what enable graphene to break so many records in terms of strength, electricity, and heat conduction (as well as many others). This book gathers valuable information about the surface chemistry of graphene, some of its properties (electrical, mechanical, etc.), and many of its modifications that can be taken into account.

With examples and clear explanation throughout, this step-by-step approach makes quantum theory of plasmons accessible to readers without specialized training in theory. Jacak uses original research results to offer a fully analytical theory formulation suitable for further development and applications. The theory is focused on the Random Phase Approximation description of plasmons in metallic nano-structures, previously defined for bulk metal. Particular attention is paid to large damping of plasmons in nanostructures including electron scattering and Lorentz friction losses, quantum description of plasmon photovoltaic effect is presented and there is in-depth analysis of plasmon-polariton kinetics in metallic nano-chains. Suitable for students in the field of plasmonics, opto-electronics and photonics, and for researchers active in the field of photo-voltaics, opto-electronics, nano-plasmonics and nano-photonics. Also of help to researchers in soft plasmonics with applications to electro-signalling in neurons.

Quantum Boundaries of Life, Volume 82 in the Advances in Quantum Chemistry series, presents current topics in this rapidly developing field that have emerged at the cross section of mathematics, physics, chemistry and biology. Topics covered include Quantum Considerations of Neural Memory, Functional Neural Electron Transport, Plasmon-polariton mechanism of the saltatory conduction in myelinated axons, Quantum Field Theory Formulation of Brain Dynamics: Nonequilibrium, Multi Field Theory Formulation of Brain Dynamics, Quantum Protein Folding, Classical-Quantum Interplay in Living Neural Tissue Function, Quantum Effects in Life Dynamics, Quantum transport and utilization of free energy in protein a-helices, and much more. The book's message is simple. Mystics prefer to put consciousness in the cosmos to avoid Darwinism. If the seat of consciousness is found to evolve within all animals, then we have a Darwinian understanding not only of the origin of life and species according to natural selection but also concerning consciousness and, in particular, life being quantum Darwinian. - Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry and biology - Features detailed reviews written by leading international researchers