Dynamical Symmetries For Nanostructures

Group theoretical concepts elucidate fundamental physical phenomena, including excitation spectra of quantum systems and complex geometrical structures such as molecules and crystals. These concepts are extensively covered in numerous textbooks. The aim of the present monograph is to illuminate more subtle aspects featuring group theory for quantum mechanics, that is, the concept of dynamical symmetry. Dynamical symmetry groups complement the conventional groups: their elements induce transitions between states belonging to different representations of the symmetry group of the Hamiltonian. Dynamical symmetry appears as a hidden symmetry in the hydrogen atom and quantum rotator problem, but its main role is manifested in nano and meso systems. Such systems include atomic clusters, large molecules, quantum dots attached to metallic electrodes, etc. They are expected to be the building blocks of future quantum electronic devices and information transmitting algorithms. Elucidation of the electronic properties of such systems is greatly facilitated by applying concepts of dynamical group theory.

"This book is a collection of lecture notes which were presented by invited speakers at the Eleventh School on Theoretical Physics "Symmetry and Structural Properties of Condensed Matter SSPCM 2014" in Rzeszów (Poland) in September 2014. The main challenge for the lecturers was the objective to present their subject as a review as well as in the form of introduction for beginners. Topics considered in the volume concentrate on: spin dynamics and spin transport in magnetic and non-magnetic structures, spin-orbit interaction in two-dimensional systems and graphene, and new mathematical method used in the condensed matter physics."--

This book is a collection of lecture notes which were presented by invited speakers at the Eleventh School on Theoretical Physics "Symmetry and Structural Properties of Condensed Matter SSPCM 2014" in Rzeszów (Poland) in September 2014. The main challenge for the lecturers was the objective to present their subject as a review as well as in the form of introduction for beginners. Topics considered in the volume concentrate on: spin dynamics and spin transport in magnetic and non-magnetic structures, spin-orbit interaction in two-dimensional systems and graphene, and new mathematical method used in the condensed matter physics. Contents: Lectures on Non-Abelian Bosonization (A M Tsvelick)Electrical and Thermal Control of Magnetic Moments (J Barnaś, P Balaz, A Dyrdał and V K Dugaevk)Rigged String Configurations, Bethe Ansatz Qubits, and Conservation of Parity (T Lulek)Nonequilibrium Spin Dynamics: From Protons in Water to a Gauge Theory of Spin-Orbit Coupling (I V Tokatly and E Ya Sherman)Non-Markovian Effects in the Lindblad Master Equation Approach to Electronic Transport (P Ribeiro and V R Vieira)Quantum Transport in Hybrid Nanostructures (K I Wysokiński, T Domański and B Szukiewicz)Resonant Scattering Off Magnetic Impurities in Graphene: Mechanism For Ultrafast Spin Relaxation (D Kochan, M Gmitra and J Fabian)Spin-Orbit Interaction and Related Transport Phenomena in 2D Electron and Hole Systems (A Khaetskii)Landau Weak Crystallization Theory and Its Applications (E I Kats)Coupled Polarization/Magnetization Dynamics in Composite Multiferroics: An Overview (A Sukhov, L Chotorlishvili, C L Jia and J Berakdar)Reservoir Approach to Two-Dimensional Electron Gas in a Magnetic Field (W Zawadzki, A Raymond and M Kubisa)From Graphene and Topological Insulators to Weyl Semimetals (R D Y Hills, M Brada, Yang Liu, M Pierpont, M B Sobnack, W M Wu and F V Kusmartsev) Readership: For graduate students and junior condensed matter theorists. Key Features:Intermediate level between students textbook and monographProminent contributorsVarious modern aspects of condensed matter theoryKeywords:Symmetry;Spin Dynamics;Graphene;Topological Insulators;Nanostructures

The focus here is on density matrix theory cast into a representation - SU(n) algebra - since this is particularly adapted to describing networks of quasi-molecular subsystems. This approach allows an understanding of how classical properties emerge within a quantum mechanical world and how non-classical features survive in a classical environment. The authors introduce and discuss non-classical aspects such as single-particle and multi-particle coherence such that a picture evolves of how these features are generated and destroyed by interactions with the environment. The outcome is a description of how the dynamics of individual quantum systems are interrelated with information dynamics.

This book focuses on complex shaped micro- and nanostructures for future biomedical and sensing applications that were investigated by both theory and experiments. The first part of the book explores rotation-translation coupling of artificial microswimmers at low Reynolds numbers. Usually corkscrew shapes, i.e chiral shapes, are considered in such experiments, due to their inspiration from nature. However, the analysis of the relevant symmetries shows that achiral objects can also be propulsive, which is experimentally demonstrated for the first time. In the second part, a new single-particle spectroscopy technique was developed and the role of symmetry in such measurements is carefully examined. Spectra stemming from one individual nanoparticle that is moving freely in bulk solution, away from a surface, and only due to Brownian motion, are presented. On that basis, the rotationally averaged chiroptical spectrum of a single nanoparticle is measured - a novel observable that has not been accessible before.

This book summarizes the state of the art in the theoretical modeling of inorganic nanostructures. Extending the first edition, published in 2015, it presents applications to new nanostructured materials and theoretical explanations of recently discovered optical and thermodynamic properties of known nanomaterials. It discusses the developments in theoretical modeling of nanostructures, describing fundamental approaches such as symmetry analysis and applied calculation methods. The book also examines the theoretical aspects of many thermodynamic and the optical properties of nanostructures. The new edition includes additional descriptions of the theoretical modeling of nanostructures in novel materials such as the V2O5 binary oxide, ZnS, CdS, MoSSe and SnS2.

This contributed volume is inspired by the seminal discovery and identification of C60. Starting with a comprehensive discussion featuring graphene based nanostructures, subsequent chapters include topological descriptions of matrices, polynomials and indices, and an extended analysis of the symmetry and topology of nanostructures. Carbon allotropes such as diamond and its connection to higher-dimensional spaces is explored along with important mathematical and topological considerations. Further topics covered include spontaneous symmetry breaking in graphene, polyhedral carbon structures, nanotube junction energetics, and cyclic polyines as relatives of nanotubes and fullerenes. This book is aimed at researchers active in the study of carbon materials science and technology.