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 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 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.

Over the last 25 years, dynamical mean-field theory (DMFT) has emerged as one of the most powerful new developments in many-body physics. Written by one of the key researchers in the field, this book presents the first comprehensive treatment of this ever-developing topic. Transport in Mutlilayered Nanostructures is varied and modern in its scope, and:A series of over 50 problems help develop the skills to allow readers to reach the level of being able to contribute to research. This book is suitable for an advanced graduate course in DMFT, and for individualized study by graduate students, postdoctoral fellows and advanced researchers wishing to enter the field.