Line Groups in Physics Theory and Applications to Nanotubes and Poly
This volume gives a detailed and up-to-date overview of the line groups, the groups that describe the symmetry of quasi-one dimensional crystals. Nanotubes, nanowires, nanosprings, nanorods, and polymers are examples remarkable enough to have kept nanosci
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Introduction
Polymers, due to palette of remarkable and applicable properties, attract interest of physicists, chemists, and biologists over decades. Most of these extraordinary characteristics originate from their reduced dimensionality and regular structure. Discovery of carbon nanotubes by Iijima in 1991, and the revolution they caused in material science, additionally stressed out that quasi-one-dimensionality was crucially responsible for the peculiarities of these systems. The well-established notions of nanoscience, nanotechnology, and/or nanobiotechnology illustrate impact of these systems on both the fundamental science and technology. Actually, the acronym N&N, stressing out only the nanoscale, is the best description of the whole bunch of interrelated classical sciences and high-tech breakthroughs of the fastgrowing field initialized by the discovery of nanotubes. This is probably the most remarkable example how development of the fundamental and applied science is interrelated through endless series of feedbacks. Quantum mechanics proved to be the key to the nano-world. Over seven decades before the dawn of N&N quantum mechanical formalism and techniques have been developing intensively and successfully through many challenges. Various approaches to many-body problems, correlation and interference effects, advanced numerical algorithms, and many other quantum mechanical achievements have been already at nano-researchers disposal. However, symmetry, one of the deepest concepts in science and philosophy, which after the work of Wigner in the second quarter of the previous century became one of the roots as well as a powerful technical tool of quantum mechanics, has not been fully exploited. This is a bit strange in a view of its cornerstone status in particle physics and its long and extensive use in solid state physics over more than half a century, to mention only the Bloch theorem, through which symmetry underlies all the results for crystals. Nevertheless, in nanoscience symmetry is not used in a systematic way. This is even more surprising since the translational invariance from the very beginning proved to be extremely fruitful in the theoretical studies of nanotubes and stereo-regular polymers, enabling many important predictions. In particular, due to the symmetry electronic bands of carbon nanotubes are easily found analytically (in a simplified model though). Prediction of a wide variety of the conducting properties was probably the first major result, which paved the way Damnjanovi´c, M., Miloševi´c, I.: Introduction. Lect. Notes Phys. 801, 1–5 (2010) c Springer-Verlag Berlin Heidelberg 2010 DOI 10.1007/978-3-642-11172-3_1
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1 Introduction
for N&N. And almost a decade after the discovery of nanotubes, their full symmetry was reported and the symmetry-based results started to appear, although still rarely enough. One possible reason for such a delay is that there is no systematic monograph on the symmetry of quasi-one-dimensional structures, unlike the vast number of books devoted to the
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