By A. O. Caldeira

Reviewing macroscopic quantum phenomena and quantum dissipation, from the phenomenology of magnetism and superconductivity to the presentation of different versions for quantum dissipation, this ebook develops the fundamental fabric essential to comprehend the quantum dynamics of macroscopic variables. Macroscopic quantum phenomena are awarded via numerous examples in magnetism and superconductivity, constructed from common phenomenological methods to every sector. Dissipation evidently performs an immense position in those phenomena, and for this reason semi-empirical types for quantum dissipation are brought and utilized to the learn of some very important quantum mechanical results. The e-book additionally discusses the relevance of macroscopic quantum phenomena to the keep watch over of meso- or nanoscopic units, relatively people with capability functions in quantum computation or quantum details. it truly is excellent for graduate scholars and researchers.

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**Sample text**

This is known as the single ion anisotropy. However, this is not the only possible source of anisotropy in the problem. When more electrons are present, exchange terms together with the spin–orbit interaction may cause what is called the exchange anisotropy. A very accessible presentation of the general mechanisms of anisotropy in magnetic systems can be found in Bertotti (1998). The above brief analysis of the different magnetically active microscopic terms of the electronic Hamiltonian led us basically to four important observed effects: exchange, anisotropy, demagnetization, and external field energies.

88) √ E w2 (L) R ∝ L. 87). 16 Random potential 2004) and allow for small distortions of the wall, its segments of that specific length will be independently pinned. 87) in an approximate form for a wall of length L and H = 0 as E w (u, L) = b kw u 2 + bv R 2 L L . 90) which implies that for pinning energies much weaker than the typical elastic energy scale we have L c >> ζ . This means that in the absence of an external field the wall finds its optimum profile accommodating long segments of length L c independently through the valleys of the landscape resulting from the presence of the pinning centers as in Fig.

1 Magnetic particles The first problem we want to treat now is that of a small number of magnetic moments which interact ferromagnetically. The number of constituents, although small compared with Avogadro’s number, is considered large enough to allow the system to become ordered below a certain critical temperature. So, this whole set of particles would behave as a single huge spin with S >> 1. This is what we call a magnetic particle and a possible example thereof is a small ferromagnetic region with linear nanoscopic dimensions.