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 e-book develops the elemental fabric essential to comprehend the quantum dynamics of macroscopic variables. Macroscopic quantum phenomena are offered via numerous examples in magnetism and superconductivity, built from basic phenomenological methods to every sector. Dissipation evidently performs an immense function in those phenomena, and for this reason semi-empirical types for quantum dissipation are brought and utilized to the research of some very important quantum mechanical results. The booklet additionally discusses the relevance of macroscopic quantum phenomena to the keep watch over of meso- or nanoscopic units, fairly people with power purposes in quantum computation or quantum details. it really is excellent for graduate scholars and researchers.

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**Additional resources for An Introduction to Macroscopic Quantum Phenomena and Quantum Dissipation**

**Example text**

Let us now propose a phenomenological Hamiltonian to the magnetic system written as a functional of the magnetization. 5) by δ(r − ri ). 42) is still a quantum mechanical expression, we could, at least for high spin values ( s >> 1 ), replace M(r) by its average value, namely, the classical magnetization M(r). 43) from which a simple dimensional analysis tells us that αi = [L]2 and βa is dimensionless. 37) and measures basically the energy to distort the magnetization of the system. The minimum energy configuration is clearly the one which is uniform like the ferromagnetic phase.

Therefore, as one reaches the depinning field value, the wall moves to accommodate new metastable configurations of lower energy of the tilted random potential energy landscape as shown in Fig. 17. Once again, the same reasoning which led us to argue in favor of depinning for H < Hdep can also be used here. As one approaches the depinning field it becomes easier for the pinned segments of length L c (H ) to be, for example, thermally acti(e f f ) vated over the effective potential barrier Uc (H ).

Therefore, droplets can appear and shrink at any point of the sample until one of them is formed with volume above the critical size, which expands and converts the whole sample into the more stable configuration. This is the phenomenon of nucleation, which is very well known in statistical mechanics (Landau and Lifshitz, 1974). The solution whose behavior is presented in Fig. 10 represents exactly the physics discussed above. At t = 0 the variable ρ is nothing but the radial coordinate r relative to a given origin.