## An Introduction to Macroscopic Quantum Phenomena and Quantum by A. O. Caldeira

By A. O. Caldeira

Reviewing macroscopic quantum phenomena and quantum dissipation, from the phenomenology of magnetism and superconductivity to the presentation of different types for quantum dissipation, this publication 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, built from common phenomenological methods to every quarter. Dissipation clearly performs a big function in those phenomena, and accordingly semi-empirical versions for quantum dissipation are brought and utilized to the learn of some vital quantum mechanical results. The ebook additionally discusses the relevance of macroscopic quantum phenomena to the keep an eye on of meso- or nanoscopic units, relatively people with capability purposes in quantum computation or quantum info. it really is perfect for graduate scholars and researchers.

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

**Sample text**

A final remark about the dynamics of the magnetization is now in order. 42) magnetization expressions. , 1996), which would ultimately be responsible for the description of the equilibrium properties of our systems at high or low temperatures. Although they do not influence the relaxation of the average value of the magnetization to equilibrium, they are crucial to account for the fluctuations shown by the dynamical variable about its equilibrium configuration. 1 Magnetic particles The first problem we want to treat now is that of a small number of magnetic moments which interact ferromagnetically.

If the particle is in its magnetic ground-state configuration one has μ = +μˆz. 68) develops, as we have described above. 67). 70) √ with ω0 ≡ 2γg K 1 K 2 /μ. 69), are only valid for fields not so close to Hc . For Hc > H > 0, the potential energy U (θ) develops local minima U (0) = 0 and U (π) = 2ω02 H/Hc as shown in Fig. 5. The former is the absolute minimum of the function, representing the stable configuration for the magnetic moment, whereas the latter, a relative minimum of the energy, is a metastable configuration of that quantity.

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. In what follows we will approach the physics of the magnetic system from a slightly different point of view, which will be more appropriate for our future needs.