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 booklet develops the fundamental fabric essential to comprehend the quantum dynamics of macroscopic variables. Macroscopic quantum phenomena are provided via a number of examples in magnetism and superconductivity, built from basic phenomenological methods to every zone. Dissipation obviously performs a major 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 e-book additionally discusses the relevance of macroscopic quantum phenomena to the regulate of meso- or nanoscopic units, rather people with strength purposes in quantum computation or quantum info. it's perfect for graduate scholars and researchers.
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Additional info for An Introduction to Macroscopic Quantum Phenomena and Quantum Dissipation
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 ).
However, as we have already mentioned, we are treating here a small particle of a hard magnetic material. Quantum mechanically what can be very useful for analyzing this system is the problem of addition of N spins 1/2. This problem is well known and can be found in any textbook of quantum theory (see, for example, Merzbacher (1998)). What we look for is a simultaneous (z) eigenstate of S 2 = ( k Sk )2 and S (z) = k Sk , where k refers to any given spin of the system. The eigenstates of this problem are labeled by |S, M S , where S = N /2, (N − 2)/2, (N − 4)/2, .
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. 70) it can be shown that the magnetic moment can oscillate with frequencies ω0 (1 ± H/Hc ) about each minimum of the potential, where the plus sign applies to θ = 0 and the minus sign to θ = π .