Mechanical/magnetic degrees of freedom

V. Nonlinear Susceptibilities of Magnetic Suspensions Interplay of Mechanical and Magnetic Degrees of Freedom... 

A. Dynamic Field-Induced Birefringence in the Framework of the Egg Model Interplay between Mechanical and Magnetic Degrees of Freedom of the Particles... 

V. NONLINEAR SUSCEPTIBILITIES OF MAGNETIC SUSPENSIONS INTERPLAY OF MECHANICAL AND MAGNETIC DEGREES OF FREEDOM... 

Mc/s and the spontaneous emission lifetime is 10 sec. Obviously this lifetime is too long and the transitions will be saturated exceedingly easily. In other words, the populations of the two levels become essentially equal and no net transition can be observed. Fortunately there are a number of nonradiative relaxation mechanisms open to the upper spin level including interactions with other electrons, with nuclei having nuclear magnetic moments, and with the lattice. The latter process is often known as spin-lattice relaxation. The term "lattice" generally refers to the degrees of freedom of the system other than those directly related with spin. Spin... 

In summary, statistical quantum mechanics permits us to derive strictly classical observables (such as the classical specific magnetization operator) by appropriate limit considerations (such as a limit of infinitely many spins in case of the Curie-Weiss model). However, statistical quantum mechanics cannot cope with fuzzy classical observables (for finitely many degrees of freedom) since different decompositions of a thermal state Dp are considered to be equivalent. The introduction of a canonical decomposition of Dp into pure states will give rise to an individual formalism of quantum mechanics in which fuzzy classical observables can be treated in a natural way. 

The next most familiar part of the picture is the upper right-hand corner. This i s the domain of classical applied mathematics and mathematical physics where the linear partial differential equations live. Here we find Maxwell s equations of electricity and magnetism, the heat equation, Schrodinger s wave equation in quantum mechanics, and so on. These partial differential equations involve an infinite continuum of variables because each point in space contributes additional degrees of freedom. Even though these systems are large, they are tractable, thanks to such linear techniques as Fourier analysis and transform methods. 

The continuum mechanics of solids and fluids serves as fhe prototypical example of the strategy of turning a blind eye to some subset of the full set of microscopic degrees of freedom. From a continuum perspective, the deformation of the material is captured kinematically through the existence of displacement or velocity fields, while fhe forces exerted on one part of the continuum by the rest are described via a stress tensor field. For many problems of interest to the mechanical behavior of materials, it suffices to build a description purely in terms of deformation fields and their attendant forces. A review of the key elements of such theories is the subject of this chapter. However, we should also note that the purview of continuum models is wider than that described here, and includes generalizations to liquid crystals, magnetic materials, superconductors and a variety of other contexts. 

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