By V Dotsenko
Goals to explain purely the hot sector of statistical mechanics often called spin-glasses, encompassing structures during which quenched disease is the dominant issue.
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Extra info for An introduction to the theory of spin glasses and neural networks
This is a section of Fig. ) The aforementioned consideration leads to a very important result. The electrons in a crystal behave, for most kx values, like free electrons, except when kx approaches the value n · p/a. Besides this “periodic zone scheme” (Fig. 3), two further zone schemes are common. In the future we will use mostly the “reduced zone scheme” (Fig. 4), which is a section of Fig. 3 between the limits Æp/a. In the “extended zone scheme” (Fig. 5), the deviations from the free electron parabola at the critical points kx ¼ n · p/a are particularly easy to identify.
1). This statement seems to be trivial at this point. The difference to the bound electron case will become, however, evident in the next section. 5) to be the wave number, k. Thus, a is here identical with k. 7) that the quantity k is proportional to the momentum p and, because of p ¼ mv, also proportional to the velocity of the electrons. Since both momentum and velocity are vectors, it follows that k is a vector, too. ” We shall use the wave vector in the following sections frequently. The k-vector describes the wave properties of an electron, just as one describes in classical mechanics the particle property of an electron with the momentum.
8)). 6) provides E¼À 2 In most cases we shall denote the rest mass by m instead of m0. 17 3. 8) It should be noted here that quantum mechanical equations can be obtained from classical equations by applying differential operators to the wave function C (Hamiltonian operators). 8). 3. Special Properties of Vibrational Problems The solution to an equation for a vibration is determined, except for certain constants. 2, only certain vibrational forms are possible when boundary conditions are imposed.
An introduction to the theory of spin glasses and neural networks by V Dotsenko