By Jan L. van Hemmen, Ingo Morgenstern

This booklet comprises many of the invited contributions to the Heidelberg Colloquium on Glassy Dynamics, held in June 1986 and masking the 3 subject matters: spin glasses, optimization and neural networks. It contains experimental papers on spin glasses and glasses in addition to theoretical paintings at the spin-glass transition, the outline of the spin-glass part, and gradual rest phenomena. New recommendations for fixing combinatorial optimization difficulties are awarded with specific emphasis put on simulated annealing. ultimately, a complete assessment of the statistical mechanics of neural networks is given. The thorough and in part review-like therapy of a few of the issues makes this booklet imperative analyzing for researchers and graduate scholars in physics, biophysics and optimization with unique curiosity in magnetic platforms, glasses and mind learn, repectively. N

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**Example text**

In this limit, one obtains the London equation, ne2 J= A A. me As was shown in Chapter 1, the Meissner effect can be derived if the above equation is solved simultaneously with the Maxwell equations. Note that if one takes A = 0 in Eq. 60), one obtains K = ne2/me, which exactly cancels the first term of (ji(q,co)). In a normal state, no current proportional to the vector potential A exists and, as in the Ohmic law, the lowest order contribution to the current response is from terms proportional to coA.

60) Let us consider a static magnetic field, co = 0, first. /'Ao)2) provided that qv?

57) Since v? >> ^s? sound absorption takes place when quasi-particles near the equator of the Fermi surface with momenta perpendicular to q are scattered by the sound wave. Therefore A(T) in Eq. 57) is the energy gap averaged over the equator. As is shown in Fig. 4, a s /a n directly measures the temperature dependence of the gap. It should be added that in the case of transverse waves the absorption suddenly becomes small as the temperature is reduced below Tc. This is due to the Meissner effect since, in the free electron model, the vector potential appears in the absorption coefficient.