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The devil is in the details: spectrum and eigenvalue distribution of the discrete Preisach memory model. (English) Zbl 1524.82012

Summary: We consider the adjacency matrix associated with a graph that describes transitions between the states of the discrete Preisach memory model. This matrix can also be associated with the “last-in-first-out” inventory management rule. We present an explicit solution for the spectrum by showing that the characteristic polynomial is the product of Chebyshev polynomials. The eigenvalue distribution (density of states) is explicitly calculated and is shown to approach a scaled Devil’s staircase. The eigenvectors of the adjacency matrix are also expressed analytically.

MSC:

82B23 Exactly solvable models; Bethe ansatz
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
41A50 Best approximation, Chebyshev systems
82D40 Statistical mechanics of magnetic materials

Software:

HysterSoft; KronFit
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References:

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