Random Hierarchical Matrices: Spectral Properties and Relation to Polymers on Disordered Trees - Condensed Matter > Disordered Systems and Neural NetworksReportar como inadecuado




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Abstract: We study the statistical and dynamic properties of the systems characterizedby an ultrametric space of states and translationary non-invariant symmetrictransition matrices of the Parisi type subjected to -locally constant-randomization. Using the explicit expression for eigenvalues of such matrices,we compute the spectral density for the Gaussian distribution of matrixelements. We also compute the averaged -survival probability- SP having senseof the probability to find a system in the initial state by time $t$. Using thesimilarity between the averaged SP for locally constant randomized Parisimatrices and the partition function of directed polymers on disordered trees,we show that for times $t>t { m cr}$ where $t { m cr}$ is some criticaltime a -lacunary- structure of the ultrametric space occurs with theprobability $1-{ m const}-t$. This means that the escape from some boundedareas of the ultrametric space of states is locked and the kinetics is confinedin these areas for infinitely long time.



Autor: V.A. Avetisov, A.Kh. Bikulov, S.K. Nechaev

Fuente: https://arxiv.org/



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