Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2008-05-22
Physics
Condensed Matter
Disordered Systems and Neural Networks
7 pages, 2 figures (the paper is essentially reworked)
Scientific paper
10.1088/1751-8113/42/7/075001
We study the statistical and dynamic properties of the systems characterized by an ultrametric space of states and translationary non-invariant symmetric transition 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 matrix elements. We also compute the averaged "survival probability" (SP) having sense of the probability to find a system in the initial state by time $t$. Using the similarity between the averaged SP for locally constant randomized Parisi matrices and the partition function of directed polymers on disordered trees, we show that for times $t>t_{\rm cr}$ (where $t_{\rm cr}$ is some critical time) a "lacunary" structure of the ultrametric space occurs with the probability $1-{\rm const}/t$. This means that the escape from some bounded areas of the ultrametric space of states is locked and the kinetics is confined in these areas for infinitely long time.
Avetisov Vladik A.
Bikulov Albert Kh.
Nechaev S. K.
No associations
LandOfFree
Random Hierarchical Matrices: Spectral Properties and Relation to Polymers on Disordered Trees does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Random Hierarchical Matrices: Spectral Properties and Relation to Polymers on Disordered Trees, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random Hierarchical Matrices: Spectral Properties and Relation to Polymers on Disordered Trees will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-500042