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DTSTAMP:20260825T154027Z
LAST-MODIFIED:20161011T133923Z
DTSTART:20161013T160000Z
DTEND:20161013T170000Z
UID:event1678@bu.edu
URL:http://physics.bu.edu/internal/events/show/1678
SUMMARY:Eigenvalue distributions of the correlation matrix: A sensitive ind
	icator for phase transitions?
DESCRIPTION:Featuring Thomas H. Seligman\, Instituto de Ciencias Fisicas\n\
	nPart of the Biophysics/Condensed Matter Seminar Series.\n\nUnder a long ti
	me project to discover early warning signals of abrupt changes in complex s
	ystems\, we have undertaken to study the effect on the spectrum of the corr
	elation matrix of synthetic data obtained from dynamical models. I will pre
	sent analytic results for equilibrium states at phase transitions for discr
	ete models with power-law decay in an arbitrary number of dimensions suppor
	ted by numerics that include studies of short time series. We find that pow
	er-law behavior in space carries over to the spectrum with a power we give 
	explicitly. This behavior can be traced also if we have many short time ser
	ies. Going beyond equilibrium dynamics we study the non-equilibrium steady 
	states corresponding to various phases in the totally asymmetric simple exc
	lusion process\, a soluble stochastic model of a one lane one way street wi
	th given and probabilities of entrance and exit.  In particular we consider
	 the transition limit between the high-density and low-density conditions o
	f the entrance and exit probabilities\, known to carry a first order phase 
	transition. Again we find a power law\, although there is no power law in t
	he exactly know space correlations. At the other critical lines and in the 
	constant current regions we find unusual behavior for the lowest eigenvalue
	s\, as yet not understood. In the high and low density regions respectively
	 the Marchenko Pastur distribution\, corresponding to white-noise time-seri
	es is found for the eigenvalues to excellent numerical accuracy.
LOCATION:SCI 352\, 590 Commonwealth Avenue\, 02215
STATUS:CONFIRMED
CLASS:PUBLIC
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