2 seminars coming up

[CM ICTP - Trieste]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR





Tuesday, 2 December    -    12:30 hrs.





Seminar Room   ICTP Leonardo Building - 1st floor





R. KÜHN   ( King's College, London )



" Spectra of sparse random matrices and localization on random graphs "



Abstract



We compute the spectral density for ensembles of sparse symmetric  
random matrices using replica. Our formulation of the replica- 
symmetric ansatz shares the symmetries of the one suggested in a  
seminal paper by Rodgers and Bray (symmetry with respect to  
permutation of replica / and/ rotation symmetry in the space of  
replica), but uses a different representation in terms of  
superpositions of Gaussians. It gives rise to a pair of integral  
equations which can be solved by a stochastic population-dynamics  
algorithm. Remarkably our representation allows to identify pure- 
point contributions to the spectral density related to the existence  
of normalizable eigenstates. Our approach is not restricted to  
matrices defined on graphs with Poissonian degree distribution.  
Matrices defined on regular random graphs or on scale-free graphs,  
are easily handled. We also look at matrices with row constraints  
such as discrete graph Laplacians, and at Random Schroedinger  
Operators defined on random graphs.  Our approach naturally allows to  
unfold the total density of states into contributions coming from  
vertices of different local coordination and an example of such an  
unfolding is presented. Our results are well corroborated by  
numerical diagonalization studies of large finite random matrices.

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SEMINAR on  Disorder and strong electron correlations



Thursday, 4 December      -  11:00 a.m.



Seminar Room,  Leonardo Building - first floor



D. BAGRETS   ( Forschungszentrum Karlsruhe )



" Nonequilibrium kinetics of a  disordered Luttinger liquid "



Abstract



We develop a kinetic theory for strongly correlated one-dimensional  
electron systems  out of equilibrium, within the framework of the  
Luttinger liquid model. In the absence  of disorder (backscattering  
off impurities), the model is completely integrable and  as such  
exhibits no relaxation to equilibrium. We formulate a theoretical  
framework  to study relaxation processes due to the interplay of  
disorder and electron-electron interactions, based on kinetic  
equations for electron and plasmon distribution functions. We  
calculate the rate of energy relaxation (equilibration) in a  
disordered Luttinger liquid, relevant to the transport properties of  
quantum wires at finite bias voltage. Remarkably, for not too low  
temperature and bias, the energy-relaxation rate is found to be given  
by the rate of elastic scattering off disorder, independent of the  
strength  of electron-electron interaction and temperature.