DOI: 10.1140/epje/i2002-10088-x
Euclidean random matrices, the glass transition and the boson peak
G. ParisiDipartimento di Fisica, Sezione INFN, SMC and UdRm1 of INFM, Università di Roma "La Sapienza", Piazzale Aldo Moro 2, I-00185 Rome (Italy) giorgio.parisi@roma1.infn.it
(Received 4 May 2002 / Published online: 23 December 2002)
Abstract
In this paper I will describe some results that have been recently
obtained in the study of random Euclidean matrices, i.e. matrices
that are functions of random points in Euclidean space.
In the case of translation invariant matrices one generically finds
a phase transition between a phonon phase and a saddle phase.
If we apply these considerations to the study of the Hessian of the
Hamiltonian of the particles of a fluid, we find that this
phonon-saddle transition corresponds to the dynamical phase
transition in glasses, that has been studied in the framework of the
mode coupling approximation. The boson peak observed in glasses
at low temperature is a remanent of this transition.
61.43.Fs - Glasses.
63.50.+x - Vibrational states in disordered systems.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002