Spectra of large random matrices and phase transitions
主 题: Spectra of large random matrices and phase transitions
报告人: Thierry Lévy（Universite Pierre et Marie Curie）
时 间: 2014-03-07 15:00-16:00
地 点: 理科一号楼1114（数学所活动）
The quantum mechanical Hamiltonian of any physical sytem which contains more than a handful of particles is a very large matrix from which it is practically impossible to extract any physical information.The point of statistical physics is that its large size is precisely what makes this system amenable to computations : one expects its Hamiltonian to share the typical properties of a very large (sensibly-chosen) random matrix.
I will discuss a duly celebrated theorem of Wigner who, in the 1950\'s, made accurate predictions about the spacings of energy levels of heavy atoms by studying the spectrum of large Gaussian random Hermitian matrices.We will then replace Hermitian matrices by unitary matrices and see why phase transitions occur in this new context, in accordance with old predictions of physicists and more recent work of mathematicians.
* This talk will be accessible to graduate students and I will assume no prior familiarity with the theory of random matrices. *