Boris	Altshuler - Columbia University	#
Integrability: from KAM theory to Anderson Localization # 	
Localization of the eigenfunctions of quantum particles in a 
random potential was discovered
by P.W. Anderson more than 50 years ago. In spite of its 
respectable maturity and intensive
theoretical and experimental studies this field is far from 
being exhausted. Anderson
localization was originally discovered in connection with spin 
relaxation and charge transport
in disordered conductors. Later this phenomenon was observed for 
light, microwaves, sound,
and more recently for cold atoms. Moreover, it became clear that 
the domain of applicability
of the concept of localization is much broader. For example, it 
provides an adequate
framework for discussing the transition between integrable and 
chaotic behavior in quantum
systems. We will discuss the connection between the classical 
(Kolmogorov, Arnold, Moser
theory) and quantum (Anderson Localization) transitions between 
integrable and chaotic
types of behavior of complex physical systems. We will consider 
several examples of the
manifestation of this paradigm - from adiabatic quantum 
computation to many-body
statistical mechanics.