QUANTUM
   INTEGRABLE
   SYSTEMS and
   GEOMETRY
   2012









 3-7 SEPTEMBER 2012
 OLHÃO, PORTUGAL

Long-time and large-distance asymptotic behavior of correlation functions in quantum integrable models

Karol Kozlowski

(download presentation)

Quantum integrable models in one dimension constitute a class of non-trivial many-body quantum Hamiltonians where a great number of calculations is feasible to the very end, this without any approximations.It has been shown over the years that it is possible to give a precise description of the spectrum of these model. Recently, there appeared various techniques allowing one to provide representations for the correlation functions in terms of series of multiple integrals. These depend on various parameters (distance, time, coupling constant,...) characterizing the correlator and can be thought of as generalizations of the Fredholm series for a determinant. In this talk, I will briefly discuss the structure of such series of multiple integrals and then overview the recent developments in respect to the extraction of the large-distance and/or long-time asymptotic behavior out of such representations. These results allow one to access to the long-time/large-distance asymptotic behavior of the two-point functions in the so-called non-linear Schrodinger model.