Joint ICTP/SISSA STAT_PHYS Seminar on 31 January 2012

[ivanisse]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR

Tuesday, 31 January 2012  -   11:30 a.m.

SISSA, Santorio Building, Room 128


Paulo Eduardo Conçalves de Assis (SISSA)


" Higher level Integrals of Motion from ODEs in the complex plane "


Abstract

In this talk I will revise the basic ideas underlying a powerful 
correspondence between integrable models and ordinary differential 
equations (or IM/ODE correspondence, for short). This spectral 
equivalence played an important role in the study of PT-symmetry, 
providing rigorous proofs about the spectra of an important class of 
non-Hermitian Hamiltonians based on known integrable results. My 
intention is to make progress in the opposite direction, namely to 
extract information about integrable systems by using differential 
equations. The comparison between the eigenvalues of the ODEs and the 
spectral parameters in certain Quantum Integrable Models is considerably 
well understood for the vacuum state of the latter. For excited states, 
however, results are only known for the problem with su(2) symmetry. 
Here I will show this can be extended to the su(2|1) super-symmetric 
problem in order to establish the exact correspondence also for excited 
states.