New Developments in Relativistic Quntum Theory

Peter Bongaarts

Onuma Toshiro

Kundu, A

A new integrable class of quantum models representing a family of different discrete-time or relativistic generalisations of the periodic Toda chain (TC), including that of a recently proposed classical close to TC model [7] is presented. All such models are shown to be obtainable from a single ancestor model at different realisations of the underlying quantised algebra. As a consequence the $(2\\times 2)$ Lax operators and the associated quantum $R$-matrices for these models are easily derived ensuring their quantum integrability. It is shown that the functional Bethe ansatz developed for the quntum TC is trivially generalised to achieve seperation of variables also for the present models.

Detlef Dürr, Dustin Lazarovici

James E. Dodd, Ben M. Gripaios

YI Xue-hu

The quantum traditional adiabatic theorem was present and traditional approximation conditions were given.Based on existence of insufficence about quntum traditional adiabatic approximation condition,the new adiabatic theory and approximation condition were proposed and discussed by means of perturbative approach and U(1)-invariant expasion.The properties of quantum geometric potential contained in the new adiabatic condition were analyzed and discussed.