No abstract

We discuss some natural maps from a unitary group U(n) to a smaller group U(n−m). (These maps are versions of the Livšic characteristic function.) We calculate explicitly the direct images of the Haar measure under some maps. We evaluate some matrix integrals over classical groups and some symmetric spaces. (Values of the integrals are products of -functions.) These integrals generalize Hua integrals. We construct inverse limits of unitary groups equipped with analogues of Haar measure and evaluate some integrals over these inverse limits.

Based on the inversion pair potentials, the molecular dynamics simulations were performed to study the pressure-induced B1-B2 phase transition in NaCl crystal. Under a transition pressure close to the experimental value, it is found at the temperature of 600 K that there is a transformation from the six-fold coordinated B1 structure to the eight-fold coordinated B2 phase. But at the same temperature, the reversible transformation B2-B1 was presented under zero pressure by the same interionic potentials. These are in good agreement with the experimental observations. The atomistic mechanism of the phase transition was discussed in terms of the configurations under different pressures.