Let (E,ζ)= indlim (E n ,ζ n ) be an inductive limit of locally convex spaces. We say that ( DST ) holds if each bounded set in (E,ζ) is contained and bounded in some (E n ,ζ n ). We introdu...Let (E,ζ)= indlim (E n ,ζ n ) be an inductive limit of locally convex spaces. We say that ( DST ) holds if each bounded set in (E,ζ) is contained and bounded in some (E n ,ζ n ). We introduce a property which is weaker than fast completeness, quasi-fast completeness, and prove that for inductive limits of strictly webbed spaces, quasi-fast completeness implies that ( DST ). By using De Wilde’s theory on webbed spaces,we also give some other conditions for ( DST ). These results improve relevant earlier results.展开更多
The ultracold polar molecules with the tunable dipole-dipole interaction, not only would enable explorations of a large class of exotic many-body physics phenomena, but also could be used for quantum information proce...The ultracold polar molecules with the tunable dipole-dipole interaction, not only would enable explorations of a large class of exotic many-body physics phenomena, but also could be used for quantum information processing. In the present paper we demonstrate that this dipole-dipole interaction can generate the degenerate chiral quantum states acting as a qubit robust against noise when the ultracold polar molecules are confined by a triangular lattice. Moreover, we also find two first-order quantum phase transitions by controlling an external driving t^eld. One is the transition with the change of the different degenerate chiral quantum states. The other is the transition with the breaking of the degenerate quantum chirAL states to the nondegenerate state. In experiment, these first-order quantum phase transitions can be detected by measuring the collective molecular population.展开更多
文摘Let (E,ζ)= indlim (E n ,ζ n ) be an inductive limit of locally convex spaces. We say that ( DST ) holds if each bounded set in (E,ζ) is contained and bounded in some (E n ,ζ n ). We introduce a property which is weaker than fast completeness, quasi-fast completeness, and prove that for inductive limits of strictly webbed spaces, quasi-fast completeness implies that ( DST ). By using De Wilde’s theory on webbed spaces,we also give some other conditions for ( DST ). These results improve relevant earlier results.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10904092,10934004,60978018,11074154,61008012,and 11075099the ZJNSF under Grant No.Y6090001
文摘The ultracold polar molecules with the tunable dipole-dipole interaction, not only would enable explorations of a large class of exotic many-body physics phenomena, but also could be used for quantum information processing. In the present paper we demonstrate that this dipole-dipole interaction can generate the degenerate chiral quantum states acting as a qubit robust against noise when the ultracold polar molecules are confined by a triangular lattice. Moreover, we also find two first-order quantum phase transitions by controlling an external driving t^eld. One is the transition with the change of the different degenerate chiral quantum states. The other is the transition with the breaking of the degenerate quantum chirAL states to the nondegenerate state. In experiment, these first-order quantum phase transitions can be detected by measuring the collective molecular population.
