Some new properties of polarizable Carnot group are given.By choosing a proper constant a nontrivial solution of a class of non-divergence Dirichlet problem on the polarizable Carnot group is constructed.Thus the mult...Some new properties of polarizable Carnot group are given.By choosing a proper constant a nontrivial solution of a class of non-divergence Dirichlet problem on the polarizable Carnot group is constructed.Thus the multi-solution property of corresponding non-homogeneous Dirichlet problem is proved and the best possible of LQ norm in the famous Alexandrov-Bakelman-Pucci type estimate is discussed.展开更多
By using the dispersion theory instead of the Frohlich Hamiltonian, the polaron energy in a quantum aot with a parabolic confinement potential is investigated at finite temperatures. It is found that the self-trapping...By using the dispersion theory instead of the Frohlich Hamiltonian, the polaron energy in a quantum aot with a parabolic confinement potential is investigated at finite temperatures. It is found that the self-trapping energy of the polaron decreases with the increasing temperature, and the temperature effect is more obvious in quantum dots with weaker confinement.展开更多
文摘Some new properties of polarizable Carnot group are given.By choosing a proper constant a nontrivial solution of a class of non-divergence Dirichlet problem on the polarizable Carnot group is constructed.Thus the multi-solution property of corresponding non-homogeneous Dirichlet problem is proved and the best possible of LQ norm in the famous Alexandrov-Bakelman-Pucci type estimate is discussed.
基金Supported by Shanghai Leading Academic Discipline Project(B408)National Key Project for Basic Research of China under Grant Nos.2010CB923203,2006CB806006,and 2006CB921105+1 种基金National Natural Science Foundation of China under Grant Nos.10904038 and 10874044Shanghai Municipal Science and Technology Commission under Grant Nos.09JC1404700 and 08PJ1404800
文摘By using the dispersion theory instead of the Frohlich Hamiltonian, the polaron energy in a quantum aot with a parabolic confinement potential is investigated at finite temperatures. It is found that the self-trapping energy of the polaron decreases with the increasing temperature, and the temperature effect is more obvious in quantum dots with weaker confinement.
