The highly excited vibrational states of asymmetric linear tetratomic molecules are studied in the framework of Lie algebra. By using symmetric group U1(4) U2(4) U3(4), we construct the Hamiltonian that includes not o...The highly excited vibrational states of asymmetric linear tetratomic molecules are studied in the framework of Lie algebra. By using symmetric group U1(4) U2(4) U3(4), we construct the Hamiltonian that includes not only Casimir operators but also Majorana operators M12,M13 and M23, which are useful for getting potential energy surface and force constants in Lie algebra method. By Lie algebra treatment, we obtain the eigenvalues of the Hamiltonian, and make the concrete calculation for molecule C2HF.展开更多
Some new characterizations of nonnegative Hamiltonian operator matrices are given. Several necessary and sufficient conditions for an unbounded nonnegative Hamiltonian operator to be invertible are obtained, so that t...Some new characterizations of nonnegative Hamiltonian operator matrices are given. Several necessary and sufficient conditions for an unbounded nonnegative Hamiltonian operator to be invertible are obtained, so that the main results in the previously published papers are corollaries of the new theorems. Most of all we want to stress the method of proof. It is based on the connections between Pauli operator matrices and nonnegative Hamiltonian matrices.展开更多
In his paper (Phys., Lett., 94A(1983), p. 340),Tu Guizhang, based on a linear spectral problem, discussed the following hierarchy of coupled nonlinear evolution equations:
We investigate the effect of photons and phonons on Frenkel exciton spectrum. The Hamilto nian for a coupled system of the Frenkel excitons. the photons and the phonons is derived. The phonon-exciton interaction makes...We investigate the effect of photons and phonons on Frenkel exciton spectrum. The Hamilto nian for a coupled system of the Frenkel excitons. the photons and the phonons is derived. The phonon-exciton interaction makes the energy band of the Frenkel excitons narrow. The photons and the Frenkel excitons make up Frenkel exciton polaritons which are quasi-particles. The Frenkel exciton polariton spectrum consists of two branches. It is found that the photon-exciton interaction makes the ground energy of the Frenkel excitons increase.展开更多
基金the National Natural Science Foundation of China (Grant No. 20173031)the State Key Laboratory of Theoretical and Computational Chemistry of Jilin University at Changchun (Grant No. 9801)the Science Foundation of Shandong Province of China (Grant No.Y98B08027)
文摘The highly excited vibrational states of asymmetric linear tetratomic molecules are studied in the framework of Lie algebra. By using symmetric group U1(4) U2(4) U3(4), we construct the Hamiltonian that includes not only Casimir operators but also Majorana operators M12,M13 and M23, which are useful for getting potential energy surface and force constants in Lie algebra method. By Lie algebra treatment, we obtain the eigenvalues of the Hamiltonian, and make the concrete calculation for molecule C2HF.
基金Supported by Natural Science Foundation of China(Grant Nos.11361034,11371185,11101200)Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20111501110001)+1 种基金Major Subject of Natural Science Foundation of Inner Mongolia of China(Grant No.2013ZD01)Natural Science Foundation of Inner Mongolia of China(Grant No.2012MS0105)
文摘Some new characterizations of nonnegative Hamiltonian operator matrices are given. Several necessary and sufficient conditions for an unbounded nonnegative Hamiltonian operator to be invertible are obtained, so that the main results in the previously published papers are corollaries of the new theorems. Most of all we want to stress the method of proof. It is based on the connections between Pauli operator matrices and nonnegative Hamiltonian matrices.
文摘In his paper (Phys., Lett., 94A(1983), p. 340),Tu Guizhang, based on a linear spectral problem, discussed the following hierarchy of coupled nonlinear evolution equations:
文摘We investigate the effect of photons and phonons on Frenkel exciton spectrum. The Hamilto nian for a coupled system of the Frenkel excitons. the photons and the phonons is derived. The phonon-exciton interaction makes the energy band of the Frenkel excitons narrow. The photons and the Frenkel excitons make up Frenkel exciton polaritons which are quasi-particles. The Frenkel exciton polariton spectrum consists of two branches. It is found that the photon-exciton interaction makes the ground energy of the Frenkel excitons increase.
基金Supported by"National Natural Science Foundation of China(60671051)","Research Fundfor Doctoral Programof Higher Education (20060357004)"and Key Project of Education Department of Anhui Province(KJ2008A100).
