An effective theory for the hole-doped spin-1 antiferromagnetic chain is proposed in this paper. The two branches of low-energy quasiparticle excitation is obtained by the diagrammatic technique. In the large t limit (in which t is the hole hopping term), the lower band is essentially the bound state of one hole and one magnon and the other band is the single-hole state. We find a critical value of t, tc50.21DH in which DH is the Haldane gap!. For t.tc, with the decrement of t, the mixing of these two bands become stronger and stronger, and at the same time the effective band mass becomes larger and larger. When t,tc the minimum of the lower band moves away from zero to the other point between zero and p/2. The spin structure factor is also calculated in this paper, and we find that for the larget limit the main contribution is from the interband transition, which induces a resonant peak in the Haldane gap. For the small t limit the main contribution is from the intraband transition, which only causes a diffusionlike broad bump in the Haldane gap.

The Schwinger-boson mean-field theory is applied to the quantum ferrimagnetic Heisenberg chain. There is a ferrimagnetic long-range order in the ground state. We observe two branches of the low-lying excitation and calculate the spin reduction, the gap of the antiferromagnetic branch, and the spin fluctuation at T50K. These results agree with the established numerical results quite well. At finite temperatures, the long-range order is destroyed because of the disappearance of the Bose condensation. The thermodynamic observables, such as the ree energy, magnetic susceptibility, specific heat, and the spin correlation at T.0 K, are calculated. The Txuni has a minimum at intermediate temperatures and the spin-correlation length behaves as T21 at low temperatures. These qualitatively agree with the numerical results and the difference is small at low temperatures.

A quantum theory for mesoscopic electric circuits in accord with the discreteness of electric charges is proposed. On the basis of the theory, the Schrodinger equation for the quantum LC design and L design is solved exactly. The uncertainty relation for electric charge and current is obtained and a minimum uncertainty state is solved. By introducing a gauge field, a formula for persistent current arising from magnetic flux is obtained.

Based on the singly occupied aio. picture and the mechanism of charge fluctuation, the effective Hamiltonian of the two-band Hubbard model is derived by using the degeneracy perturbation theory for the noncuprate compound Bal_xKxBiO 3. By considering the next-neighbour pairing of two opposite spin holes in coordinate space, the Green's function equation of motion and the superconductivity equation are obtained. Furthermore, how the superexchange interaction and the hopping energy affect the next-neighbour pairing has been reasonably explained, and the superconductivity window is due to the Cooper pairing in coordinate space.

On the basis of the equation of motion for a RLC circuit with source, the energy fluctuation of the circuit is discussed by using the fluctuation-dissipation theorem. It is found that the fluctuation is a quantum effect at low temperature but becomes a classical thermodynamic effect when the temperature increases. We have quantized the circuit at zero temperature, and btained the fluctuations of charge and current as well as the uncertainty relation.