“数学物理方法”中关于希尔伯特空间的教学改革实践

目前国内物理专业为期一学期的“数学物理方法”课程多缺乏对于希尔伯特空间及相关概念的讲解,然而此部分内容对于物理专业的后续学习非常重要.为了进一步提高“数学物理方法”课程的教学效果,针对希尔伯特空间部分进行了教学改革实践.本文阐述了本次教学改革的教学安排和授课内容,展示了收集到的效果反馈,并对其进行了讨论和分析,从而得出一些具有建设性的改革方向,为大家进一步教学改革提供参考.     

Effect of Temperature on Polaron Stability in a One-Dimensional Organic Lattice

Effect of temperature on the polaron stability in a one-dimensional organic lattice is investigated within the Su-Schrieffer-Heeger model. The temperature effect is simulated by introducing random forces to the equation of the lattice motion. It is found that the localized polaron state becomes delocalized even at low temperatures. The time of polaron keeping localized depends on the magnitude of temperatures. By taking into account the thermal effect, we find that the dissociation field is weaker as compared with earlier works.     

Antiresonance induced spin-polarized current generation

According to the one-dimensional antiresonance effect (Wang X R, Wang Y and Sun Z Z 2003 Phys. Rev. B 65 193402), we propose a possible spin-polarized current generation device. Our proposed model consists of one chain and an impurity coupling to the chain. The energy level of the impurity can be occupied by an electron with a specific spin, and the electron with such a spin is blocked because of the antiresonance effect. Based on this phenomenon our model can generate the spin-polarized current flowing through the chain due to different polarization rates. On the other hand, the device can also be used to measure the generated spin accumulation. Our model is feasible with today's technology.     

Effect of interchain coupling on a biexciton in organic polymers

The effect of interchain coupling on the formation and the stability of a biexciton is studied in poly (p-phenylene vinylene) chains in the framework of the tight-binding approach. We obtain an intrachain exciton and biexciton as well as an interchain exciton and biexciton through a double-photon excitation. It is found that a biexciton is energetically favourable to two single excitons even when there exists an interchain coupling. There is a turnover value t_⊥C of the interchain coupling for the formation of a biexciton, beyond which two excitons are combined into one biexciton. The binding energy of a biexciton is calculated to decrease with the increase of interchain coupling, which indicates that a biexciton is relatively stable in polymers with a weak interchain coupling. The conclusion is consistent with the experimental observations. In addition, a suggestion about how to improve the yielding efficiency or the formation of biexcitons in actual applications is given.