Using squeezing transform in the context of quantum optics and based on the Fourier series expansion we rigorously derive a new Poisson sum formula. Application of this new formula to the representation transformation...Using squeezing transform in the context of quantum optics and based on the Fourier series expansion we rigorously derive a new Poisson sum formula. Application of this new formula to the representation transformation of kq-wave function for describing electrons in periodic lattice is demonstrated. In so doing, the transition matrix element of harmonic oscillator in kq representation is derived.展开更多
The development of a two dimensional numerical wave tank （NWT） with a rocker or piston type wavemaker based on the high order boundary element method （BEM） and mixed Eulerian-Lagrangian （MEL） is examined. The ca...The development of a two dimensional numerical wave tank （NWT） with a rocker or piston type wavemaker based on the high order boundary element method （BEM） and mixed Eulerian-Lagrangian （MEL） is examined. The cauchy principle value （CPV） integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the comer problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.展开更多
基金Supported by the President Foundation of Chinese Academy of Sciencethe Specialized Research Fund for the Doctorial Progress of Higher Education in China under Grant No. 20070358009
文摘Using squeezing transform in the context of quantum optics and based on the Fourier series expansion we rigorously derive a new Poisson sum formula. Application of this new formula to the representation transformation of kq-wave function for describing electrons in periodic lattice is demonstrated. In so doing, the transition matrix element of harmonic oscillator in kq representation is derived.
基金Foundation item： Supported by the National Natural Science Foundation of China （Grant No.51009038/E091002）.
文摘The development of a two dimensional numerical wave tank （NWT） with a rocker or piston type wavemaker based on the high order boundary element method （BEM） and mixed Eulerian-Lagrangian （MEL） is examined. The cauchy principle value （CPV） integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the comer problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.
