Phononic Crystal Resonators

In this chapter we present the theory of phononic crystal, classification of PnC according to its physical nature, and phononic crystal (PnC) phenomena in locally resonant materials with 2D, and 3D crystals structure. In this chapter, phononic crystal (PnC) micro-electro mechanical system (MEMS) resonators with different transduction schemes such as electrostatically, piezoresistively, piezoelectrically transduced MEMS resonators are explained. In this chapter, we employed phononic crystal strip in MEMS resonators is explained to reduce anchor loss, and analysis of eigen frequency mode of the resonators. The phononic crystal strip with supporting tethers is designed to see the formation of band gap by introducing square holes, and improvement of quality factor and harmonic response. We show that holes can help to reduce the static mass of PnC strip tether without affecting on band gaps

A new quasi-exactly solvable problem and its connection with an anharmonic oscillator

The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods. Furthermore the connection between the model and an anharmonic oscillator had been investigated by methods of KS transformation

Geometric phase for nonlinear coherent and squeezed state

The geometric phases for standard coherent states which are widely used in quantum optics have attracted a large amount of attention. Nevertheless, few physicists consider about the counterparts of non-linear coherent states, which are useful in the description of the motion of a trapped ion. In this paper, the non-unitary and non-cyclic geometric phases for two nonlinear coherent and one squeezed states are formulated respectively. Moreover, some of their common properties are discussed respectively, such as gauge invariance, non-locality and non-linear effects. The non-linear functions have dramatic impacts on the evolution of the corresponding geometric phases. They speed the evolution up or down. So this property may have application in controlling or measuring geometric phase. For the squeezed case, when the squeezed parameter r -> \infinity, the limiting value of the geometric phase is also determined by non-linear function at a given time and angular velocity. In addition, the geometric phases for standard coherent and squeezed states are obtained under a particular condition. When the time evolution undergoes a period, their corresponding cyclic geometric phases are achieved as well. And the distinction between the geometric phases of the two coherent states maybe regarded as a geometric criterion

Demonstrating Additional Law of Relativistic Velocities based on Squeezed Light

Special relativity is foundation of many branches of modern physics, of which theoretical results are far beyond our daily experience and hard to realized in kinematic experiments. However, its outcomes could be demonstrated by making use of convenient substitute, i.e. squeezed light in present paper. Squeezed light is very important in the field of quantum optics and the corresponding transformation can be regarded as the coherent state of SU(1; 1). In this paper, the connection between the squeezed operator and Lorentz boost is built under certain conditions. Furthermore, the additional law of relativistic velocities and the angle of Wigner rotation are deduced as well