Mechanism Study Of Quantum Interference Phenomenon

With the development of modern science and technology, people get deep understanding into the law of nature, and mesoscopic field has become the focus of physics research. During the past decades, many novel phenomenons have been discovered in mesoscopic systems and we never know when it's going to end. Among these fancy properties, quantum interference effect holds a main position. Thus revealing the interference process becomes a common concern. In this thesis we apply some different methods to investigate quantum interference phenomenon like resonant transmit of quantum dot, quantum revival, Talbot effect etc. We give intuitional descriptions to the quantum interference process in these phenomenons, and gain essential understanding on the interference mechanism. The full text is divided into four parts as follows:In first chapter we review the reasons for quantum interference effect dominate the mesoscopic system, and introduce some famous quantum interference phenomenon. As the interference effect is very complicate, to solve such problems needs the help of numerical simulations. We present some usual numerical methods including Finite-Difference method, Split-Operator method and Time-independent-Scattering-Matrix etc. At the same time, for intuitional analysis, we introduce semiclassical theory and Bohmian theory, they all provide intuitive explanations to the quantum interference process.In chapter two we study the transport property of open elliptic quantum dot, and discuss the effect of finite length lead on the conductance. By using Scattering Matrix method we calculate the conductance and transport wave function of open quantum dot, we compare the conductance with eigen levels and compare the transport wave function with eigen function as well, we find there are correspondences between conductance and eigen states of elliptic quantum dot. Due to the character of eigen states in elliptic dot, the influence of connecting lead to the eigen states is quite small, every bound state can sit stable in the dot and show their existence in the conductance curve. Meanwhile, because of the mode coupling effect, the incident electron wave can selective probe the eigen states in the dot, odd (even) symmetry incident mode only activate odd (even) symmetry eigen states. For the finite lead effect, we compare the conductance of finite lead and infinite lead configuration, and find it mainly introduce two effects: bringing in the contribution of evanescent mode of the lead and adding oscillate structure on top of the conductance plateau.In chapter three we apply the semiclassical method in investigating quantum revival phenomenon for the first time. We study both local linear finite square well system and nonlinear Morse potential system. Analytic semiclassical result is found in local linear finite square well system, and the wave packet revival only comes from the contributions of classical trajectories which bounce off the boundary wall even times. We derivate quite accurate semiclassical result of quantum revival in Morse potential, it indicates semiclassical method is capable to capture the long term quantum interference effect in nonlinear system. By analyzing the phase space distribution of classical trajectories and their evolution of phase, we find that quantum revival is basically a result of rearrangement of classical trajectories with different states after long time evolution.In chapter four we apply time-dependent method to study the influence of phase modulation on Talbot effect, and with the help of Bohm trajectories method we analyze the interference process of electron wave. We find that only a single slit modulation will destroy the whole Talbot image, but the phase modulation in one slit affect the distribution intensity without charging their positions. A periodic modulation acts like changing the grating with multiplicative period. We use a Gaussian well to imitate the effect of STM tip or donor impurity, and find it can focus the electron wave like lens focus light. We calculate the Bohm trajectories of corresponding distribution, and obtain distinct understanding comparing to classical description. In classical theory, the Talbot image is a summation of contributions from all the slits, whereas from Bohm trajectories viewpoint the Talbot image comes from contributions of proximate trajectories. More over, the evolution of Bohm trajectories provides us information which cannot been seen from classical description. The trajectories show there is a transfer process of phase mismatch influence to the distribution of Talbot image.Chapter five is the summary of the thesis.