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研究生: 王敬皓
Wang, Ching-Hao
論文名稱: Nonlinear Scattering and Localised Bound State of One-dimensional Bright Solitons
指導教授: 王道維
Wang, Daw-Wei
口試委員: 洪在明
Hong, Tzay-Ming
仲崇厚
Chung, Chung-Hou
學位類別: 碩士
Master
系所名稱: 理學院 - 物理學系
Department of Physics
論文出版年: 2011
畢業學年度: 99
語文別: 英文
論文頁數: 38
中文關鍵詞: 非線性物理冷原子原子分子與光學物理量子力學
外文關鍵詞: nonlinear physics, cold-atom, AMO physics, quantum mechanics
相關次數: 點閱:3下載:0
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  • Soliton, by definition, is a non-linear collective dynamics, exhibiting a non-dispersive wavefront during its propagation in space. A direct but nontrivial question is how stable a soliton can be against collisions with a disorder potential and to what extent the nonlinearity changes the qualitative behaviour of the scattering. In this work, we systematically investigate the scattering of bright solitons through a simple delta function defect. Different from existing literature, we present a global phase diagram of transmission coefficients and derive the phase boundary for transition of quantum reflection/transmission. Moreover, we give a necessary condition for the existence of bound states using simple arguments. Finally, we proposed a practical model that captures the location of this transition in the phase diagram.


    1 Introduction 2 Dimensionality and numerical convention used 3 Attractive delta-function scattering: phase diagram and bound state profiles 3.1 Existing theories 3.2 Phase diagram of transmission coefficient 3.3 Existence criterion and general profile for bound states 4 Repulsive delta-function scattering: phase diagram and bound sate profiles 4.1 Existing theories 4.2 Phase diagram of transmission coefficient 4.3 Existence criterion and general profile for bound states 5 A Theoretical Model for Quantum Transmission 6 Conclusions A From 3D GPE to 1D B Deviation from linear QM C Summary of the scattering behaviour

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