School of Science Department of Physics 70 Tensor-Network Representation of Gapless Frustration-Free Free Fermions Supervisor: PO Hoi Chun / PHYS Student: NGUYEN Tuan Phong / PHYS-IRE Course: UROP 1100, Summer Frustration freeness describes the presence of a ground state that minimizes the energy of every local term within a Hamiltonian simultaneously. These ground states are amenable to a tensor network representation, which offers powerful tools for exploring their structure. In this project, we investigate how tensor networks can capture the physical properties of a free-fermion system under the conditions of being both frustrationfree and gapless. We first derive the necessary and sufficient condition for a free fermion model to be frustration-free, then construct the matrix product state (MPS) representation for simple models. Our studies show a foundation for studying frustration-free fermionic systems, and how two-point correlation functions capture all physical observables in a Gaussian state. Using Laser Confocal Microscopy to Study Dynamic Interfaces Supervisor: XU Qin / PHYS Student: CHEN Yifan / PHYS Course: UROP 1100, Fall In this experiment, I mainly use confocal microscopy to study dynamic interface. Liquid droplets or solid particles on soft materials, like polymeric gels, can significantly deform the surface, creating wetting ridges or simply a where they make contact. In this experiment, I want to use different particles of different diameters and different thickness of surfaces to study this phenomenon and connect our observations to the knowledge we have learnt before. By comparing my model imagined with the experiment results, I hope to strengthen my understanding of microphysics. In this report I will introduce how I prepare, observe and process my data to get my results in detail. Develop Novel Fabrication Technology Based on Direct Laser Writing Supervisor: YANG Sen / PHYS Student: SHEK Wing Him / PHYS Course: UROP 1100, Summer This report details the design and simulation of diffractive filter, with pattern of micron scale resolution. Additionally, the pattern is fabricated by drilling micron scale holes of CuO coated on PVP via laser writing. Using Huygens Principle, filter pattern for optimal single-point focal brightness is obtained, then combined with optimal pattern for other focal points to form a mixed pattern. Its multi-focal property is then checked by simulation via Angular Spectrum Method (ASM). However, a focus produced by simply filtering is predicted to produces focal power far below application, this study shall proceed with method of controlling light’s phase to unlock its full potential.
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