Projects
Quantum Mechanics II
(Spring 2023)
Title: Anyons and Identical particles
Abstract: We will introduce some basic knowledge about a fascinating topic, namely, the anyons which stays in 2-dimensional space+1-dimensional time. Some of the Math structure including braid group will be stated and we shall give the important difference between 2D and 3D. Lastly, it's naturally to use anyons to explain some truth in Fractional Quantum Hall Effect (FQHE).
Authors: Quan Wan, et al.
Department of Physics, Fudan University, Shanghai, China
Deep Learning and Neural Network
(Spring 2023)
Title: Final Project of Deep Learning and Neural Network
Abstract:This paper studies three Tasks including:(1) Traning an Implicit Network: Functa,(2) The Task for Network Sparsity: Pruning Transformer via Sparsity, (3) Optimization: questions following Project before.
Authors: Quan Wan and Haowen Shen
Department of Physics, Fudan University, Shanghai, China
Statistical Physics II
(Fall 2023)
Title: A Brief Study of Quantum Phase Transition in the one-dimensional Bose-Hubbard Model
Abstract: We use the dynamic mean-field method to capture the phase diagram and phase boundaries of the one-dimensional Bose-Hubbard model. The coherent state path integral method is used to obtain the effective field theory in the vicinity of the phase boundary. By analyzing the effective action, we re-derive the mean-field results and show that there are two types of quantum phase transition, namely BKT-type transition and generic transition. Numerically, we use three different methods, including dynamic mean-field, exact diagonalization, and density matrix renormalization group to determine the BKT transition point.
Authors: Zichun Zhou, Quan Wan and Xujing Wang
Department of Physics, Fudan University, Shanghai, China