DSpace Collection:
https://hdl.handle.net/10356/2323
2020-09-24T11:54:59ZStandard model as a Wilsonian effective theory
https://hdl.handle.net/10356/143218
Title: Standard model as a Wilsonian effective theory
Authors: Zhang, Jiahao
Abstract: Quantum Field Theory provides a fundamental framework for modelling and predicting
experimental results in high energy particle physics. However, the calculated quantities often
diverge, and so a renormalisation framework was introduced to extract meaningful, finite
quantities from the theory. In the process, counterterms have to be introduced to cancel
off the diverging terms. In renormalisable theories, all divergences can be absorbed into
the redefinitions of the mass, field and the coupling constant, but this fact would seem to
fortuitous. Wilsonian effective field theory gave a different interpretation of the framework
and gave physical insight into how it worked. In this report, an introduction to field theory
is presented and a discussion of the Wilsonian effective theory2020-01-01T00:00:00ZWeil numbers in cyclotomic fields
https://hdl.handle.net/10356/140949
Title: Weil numbers in cyclotomic fields
Authors: Shi, Luozi
Abstract: Let X be an algebraic integer in the cyclotomic field Q(ζm). We say X is an n-Weil number if |Xσ|^2 = n for all automorphisms σ: Q(X)→C. This FYP report aims to study methods to find p^a-Weil numbers and make Weil numbers be in the decomposition field. The results contain several theoretical results and a list of Weil numbers with m <80 and p <20, where n is a prime.2020-01-01T00:00:00ZTheoretical description of interacting topological condensed matter systems
https://hdl.handle.net/10356/140937
Title: Theoretical description of interacting topological condensed matter systems
Authors: Terh, Yun Yong
Abstract: This thesis aims to review the theory of non-interacting topological insulators and to develop a path towards the treatment of interacting systems. Starting from how Berry phase arises in a system with non-trivial topology, we will develop the underlying mathematical description of topology and talk about the topological invariant that characterizes the topology. We will then study the integer quantum Hall effect, which is an experimentally well-established topological system. We further the discussion to non-interacting systems with time reversal symmetry that gives rise to (2+1)D and (3+1)D topological insulators with another experimentally verified model – the BHZ model. We will also show how topological band theory and field theory can arrive at the same result and briefly discuss the role of the topological invariant in the context of differential geometry. Next, we will prepare the techniques to work with interacting system by constructing the framework of finite temperature many- body condensed matter field theory using Matsubara Green’s function. We will calculate the one-loop electron-phonon self energy in electron-phonon interaction to investigate how interaction change the behaviour of electrons. Finally, we will apply the dimensional reduction method to time reversal invariant integer quantum Hall effect in (4+1)D, which enables us to obtain the (3+1)D topological insulator.2020-01-01T00:00:00ZMaxwell demon in Parrando's game : a toy model for work extraction from partial information
https://hdl.handle.net/10356/140835
Title: Maxwell demon in Parrando's game : a toy model for work extraction from partial information
Authors: Too, Hon Lin
Abstract: Szilard engine and feedback-controlled flashing ratchet convert information about the system to useful work through measurement feedback control mechanism. What would happen if the extracted information is incomplete? We explore the idea of work extraction from partial information in feedback mechanism and implement the idea onto Parrando’s game – a toy model for flashing ratchet. Specifically, we study the demon and the physical system’s mutual information, and their entropy production. We observe that a demon that utilizes partial information will face the explore-exploit dilemma, which is not observed in a demon possessing complete information.2020-01-01T00:00:00Z