QuEST Meeting 2024

QuEST Group Meeting 2024

Every Tuesday, 12 noon (Theoretical and Computational Physics Lab)

Presenter: Zain Ullah

Date: 6 August 2024

Title: Quantum Walks in the generalized Aubrey Andre Harper Model 

Abstract. 

Quantum walks, the quantum analog of classical random walks,  describe the random dynamics of quantum particles on a discrete lattice, which is inherently governed by the time dependent wave function of the system. Moreover,  Aubrey Andre Harper (AAH) model describes the dynamics of a quantum particle on a one dimensional tight binding lattice with on site modulation. The AAH model is used to study the localization phenomena and topological states in one dimension. 

Key words : Quantum walks, classical random walks, Aubrey Andre Harper model, localization phenomena ,topological states

Presenter: Wan Zul
Date: 16 July 2024

Title: Exploring Boltzmann Transport Theory for Thermoelectric Calculation

Abstract. 

The thermoelectric efficiency of a material can be calculated by comprehensively studying the Seebeck coefficient, electrical conductivity, electronic and phonon thermal conductivity and thermoelectric power factor by using density functional theory and Boltzmann Transport Theory. This presentation discuss the Boltzmann Transport Theory and how it is implemented into BoltzTrap2 software to calculate the transport coefficients. 

Keywords: Transport properties; Density functional theory; Boltzmann Transport Theory

Presenter: Farhana
Date: 24 June

Title: Exploring Mechanical Properties Through Density Functional Theory

Abstract. 

The exploration of mechanical properties in both 3D and 2D materials is critical for the advancement of various technologies, including energy storage, flexible electronics, and structural applications. This study leverages first-principles calculations based on density functional theory (DFT) to investigate these properties comprehensively. DFT provides a robust and reliable method for predicting the mechanical behavior of materials at the atomic scale. 

Keywords: Mechanical properties; Density functional theory; Quantum ESPRESSO

Presenter: Jessica Liang

Date: 4 June

Title: Fractals corresponding to the metallic means sequences

Abstract: 

In this work, we investigate aperiodically ordered sequences that correspond 1-dimensional tilings (i.e. of the interval of [0,1]). These sequences are used to model quasicrystals. By recursively removing the tiles we can generate a fractal similar to the Cantor set. Lastly, we show the fractal using figures and how to calculate the similarity dimension.

Presenter: C.O Edet, UniMaP

Date: 4 June

Title: A simplified method for solving quantum wave equation

Abstract: 

We propose a simplified formalism named "Nikiforov-Uvarove-Functional-Analysis (NUFA) method" for solving quantum wave equations. We derive an expression for the energy spectrum and the wave functions in terms of generalized hypergeometric functions. In order to demonstrate the accuracy of this proposed formalism, we obtain the eigensolutions of the radial Schrodinger equation with selected potential models. The NUFA method is seen to be easy and efficient, eliminating the rigorous mathematical manipulations encountered in other methods. Our results agree perfectly with what obtains in literature.

Presenter: Aqwa

Date: 14 May

Title: Classical and quantum structure via sheaf of monoidal categories

Abstract: 

Topos quantum theory (TQT) and categorical quantum mechanics (CQM) both use category theory to model some aspects of quantum theory. TQT focuses on contextuality whereas CQM is more geared towards entanglement. In this talk we will go through the ideas of Bohrification based on Chris Heunen’s works, discuss the limitations and compare them with the work of Samson Abramsky et.al. Subsequently, we try to come out with a plan on how to study contextuality in the framework of monoidal categories. The ultimate aim of this proposed research is to see whether we can define contextuality by using tensor product (i.e monoidal categories). 

Summary: 

Bohrification is a research programme proposed by Chris Heunen, Klaas Landsman, and Bas Spitters to interpret mathematically Bohr’s doctrine of classical concepts, saying that a quantum mechanical system is to be understood through its classical fragments. It is based on topos approach inspired by the work of Butterfield, Isham and Doering. The main result is one can say that a quantum mechanical system can be seen as a classical one, if one agrees that nothing physically relevant is lost by considering its classical fragments and if one is willing to change the logic from a classical into an intuitionistic one. 

Abramsky et.al gives a different approach to talk about contextuality. The starting point of their approach is based on empirical data and does not assume quantum theory. The reason is because Bell’s theorem and related results not just apply to quantum mechanics, but to all theories with certain structural properties. Therefore, the mathematics of sheaf theory is used to analyze the structure of non-locality and contextuality. By doing so, they characterized the phenomena of non-locality and contextuality precisely in terms of obstructions to the existence of global sections and gave linear algebraic methods for computing these obstructions.   

Categorical quantum mechanics is the formulation of quantum theory in terms of categorical algebraic structures. It is equipped with a powerful graphical calculus which can be used to understand the compositional aspects of quantum systems. Recently, substantial works have been carried out by Moliner et al. (2017), Heunen & Lemay (2020), Moliner et al. (2020), and Barbosa & Heunen (2023). and found that there exists a notion of space and time in monoidal categories. This is done by observing the subobject of the tensor unit in a monoidal category corresponds to the open set in the category of sheaves. 

Remark: PhD proposal