Thesis (Bachelor of Science in Physics)

Permanent URI for this collectionhttps://hdl.handle.net/10361/28423

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Open Access
Quantum chaos, information scrambling and eigenstate thermalization in coupled harmonic oscillators
(2026-05) Nailat, Yusrat Sadia; Ali, Tibra; Department of Mathematics and Natural Sciences
This thesis investigates the connection between quantum chaos and the Eigenstate Thermalization Hypothesis (ETH) in a system of two and three coupled harmonic oscillators with non-linear coupling. First, we numerically calculate thermal out-oftime- ordered correlators (OTOCs) for systems of two and three coupled harmonic oscillators. Next, we identify an early-time exponential growth regime, from which we extract temperature-dependent quantum Lyapunov exponent. We analyze the diagonal and off-diagonal matrix elements of the local position operator acting on first degree of freedom e.g. the first oscillator, x21 , in the energy eigenbasis and examine their consistency with the ETH ansatz. We also probe a possible connection between early time exponential growth of OTOC and eigenstate thermalisation. By inserting the ETH ansatz into the fourpoint correlation function underlying the OTOC, we show that the smooth and gaussian random structure of chaotic eigenstates and observables within the ETH framework can consistently account for signatures of coarse-grained picture of information scrambling. This supports the connection between information scrambling and eigenstate thermalization.
Open Access
From local operators to extended objects: higher-form Symmetries and Axion quality
(BRAC University, 2025-12) Juberi, Yeshan; Chowdhury, Syed Hasibul Hassan; Department of Mathematics and Natural Sciences
The central conceptual shift underlying this thesis is the transition from viewing symmetries as acting only on local point operators to recognizing that symmetries can act on extended objects such as lines and higher-dimensional defects. This generalized perspective reorganizes the structure of gauge theories and provides a natural language for non-local constraints that are invisible in the traditional framework. We begin by reformulating ordinary (0-form) global symmetries in terms of topological symmetry defect operators (SDOs), emphasizing that their action on charged operators is understood purely by topological linking. We then develop the corresponding formalism for 1-form symmetries, where the charged objects are line operators. Using intersection theory and the topological nature of SDOs, we show why continuous 1-form symmetry groups are necessarily abelian and analyze their action on Wilson and ’t Hooft lines. In this framework, four-dimensional Maxwell theory provides a satisfying explanation about the massless 4d photon: the Coulomb phase can be interpreted as a phase with spontaneous breaking of a continuous electric 1-form symmetry, with the photon appearing as the associated Goldstone mode. With these structural tools in place, we turn to the strong CP problem and the axion. After reviewing the origin of the QCD θ-angle and the Peccei–Quinn mechanism, we focus on the axion quality problem, which revolves around the question of why the axion shift symmetry can be extraordinarily well preserved despite general expectations that quantum gravity effects violate global symmetries. The central application of this thesis is a higher-dimensional gauge theory realization of the axion in which the axion arises as a Kaluza–Klein zero mode of a higher-dimensional U(1) gauge field. In this setting, the would-be axion shift symmetry is embedded into an electric higher-form symmetry, sharply constraining which operators can contribute to an axion potential. We show how introducing electrically charged matter breaks the continuous electric 1-form symmetry to a discrete subgroup and how nonperturbative wrapped worldline configurations of heavy charged particles generate the allowed axion potential with exponential suppression. Thus, higher-form symmetry controls the structure of the axion potential while non-local dynamics controls its suppressed nature, providing exponentially good control over the axion quality problem.
Open Access
Feasibility study of LiSiH₃ as hydrogen storage material
(BRAC University, 2025) Shaikh, Tuhin; Hossain, Audrey Orpean; Haque, Md. Firoze; Department of Mathematics and Natural Sciences
Solid state hydrogen storage materials must simultaneously satisfy both gravimetric, volumetric, and stability requirements to be viable for onboard energy applications. In this work, first principles density functional theory (DFT) calculations are employed to investigate the structural, electronic, mechanical, thermodynamic and dynamical properties of the complex hydride LiSiH3 as a candidate hydrogen storage medium. From the crystal structure indicate a gravimetric capacity of about 7.9 wt% H2 (≈2.7 kWh kg−1) and a volumetric energy density of ≈4.6 kWh L−1, substantially exceeding the 2025 U.S. Department of Energy targets and outperforming compressed hydrogen at 700 bar. Electronic band structure and projected density of states analyses reveal strong Si–H covalent bonding and a largely ionic interaction between Li+ and the SiH−3 framework, consistent with a lightweight, hydrogen rich lattice. Elastic constants satisfy the Born criteria, confirming mechanical stability, although the calculated Pugh’s ratio and Poisson’s ratio indicate intrinsically brittle behaviour. Thermodynamic functions from the quasi harmonic Debye model approach the classical limits at high temperature, while phonon dispersion curves exhibit pronounced imaginary modes, signalling dynamical instability of the studied phase at ambient conditions. Overall, LiSiH3 offers highly attractive storage capacities.
Open Access
Assessment of U-238, Th-232, and K-40 in commonly consumed Bangladeshi fruits and age-dependent annual effective dose in Dhaka city, Bangladesh
(BRAC University, 2025-08) Rahman, Shuzosh; Siddique, Mehedat Amin; Haque, Munima; Department of Mathematics and Natural Sciences
Radionuclides in consumed food pose potential health risks via internal exposure. Fruits may accumulate radioactive isotopes via root uptake or atmospheric deposition. Previous Bangladeshi fruit studies are scarce and lack age-dependent annual ingestion dose data. This study assesses radionuclide concentrations in common Bangladeshi fruits and estimates age-dependent annual ingestion doses in Dhaka City. Thirteen fruit samples from Dhaka markets were analyzed using High-Purity Germanium (HPGe) gamma spectrometry. Using secondary data, we estimated age-stratified average fruit consumption and annual ingestion doses for infants (0-5 years), children (6-15 years), and adults (16-70 years). Activities of U-238, Th-238, and K-40 ranged from 1.23 ± 0.63 Bq/kg to 8.28 ± 0.65 Bq/kg, BDL to 6.01 ± 0.66 Bq/kg, and 30.62 ± 1.88 Bq/kg to 227.7 ± 11.14 Bq/kg, respectively. Mean concentrations were 3.62 ± 0.67 Bq/kg, 2.33 ± 0.48 Bq/kg, and 80.98 ± 18.26 Bq/kg for U-238, Th-238, and K-40, respectively. The annual effective dose from fruit ingestion was 0.0502 mSv/y, 0.0569 mSv/y, and 0.0673 mSv/y for adults, children, and infants, respectively. All values were below the international safety limit. This study provides reassurance regarding the radiological safety of fruits in Bangladesh. However, continuous monitoring is essential to ensure safety and prevent future contamination risks. Further studies and up-to-date data, like age-dependent fruit consumption, are necessary for more accurate findings.
Open Access
Understanding quantum teleportation via SIMPS formalism of tensor networks
(BRAC University, 2025-08) Pal, Rahul; Ali, Tibra; Department of Mathematics and Natural Sciences
The goal of this thesis is to explore a new formalism of Tensor Networks called SIMPS and review its feasibility at tackling the computational challenges posed by many-body systems. We will start this thesis with the review of some foundational concepts of quantum mechanics and quantum information, and we review the existing formalism of TNs. Afterwards, we will review the literature by David. T. Stephen [27] [26] which introduces the SIMPS formalism and proceed to investigating the cases where SIMPS provides obvious computational advantages over existing formalisms.
Open Access
Axion monodromy inflation and the late time universe
(BRAC University, 2025-02) Moeen, Sitima; Rasul, Saif Ar; Ali, Tibra; Department of Mathematics and Natural Sciences
In this paper we analyse the viability of a solution for early and late time evolution of the universe. The standard model of cosmology, the Λ𝐶𝐷𝑀 model, contains subtle inconsistencies with the nature of the Cosmic Microwave Background radiation. To alleviate these problems cosmic inflation of some form is required to explain early universe evolution. In this paper, we focus on a large-field inflationary model called axion monodromy inflation (AMI). Large-field models require a UV-complete to fully explain the high-energy physical phenomena. We opt to use superstring theory as the UV-complete theory. This means that we must construct a de Sitter minimum for the universe at late time from superstring theory, for which we choose the Kachru Kallosh Linde Trivedi (KKLT) mechanism. We analyse the consequences of taking these two mechanisms together and conclude that a naïve integration of the two models is not consistent, leading to an 𝜂-problem in the axion monodromy model.
Open Access
A toy-model resolving the black hole information paradox
(BRAC University, 2024-12) Dipro, Savin Shayok; Ali, Tibra; Kamal, Ahmed Rakin; Department of Mathematics and Natural Sciences
This dissertation focuses on how considering a toy model that allows non-local gravitational interaction among the Hawking radiated pairs along with the chosen bell pair state gets closer to resolving the black hole information paradox. We begin by presenting some of the required background on Hawking radiation and the small correction to the leading order Hawking state before focusing on the non-local gravitational interaction prescription of the toy model for the entanglement entropy. We show how introducing two new parameters, which depend on mass depletion rate of a Black Hole and interactions between Hawking radiated pairs leads to the decrease of the leading order Hawking state entanglement entropy resulting in the recovery of information.
Open Access
Study of pressure-induced halide double perovskite, Cs2LiGaBr6, for photovoltaic applications
(2024-07) Chaudhry, Wajiha Tarannum; Haque, Md. Firoze H.; Department of Mathematics and Natural Sciences
The production of lead-free halide double perovskites with visible spectrum bandgaps is an important advancement in the design of sustainable perovskite solar cells. In this study, DFT (Density Functional Theory) is used to examine the structural, optical, electrical, and mechanical characteristics of the lead-free Cs2LiGaBr6 double halide perovskites under hydrostatic pressure ranging from 2 GPa to 80 GPa. A decrease in the lattice constant is the result of increasing pressure. Direct band gaps are present in all Cs2LiGaBr6 compounds which progressively become wider under pressure. Changes in quantum confinement effects that are caused by compressive strain are largely responsible for the band gap variations under pressure. An examination of the optical characteristics and density of states indicates increased absorption in the visible band for the UV spectrum under pressure. The mechanical stability research highlights the compound's viability for thin-film fabrication by confirming its ductile character under pressure. This study highlights the potential of Cs2LiGaBr6 in a variety of settings and expands the knowledge of sustainable substitutes for perovskite optoelectronic applications.
Open Access
Inflationary models in string cosmology
(BRAC University, 2022-09) Ahmed, Eshika; Majumdar, Mahbubul Alam; Department of Mathematics and Natural Sciences
Inflation is an acclaimed theory for uncovering how the Universe works and how it came to be. For years, physicists have attempted to not only cement a theory where the accelerated expansion of the Universe can help us to explore primordial states of the Universe, but also to incorporate other existing theories into inflation theory to produce even more ambitious models. Such models attempt to tie quantum field theories into those of inflationary cosmology in pursuit of a unified way of describing the phenoma in the Universe from the smallest of scales to the largest scales observable to man. The goal of this thesis is to explore some of these theories and the steps that have been taken (both mathematically and in idea) to achieve inflationary models that take elements from field theories. We begin from Effective Field theories and initial ideas of inflation, to understanding why inflation is important and why it is a theory so many physicists are invested in. We attempt to analyze some problems that arise in rationalizing inflation, the changes made to overcome them as well as the newer theories where further adjustments are made to make inflation as naturally derived as possible. We venture into string theory and the ideas that lead to the construction of complex inflationary models such as the KKLMMT model. We analyze brane-antibrane interactions and the problems that these interactions bring. We explore how KKLMMT tries to account for such issues by stabilizing various contenders in the theory to possibly reach a final concrete model. Finally, we explore racetrack inflation and reheating, how they arise from the ideas presented by such string cosmology models and what implications they bring to our understanding of the Universe.
Open Access
Study of Titanium, Vanadium, Chromium and Manganese doped lead free double perovskites Cs2NaGaBr6 for potential solar cell
(BRAC University, 2024-03) Hussain, Ahmed Zabir; Haque, Md. Firoze; Rahman, Muhammad Lutfor; Department of Mathematics and Natural Sciences
Lead-free inorganic double perovskites are making notable progress in the field of solar cells and optoelectronic devices. Promising materials such as Cs2NaGaBr6 are emerging as competitive alternatives. This research work studied the structural, electronic, and optical properties of pristine Cs2NaGaBr6 and Vanadium (V), Titanium (Ti), Chromium (Cr), and Manganese (Mn), doped sample, applying density functional theory for our analysis. This study is the first theoretical exploration of the doped Cs2NaGaBr6 perovskites, uncovering extraordinary results. The study reveals that all versions with added impurities show enhanced optical absorption and high optical conductivity, covering wavelengths of the visible spectrum. The wide range of performance is especially important for optoelectronic applications since it indicates greater effectiveness in absorbing solar energy. The study analyzed the electronic properties of Cs2NaGaBr6 perovskites, revealing significant changes in the band gap for each doped variation. This allows for precise tuning of the band gap, enhancing solar energy absorption. The study also found a higher density of accessible electronic states around the fermi level in doped samples, indicating increased electrical and optical conductivity. The results suggest that doping can be used to customize and enhance optical and electronic properties, creating opportunities for advanced solar cells and sustainable energy solutions.
Open Access
Out-of-time-order correlators as a measure of quantum chaos for sinai, cardioid and diamond billiards
(BRAC University, 2023-05) Ador, Tasnim Anzum; Farid, Nayeem; Ali, Tibra; Department of Mathematics and Natural Sciences
The field of quantum chaos studies how the chaotic dynamics of a classical system manifest in its quantum counterpart. Various indicators and measures of classical chaos have been discovered, such as the classical Lyapunov exponent, that allow us to distinguish and analyze chaos in classical systems. However, the same cannot be said for quantum chaos. Measures of quantum chaos are few and far between, and the ones that have been found are not well understood. One such measure is the out-of-time-order correlator (OTOC). In this thesis, we employ out-of-time-order correlators to study quantum chaos in various billiard systems, and try to find correlations between the classical and quantum dynamics of these systems.
Open Access
An examination of the Big Bang Singularity using the matrix formulation of M-Theory
(BRAC University, 2020-09) Husain, Sadat; Majumdar, Dr. Mahbubul Alam; Ali, Dr. Tibra
M theory is a proposed quantum theory of everything which is connected to type IIA string theory via S duality. In its low energy limit, M theory is approximated by 11 dimensional supergravity. In this thesis, we look at the BFSS formulation of M theory, known as Matrix theory. We discover that this formulation yields correct expressions for the velocity dependent scattering potential between supergravitons at one and two loops. Furthermore, it also gives us the correct M2 brane tension. Another form of the BFSS conjecture at finite N is then used to show that a static potential does exist between supergravitons. This static potential falls rapidly at late times, in agreement with the flat spacetime calculation.
Open Access
Derivation of the Hawking radiation for the four dimensional Schwarzschild black hole in anti de Sitter space
(BRAC University, 2019-12) Quddus, Tahsin Nahian Bin; Majumdar, Mahbub; Department of Mathematics and Natural Sciences
Open Access
Quantum information theory and the black hole information paradox
(BRAC University, 2020-10) Rahman, Md Reshad Ur; Munshi, Josh; Ali, Tibra; Department of Mathematics and Natural Sciences
This thesis discusses the information-theoretic concepts of Black Holes. Its primary focus is describing black hole dynamics with unitary operators within the perspective of quantum information theory and AdS/CFT arguments on why black hole evaporation is likely to be unitary. This thesis also provides mathematical backgrounds of classical black holes and quantum field theory in curved space. Then we introduced entanglement entropy and compared the shell of photons in a pure state to free harmonic oscillators. Afterward, we introduce an interaction term in the hamiltonian for t > 0, which we call a sudden quench. Finally, we have calculated the time evolved entanglement entropy for N-quenched oscillators and graphically demonstrated the entanglement entropy for various N. We want to model the time dependent entanglement entropy S1 between the internal and emitted radiation of a black hole. As for a future project, we want to regularize a quantum field to the Hamiltonian of N-quenched oscillators and compute the entanglement entropy S2 that results from tracing degrees of freedom inside an imaginary sphere. Hence, as S1 increases with time as the photons’ shell begins to collapse, we have a comparable situation, using the ideas about holography, with the time evolution of the S2.
Open Access
An Introduction to Cosmic Inflation Theory
(BRAC University, 2021-01) Chowdhury, Fabliha Afroza; Majumdar, Mahbubul Alam; Department of Mathematics and Natural Sciences
This thesis provides a detailed derivation of the Friedmann Equations in the frame work of general relativity and for an FLRW universe. An introduction to the theory of cosmic inflation, the motivations for it, and, the scalar field dynamics associated with inflation presently follows. It further attempts to discuss models of inflation and endeavors to make a classical introduction to cosmological perturbations gen erated in the course of inflation, which are thought to be the originator of structure in the universe. Our metric signature is (+, −, −, −) and we will use the Einstein summation convention.
Open Access
A two loop test of Matrix Big Bang Model
(BRAC University, 2020-06) Shuvo, Md Shaikot Jahan; Haque, Md. Firoze H.; Department of Mathematics and Natural Sciences
In this thesis we expand the effective action for the Matrix Big Bang presented in [9, 10] and indicate the interaction terms. Then we compute the two loop effective potential of this Matrix Big Bang model. We show that this two loop effective potentials are attractive near the big bang and turns off very rapidly in late time. The form of the potential indicates that they are coming from a multi-D-brane contribution establishing a connection between late time physics and cosmological singularity.
Open Access
Review and application of the BenderWu Mathematica Package
(BRAC University, 2018-12) Ahsan, Tasni; Majumder, Mahbubul Alam; Department of Mathematics and Natural Sciences
This thesis is the application of the BenderWu Mathematica package to di erent physical systems. The code was developed to calculate wave function and energy data of higher order perturbation theory in quantum mechanics. The review is done by practical application of the code on the potentials in the examples accompanying the package, as well as the application of it on novel potentials of various forms. The development of the recursion relation behind the code, and the generalization of the relation are also discussed. Finally, the relation between higher order perturbation theory and non-perturbative information encoded in it is also discussed.
Open Access
Non-local gravitational interactions and the black hole information paradox
(BRAC University, 2019-12) Kamal, Ahmed Rakin; Hai, Mishaal; Majumdar, Mahbub Alam; Department of Mathematics and Natural Sciences
This thesis looks into Non-local gravitational interactions that hawking radiated quanta’s from Black holes might possess. We shall first explain Hawking’s original calculation in [1], and how such a process would lead to the catastrophic information paradox. Then we shall look into other physical models that try to resolve such a paradox, and the various pitfalls that these models face. Subsequently, the latter part of this thesis looks into how Non-local gravitational dynamics is a suitable resolve to the information paradox; furthermore, we show that our calculations are not bounded in the same way as Mathur’s is, in [3]. We then show how Nonlocal correlations would manifest itself in the wave function of the pair produced particles, and in turn, we show how the entangled entropy decreases analytically, thus preserving unitarity.
Open Access
Quantisation of Black hole horizon area and multipartite entanglement of Black hole information subsystems
(BRAC University, 2019-12) Noor, Mehdi Salman; Jahan, Sayeda Tashnuba; Majumdar, Dr. Mahbub; Department of Mathematics and Natural Sciences
We formulate a model consisting of multipartite entanglement that helps provide a physical significance to the Bekenstein-Hawking entropy obtained after quantising the horizon area of a black hole as proposed by Jacob D. Bekenstein in "Spectroscopy of the quantum black hole". We propose an entanglement between the black hole information and the information of the Hawking pairs, giving rise to such entanglement entropies. We calculate the entanglement entropy of a black hole using the W state for k > 3 qubits and attempt to obtain the Page curve
Open Access
Perturbations on time dependent Orbifold Singularities
(BRAC University, 2019-12) Salekin, Sirajush; Majumdar, Dr. Mahbub; Department of Mathematics and Natural Sciences
We start with the standard time-dependent backgrounds such as the geometry and dynamics of Freidmann-Robertson-Walker(FRW) cosmologies. First, we discuss the dynamics and geometry of FRW cosmologies. Then we introduce perturbations on this FRW cosmologies. We then study more exotic orbifold spacetimes and examine their symmetries. We examine how those symmetries determine the partition functions on such symmetrical spacetimes.

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