**Topic 1: Green functions for many-body problems in condensed-matter physics – Lecturer: Dr. NGHIEM Thi Minh Hoa**

**Overview:** In this course, we provide the fundamental background of the Green functions to the use of solving many-body problems in condensed-matter physics. To get broader audiences, we will cover the second quantization as the main language of the whole lecture, the second quantization representation for the Hamiltonian of a free electron gas and an interacting electron gas. In the main part of the lecture, we represent the connection of the Green functions to some experiments, the single-particle retarded Green function and its spectral function, the Matsubara Green function, and the use of the Green functions in the impurity scattering Hamiltonian.

**Topic 2: Computer simulations of materials: Electronic structure calculations and Machine learning – Lecturers: Dr. PHAM Tien Lam**

**Overview: **The development of computing hardware and software allows us to simulate many systems before entering the final manufacturing process, especially the computer aid-design for materials systems is considered as an indispensable component in modern industry. This course will provide a brief introduction to computer simulation on materials systems. We focus on the description of electronic structures in materials design. Initially, the course introduces the overview of computer simulation of matters: from continuum aspect to atomic and electronic description. Then we focus on solving electronic problems with density functional theory and a hands-on tutorial on Quantum Espresso software. Finally, we briefly discuss some aspects of applications of machine learning in materials design.

**Topic 3: Simulating quantum effects with waveguide arrays – Lecturers: Assoc. Prof. NGUYEN Xuan Truong**

**Overview: **This course provides some fundamental background on the simulation of quantum effects by exploiting optical analogues in waveguide arrays. Some fundamental nonrelativistic quantum effects rooted in the Schroedinger equation such as Bloch oscillations, dynamical localization, Zener tunneling; and relativistic quantum effects governed by the Dirac equation such as Zitterbewegung, Dirac solitons, topological Jackiw-Rebbi states and Klein tunneling will be covered.

**Topic 4: Energy spectrum of exciton in monolayer TMD and physics applications – Lecturer: Prof. LE Van Hoang**

**Overview: **This course provides background on the exciton concept and specifies excitons in monolayer transition-metal dichalcogenides, where the two-dimensional effects cause rich new physics. Then, separating the mass center motion from a two-body system in a magnetic field is demonstrated by giving the physics bases for this separation. Also, the algebraic technique based on annihilation and creation operators is introduced to calculate the exciton energy spectra. Finally, two physics applications are given: (1) a new mechanism for the temperature effect on the exciton lifetime, (ii) a new way to extract structural information of TMD materials from exciton spectra.

**Topic 5: Control and readout of a superconducting quantum bit – Lecturer: Dr. NGUYEN Van Duy**

**Overview: **The lecture will introduce the Josephson effects and some applications of the Josephson junctions. The lecture will focus on the qubits, control and readout of a superconducting qubit. Two types of qubits mainly addressed in the lecture are charge qubits and transmons. Participating in this course, learners will learn how to construct a Hamiltonian to describe a superconducting qubit system; how to solve the Schroedinger equation to find eigenstates of qubits. The next part of the lecture will present a theory of transmission lines, which are essential for the aim of reading-out from superconducting qubits. Learners will learn how to determine characteristic quantities of waveguides including the reflection and transmision coefficients. To complete, learners will learn the way to describe the interaction between qubits and transmission lines. The formulation of open quantum systems is invoked here wherein the qubits play the role of a quantum system and the transmision lines do the environment.

**Topic 6: Quantum nonlinear optics and Nonlinear optical response of graphene** **– Lecturer: Assoc. Prof. DO Van-Nam**

**Overview:** In this course I will present a brief and compact introduction of Nonlinear Optics with the emphasis on a procedure of making a research in this field: what quantities are determined to investigate optical properties of materials and how to calculate them. Next, I will address on the light-matter interaction. It is begun with a review of the nature of light under the Maxwell theory of electromagnetics. After that, in the light of quantum mechanics, I will highlight the photon concept through the quantization of light. The light-matter interaction is then described by a Hamiltonian using both formalisms of the first and second quantization languages; some specific assumptions are added to deduce important approximations. After introducing a system of fundamentally essential concepts, I will focus on the issue of determining physical quantities characterizing linear and nonlinear optical properties of a system. The quantum master equation is presented, then a system of equations namely the semiconductor-Bloch equations are deduced. Finally, I will illustrate the application of presented theories through a study of the high-order harmonic generation of graphene. Some practical problems are particularly designed to supplement theories and to strengthen the calculation skills of learners.