This course introduces the techniques and approaches used to understand the physics of nanoscale materials and devices. (1) Introduction to nanophysics, qubits and the density matrix formalism. (2) Nanofabrication: Overview of the most common nanofabrication techniques and Nanostructure characterisation. (3) Quantisation by confinement, effect of confinement on transport properties of solids, Effect of confinement on excitons, screening and energy renormalization. (4) Spins in quantum mechanics, spin polarisation and readout, Nuclear spin baths , Applications to quantum sensing and quantum computing. (5) Intro to superconductivity, macroscopic quantum model, London equation, Meissner effect, Josephson junctions, kinetic inductance. Devices: kinetic inductance detectors, SQUIDs, SSPDs, superconducting qubits

**Lecturer: **Margherita Mazzera, Cristian Bonato

**Institution: **Heriot-Watt

**Delivery:** Video Conference

**Hours Equivalent Credit: **20

**Assessment:** Problem Sheets (60%) and Final Oral Discussion (40%)

**Course Work:** Approximately 7 hours per week outside of class Course Summary

This course was dropped from SUPA in 2021/22.

It is no longer offered through SUPA.

This course will explore the key principles and applications of

Magnetism & Superconductivity, and their relevance to current

developments in physics. The aims of this course are:

1. To describe the key physical principles of magnetism and

superconductivity

2. To explore the theory and applications of ferromagnetism

and the macroscopic behaviour of ferromagnets

3. To explore the basic properties, phenomenology and applications of superconducting devices

From our phones to our cars to devices that diagnose medical illness, magnetism is a fundamental tool that enables modern life. This recent video by the IEEE Magnetics Society provides an overview of the applications of magnetism and why it's such an important field. This course will cover the fundamentals of many of these concepts.

**** This course is not offered in 2022/23. It is expected to return in 2023/24.****

**This course is no longer offered. **

The course will provide an overview of the field of matrix product and tensor network approaches to many body systems.

Many-body systems are hindered by an exponential complexity in the number of their constituents and thus are hard to solve. Large many body systems however present exotic emerging behaviour ( such as spin liquid, superconducting and super-fluid phases) that we want to understand from first principles. Tensor networks provide a novel theoretical and computational framework to analyse collective emergence in many body systems. We will use Tensor Networks to study classical and quantum many body systems at and out-of equilibrium. The syllabus includes an introduction to the tensor network formalism and graphical notation, the recipe for describing the partition function of a classical model as the norm of a matrix product state (1D),or tensor product state (higher D).

The characterization of the properties of these states like expectation values, correlation functions, and entropies. The renormalization group in the language of tensor networks. The correspondence between statistical mechanics and quantum mechanics and some aspects of outof- equilibrium dynamics in 1 and higher dimensions. We will describe powerful numerical algorithms based on tensor networks like DMRG in 1D and its generalizations in higher D. Students are expected to have a solid background in quantum mechanics and statistical mechanics.

Assessment: Continuous AssessmentResponse functions and Green’s functions provide a powerful mathematical language in which to describe the physics of many-body quantum systems. This course is a short introduction to them. The first few lectures define the various Green’s functions of interest, and calculate them explicitly for a few very simple systems at zero temperature. The remaining lectures give brief introductions to several more advanced topics, including Green’s functions at non-zero temperature and Green’s functions out of equilibrium. The lectures are supplemented by several problem sheets, in which the emphasis is on a strong grasp of the basics. The course is designed to be accessible to any graduate student (theoretical or experimental) who has a decent undergraduate education in quantum mechanics. Some - though not much - knowledge of the formalism of second quantisation (creation and annihilation operators) is required.