Taught Courses
Quantum Many-Body Physics
Time: Mondays and Fridays 10am to 12pm. Starts 16th September 2022
Location: Lab 4 F15.
Course information link: https://groups.oist.jp/course/quantum-many-body-physics
Lecturer: Prof. P. Höhn
Description: The course will broadly lie at the interface of condensed matter physics, quantum information theory and high-energy physics. The aim is to study correlation structures in quantum many-body systems and understand their role in determining the physical properties of these systems. Owing to the complexity of many-body systems, exploring typical quantum information concepts in them will require us to invoke efficient approximation and renormalization techniques. This will lead us to introduce tensor networks and the multi-scale entanglement renormalization ansatz, which are standard workhorses in the modern literature. We will pay special attention to ground states and their entanglement properties, such as entanglement entropy area laws and how correlations decay over distance. Quantum correlations are also intertwined with the spreading of information and we shall examine this topic in the form of Lieb-Robinson bounds. A further topic we will investigate is how (gauge) symmetries affect the correlation structure and computation of entropies. While most of the discussion will focus on finite-dimensional many-body systems, we will proceed to studying some of these questions in quantum field theory towards the end of the course.
Covariant Physics and Black Hole Thermodynamics
Time: Fridays, 1pm to 2pm. Starts 17th September 2021.
Location: Lab 4 F15.
Online (Zoom): https://groups.oist.jp/quast/online-course-zoom-access (login required)
Enrollment: https://groups.oist.jp/grad/special-topic-enrollment-application
Lecturers: Dr. Josh Kirklin, Dr. Isha Kotecha and Dr. Fabio Mele
Description: General covariance is one of the fundamental principles underlying gravity. It says that the laws of physics do not depend on our choice of coordinates. Geometrically speaking, this means that we can apply any diffeomorphism to a physical system without changing its properties. In other words, diffeomorphisms are a kind of gauge symmetry. In this course, we will explore an elegant modern perspective on general covariance, using an approach known as the covariant phase space formalism. This formalism tells you how to treat covariant theories using classical Hamiltonian mechanics. Quantum gravity must be a quantisation of this classical theory. This means that we can learn a lot about some aspects of the quantum theory using the covariant phase space approach. For example, the laws of black hole thermodynamics are a reflection of the fact that black holes are quantum objects. We will show how key fundamental thermodynamical properties of the black hole, such as its entropy, can be understood using the covariant phase space. We will also discuss more general properties of black hole thermodynamics. Finally, we will explore the connection between gauge symmetry and quantum entanglement, and how this relates to the thermodynamics of spacetime itself.
\(\mathrm{d}E = \frac{\kappa}{8\pi G}\mathrm{d}A + \Omega\,\mathrm{d}J+\Phi\,\mathrm{d}Q\)
Content:
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Hamiltonian mechanics
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Geometry of phase space, the symplectic form
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Gauge symmetry and constraints in mechanics
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Covariant field theories
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Geometry of field space
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Gauge symmetry and constraints in field theory
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Global symmetries and large gauge symmetries
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Conserved charges in general relativity
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Black hole spacetimes and symmetries
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Energy, angular momentum and electric charge
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Black hole entropy as a Noether charge
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The laws of black hole thermodynamics
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Spacetime thermodynamics and the Einstein equations
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Entanglement equilibrium and semiclassical Einstein equations
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Entanglement and gauge symmetry
Notes:
See attachments below.
Recorded lectures:
Please click here for a list of all recorded lectures: https://web.microsoftstream.com/group/4f3192e2-367a-4246-ad26-b93a56dd2230?view=videos
References:
See in the notes attached below.
