# Graduate teaching

Research students in TCM are able to take advantage of a wide range of courses offered by the University. Final year undergraduate (Part III) courses in both Physics and Mathematics can be relevant. The MPhil in Scientific Computing provide many useful courses (DFT, solid state, scientific programming); the full timetable is available here.

The TCM Group also runs its own graduate lecture programme, mostly in the Michaelmas and Lent Terms, also listed on talks.cam. Some of these lectures have recordings available on our internal site.

## Easter 2024

**TCM graduate lectures**These will take place in person in the TCM Seminar Room, some also with zoom feed.

• *Anderson Localisation,
* Prof. David Khmelnitskii, 10am on various days for eight lectures (30 April; 2, 7, 9, 13, 15, 21 and 23 May).
Lecture notes: 1,
2A,
3, Supermathematics,
5-reprint,
4,
5,
5a,
Gang of four,
Chakravarty Schmid,
7,
Levitation,
IQHE,
"8",
Brezin-Gross-Itzykson,
Bohr-Efetov.

• *Fairy Tales,* Prof. David Khmelnitskii, 10am Fridays, six lectures beginning 26 April.

**Topics of Current Research:**

• *
Introduction to machine learning in the physical sciences,* Christoph Schran, two lectures, 10am on 14 and 16 May. TCM Seminar Room.

• *
Viscous thermoelectric phenomena in solids,* Michele Simoncelli, two lectures, 10am on 29 and 30 May. TCM Seminar Room.

[Non-diffusive, hydrodynamic-like transport of charge or heat has been observed in several materials, and recent, pioneering experiments have suggested the possible emergence of electron-phonon bifluids. Here we introduce the first-principles computational framework to describe these phenomena, showing that the macroscopic viscosity of electrons-phonon bifluids is microscopically determined by composite 'relaxon' electron-phonon excitations, and these also describe electron-phonon drag effects on standard thermoelectric transport coefficients.
We demonstrate that these composite excitations emerge from the microscopic coupled electron-phonon Boltzmann transport equation, and show how the latter can be coarse-grained into a set of mesoscopic Viscous Thermoelectric Equations (VTE). The VTE unify the established hydrodynamic equation for electrons derived by Gurzhi [Sov. Phys. Usp. 11 (2) 1968], and the recently developed Viscous Heat Equations for phonons [Phys. Rev. X 10 (2022)], while also covering the mixed electron-phonon bifluid regime.
We rely on this framework to quantify phonon-drag effects, and investigate with quantitative first-principles accuracy the emergence of coupled electron-phonon hydrodynamics in several materials, comparing theory with experiments.]

• *
Continuum mechanics of active matter,* Anton Souslov, three lectures, 10am on 3,4,5 June. TCM Seminar Room.

[Abstract: I will focus on the concepts that describe and quantitatively model active materials on the largest scales. Active matter refers to any material in which the constituent particles move themselves by consuming ambient energy. These materials range from biological tissues to artificial systems designed to exhibit exotic mechanical properties. Analogously to how a liquid composed of molecules can be described using the continuum Navier-Stokes equations, fluid-like states of active matter have a hydrodynamic description at the largest scales. Because active matter violates energy conservation (and in some cases, momentum conservation), the equations for the velocity can include terms prohibited in equilibrium, leading to distinct dynamics and instabilities. Analogously, solid-like states of active matter have an elastic description that modifies the classical theory of elasticity in unexpected ways. Finally, I will discuss topics in current research that build on these continuum descriptions, including non-reciprocal interactions, pattern formation, and the role of topology.]

## Lent 2024

**TCM graduate lectures**These will take place in person in the TCM Seminar Room, but some also with zoom feed.

• *Fairy Tales,* Prof. David Khmelnitskii, 10am Fridays, nine lectures beginning 19 January. (**No lecture on Friday 1 March.** **Lecture on 8 March by Zoom only**) Lecture notes: Continuous Groups.

**Topics of Current Research:**

• *Field theory approaches to non equilibrium systems,
* Dr Orazio Scarlatella, two lectures, 10am on Mon 26 Feb and Wed 28 Feb, TCM Seminar Room.

[Abstract: In these lectures I will introduce the Keldysh field theory of non-equilibrium systems.
This is an approach to systems that strongly deviate from thermal equilibrium, and is also very successful for problems with quenched disorder.
I will first discuss the general formalism and then show some examples of open quantum systems problems and of driven-dissipative problems as commonly arise in quantum optics.
If time allows, I will also introduce the Dynamical Mean Field Theory, which is a very successful non-perturbative approach for lattice problems, especially far from equilibrium.]

• *Radioastronomy in the SKA era,
* Dr Daniel Molnar, two lectures, 10am on Tue 12 Mar and Thu 14 Mar, TCM Seminar Room.

[Abstract: I will give a general introduction to the scientific interest behind the 21cm cosmology and its theoretical basis.
An overview of the theoretical and instrumentation challenges will also be shown.
The current efforts in the Cavendish radio cosmology group will be highlighted
in the field of 21cm astronomy and cosmology.]

** Other lectures this term** (Check external links for times and locations.)

Relevant Part III Physics lectures include:

•
*Advanced Statistical Mechanics,* Eugene Terentjev

• *Phase Transitions,* Anson Cheung

• *Quantum Information,* Crispin Barnes

You may also find some of the Part III Maths lectures useful, for example:

•
*Topological Quantum Matter,* Benjamin Beri

•
*Quantum Entanglement in Many-body Physics,* Frank Verstraete

•
*Quantum Computation,* Sathyawageeswar Subramanian

•
*Topics in Mathematics for Deep Learning,* C. Esteve Yague

## Michaelmas 2023

**TCM graduate lectures**These will take place in person in the TCM Seminar Room, but also with zoom feed.

• * Physical Kinetics,* Prof. David Khmelnitskii, 10am Tuesdays and Thursdays, starting 10th
October. Location: TCM Seminar Room. Lecture notes: 1, 2, 4, 5, 6, 7, 8, 10, 12.

• *Fairy Tales,* Prof. David Khmelnitskii, 10am Fridays, starting 6th
October. Location: TCM Seminar Room.
Lecture notes: Activated Processes.

** Other lectures this term** (Check external links for times and links.)

Lectures in the
CDT / MPhil in Scientific computing
by TCM staff members include:

• *Foundation Course in QM and solid state physics* Prof. Emilio Artacho

• *Electronic Structure and DFT,* Prof. Emilio Artacho

• *Atomistic Modelling of Materials,* Dr Chuck Witt and Dr Christoph Schran

• *Introduction to Topological Materials,* Prof. Bartomeu Monserrat

Relevant Part III Physics lectures include:

• *Quantum Condensed Matter Field Theory,* Carolin Wille

• *Atomic and Optical Physics,* Zoran Hadzibabic

• *Advanced Quantum Condensed Matter Physics,* Crispin Barnes

You may also find some of the Part III Maths lectures useful, for example:

• *Quantum Information, Foundations and Gravity,* Adrian Kent

• *Statistical Field Theory,* Christopher Thomas

## Easter 2023

**TCM graduate lectures**These will take place in person in the TCM Seminar Room, but also with zoom feed.

• *Fairy Tales,* Prof. David Khmelnitskii, 10am Fridays, six lectures beginning 28 April.

Topics of Current Research:

• *
Disorder-free localisation phenomena in quantum spin liquids,* Claudio Castelnovo, four lectures, 10am, 18,23, 25, 30 May. TCM Seminar Room.

• *
Trends in Topological Phases,* Robert-Jan Slager, three lectures, 10am, 13,14,15 June. TCM Seminar Room.

[Topics: (i) Cohomology
and gauge theory. Although we will only touch upon interpretations quickly, these concepts relate to topological gauge theory via Dijkgraaf-Witten constructions, symmetry fractionalisation, and projective symmetry classifications, which were related to the
spin liquids by Wen et al. (ii) K-theory
and Dirac systems. Here the physical relevance pertains to classification of free fermion systems and even D branes in string theory.
(iii) Equivariant
K-theory from a combinatorial perspective. Physical relevance pertains to free fermion crystalline phases and those on D branes on toroidal orbifolds.]

## Lent 2023

**TCM graduate lectures**These will take place in person in the TCM Seminar Room, but also with zoom feed.

• *Condensed Matter Physics: Beyond the
Basics,* Prof. David Khmelnitskii, 12 lectures 10am Tuesdays and Thursdays, beginning 24th January. (NB There will be no lecture on 14 Feb, 28 Feb and 2 Mar.) Lecture notes: (Larkin-Pikin), (Zittartz-Langer)

• *Fairy Tales,* Prof. David Khmelnitskii, 10am Fridays, nine lectures beginning 20 January. Lecture notes: GF for free particle, Particle in box, Planar rotor and solenoid

Topics of Current Research:

• *
Symmetry-Protected Topological Phases,* Dr Max McGinley, four lectures, 10am on 8, 15, 20 and 22 February. TCM Seminar Room. Lecture notes: Lecture notes 1, Lecture notes 2, Lecture notes 3, Lecture notes 4.

** Other lectures this term** (Check external links for times and locations.)

Relevant Part III Physics lectures include:

•
*Advanced Statistical Mechanics,* Eugene Terentjev

• *Phase Transitions,* Anson Cheung

• *Quantum Information,* Crispin Barnes

You may also find some of the Part III Maths lectures useful, for example:

•
*Topological Quantum Matter,* Benjamin Beri

•
*Applications of Quantum Field Theory,* Sean Hartnoll

## Michaelmas 2022

**TCM graduate lectures**These will take place in person in the TCM Seminar Room, but also with zoom feed.

• * Physical Kinetics,* Prof. David Khmelnitskii, 10am Tuesdays and Thursdays, starting 11th
October. Location: TCM Seminar Room. Lecture notes: 2, 4, 5, 6, 7, 8, 11, 12

• *Fairy Tales,* Prof. David Khmelnitskii, 10am Fridays, starting 7th
October. Location: TCM Seminar Room. Lecture notes: Bouncing Ball, Activated Processes (Kramers Problem Review, Mel'nikov and Meshkov), Supersymmetric Quantum Mechanics, Top, Monopole and Tunnelling of Magnetisation, (Volovik and Gorkov)

** Other lectures this term** (Check external links for times and links.)

Relevant Part III Physics lectures include:

• *Theories of Quantum Matter,* Austen Lamacraft

• *Atomic and Optical Physics,* Zoran Hadzibabic

• *Advanced Quantum Condensed Matter Physics,* Crispin Barnes

You may also find some of the Part III Maths lectures useful, for example:

• *Tensor Networks,* Thorsten Wahl

• *Quantum Computation,* Sergii Strelchuk

• *Statistical Field Theory,* Christopher Thomas

• *Non-Equilibrium Statistical Field Theory,* Johannes Pausch

## Easter 2022

**TCM graduate lectures**These will be a mixture of in-person lectures and virtual lectures. The in-person lectures will take place in the TCM Seminar room.

• *Fairy Tales,* Prof. David Khmelnitskii, 10am Fridays, six lectures beginning 29 April.

The lecture on 29 April will be in person, in the TCM Seminar Room, to mark an Anniversary of these lectures. The remaining lectures are planned to be by Videoconference: send an email to David Khmelnitskii in order to be registered.

• *Localisation,
* Prof. David Khmelnitskii, 10am Tuesdays and Thursdays, eight lectures beginning 10 May. TCM Seminar Room (with Zoom feed link distributed by lecturer). Lecture notes: 1, 2, 3, Supermathematics,
4,
5,
5a,
Gang of four,
6,
7,
Levitation,
IQHE,
Dephasing.

Topics of Current Research:

• *
Ageing in Biomolecular Condensates,* Dr Jorge Rene Espinosa, two lectures, 10am Monday 16 May and Wednesday 18 May. TCM Seminar Room.

• *Tensor network Approaches to the Quantum Many-Body Problem,
* Dr Thorsten Wahl, three lectures, 10am on 30 May, 1 and 6 June. TCM Seminar Room.

• *Quantum Dimer Models,
* Prof. Claudio Castelnovo, four lectures, 10am on 8,10,13 and 14 June. TCM Seminar Room.

## Lent 2022

**TCM graduate lectures**These will be a mixture of in-person lectures and virtual lectures. The in-person lectures will take place in the TCM Seminar room.

• *Lectures on Superconductivity,* Prof. David Khmelnitskii, 10am Tuesdays and Thursdays, beginning 25th January. In TCM seminar room, with Zoom transmission.

• *Fairy Tales,* Prof. David Khmelnitskii, 10am Fridays, beginning 21st January. By Videoconference: send an email to David Khmelnitskii in order to be registered.

Topics of Current Research:

• * Physical models for the evolution of spatially growing cellular populations,
* Prof. Diana Fusco, 10am Monday 7 Feb and Monday 14 Feb. TCM Seminar Room.

• * A brief introduction to quantum metric, geometric tensor and their relation to topology,
* Dr. Nur Ünal, 10am Monday 21 Feb and Wednesday 23 Feb. TCM Seminar Room.

• * Wigner’s phase-space formulation of quantum mechanics and its application to thermal transport in solids,* Dr. Michele Simoncelli, 10am Monday 28 Feb and Wednesday 2 Mar. TCM Seminar Room.

• * Quantum Circuits,* Prof. Austen Lamacraft, 10am Monday 7 Mar and Wednesday 9 Mar. TCM Seminar Room.

• *Machine learning: a priori or a posteriori?,
* Dr Gareth Conduit, 10am Monday 14 Mar. TCM Seminar Room.

**Other lectures this term**(Check external links for times and locations.)

Relevant Part III Physics lectures include:

•
*Advanced Statistical Mechanics,* Eugene Terentjev

• *Phase Transitions,* Anson Cheung

• *Quantum Information,* Crispin Barnes

## Michaelmas 2021

**TCM graduate lectures**These will be a mixture of in-person lectures and virtual lectures. The in-person lectures will take place in the TCM Seminar room.

• *Physical Kinetics,* Prof. David Khmelnitskii, 10am Tuesdays and Thursdays, starting 12th
October. Location: TCM Seminar Room.

• *Fairy Tales,* Prof. David Khmelnitskii, 10am Fridays, starting 8th
October. By Videoconference: send an email to David Khmelnitskii
in order to be registered.

** Other lectures this term** (Check external links for times and links.)

Lectures in the
CDT / MPhil in Scientific computing
by TCM staff members include:

• *Introduction to Quantum Mechanics,* Prof. Emilio Artacho

• *Electronic Structure,* Prof. Emilio Artacho

• *Atomistic Modelling of Materials,* Dr Edgar Engel

• *Introduction to Topological Materials,* Dr Bartomeu Monserrat

• *Message Passing Interface (MPI),* Dr Michael Rutter

A general course that is very useful for anyone using TCM computers is:

• *Introduction to Linux,* Dr Philip Blakely

Anyone who wishes to attend any of the online lectures will need to contact Ms Samantha Selvini or Dr Philip Blakely so that they can be added into the appropriate part of Teams and/or Moodle, and similarly those who wish to attend the physical lectures will need to make contact in order to gain access to the Maxwell Building.

Relevant Part III Physics lectures include:

• *Theories of Quantum Matter,* Prof. Austen Lamacraft

• *Atomic and Optical Physics,* Prof. Zoran Hadzibabic

• *Advanced Quantum Condensed Matter Physics,* Prof. Crispin Barnes

You may also find some of the Part III Maths lectures useful.

## Easter 2021

**TCM graduate lectures**These will run as virtual lectures.

• *Fairy Tales,* Prof. David Khmelnitskii, 10am Fridays, six lectures beginning 30th April.

For the above lectures, please send an email to David Khmelnitskii in order to be registered. After you are registered, you will receive the link which enables you to attend all the lectures.

Topics of Current Research:

• *A brief introduction to quasiparticles in frustrated magnets,
* Claudio Castelnovo, six lectures, at 10am on Tuesdays and Thursdays, starting 4 May. Videoconference link: https://trin-cam-ac-uk.zoom.us/j/91916473035?pwd=dXplTFFLMklXdUNLdE45STd0Z2pSUT09.

• *
Machine Learning and Statistical Physics,
* Austen Lamacraft, two lectures, at 10am on Monday 24 May and Wednesday 26 May. Videoconference link:
https://us02web.zoom.us/j/86323456078?pwd=ei9ZU3lxOVoveXhTMjBBcVBRc2ttQT09
.
Lecture 1 text and slides.
Lecture 2 text and slides.

• *
Recent advances in topological material characterisations,
* Robert-Jan Slager, three lectures, at 10am on Monday 31 May, Wednesday 2 June and Thursday 3 June.
Videoconference links: Lecture 1,
Lecture 2,
Lecture 3.

• *The Modern Day Blacksmith,
* Dr Gareth Conduit, 10am Monday 14 June. Videoconference link: https://meet.google.com/ndi-sdac-smd.

## Lent 2021

**TCM graduate lectures**These will run as virtual lectures.

• *Condensed Matter Physics: Beyond the
Basics,* Prof. David Khmelnitskii, 10am Tuesdays and Thursdays, beginning 26th January.

• *Fairy Tales,* Prof. David Khmelnitskii, 10am Fridays, beginning 22nd January.

For the above courses, please send an email to David Khmelnitskii in order to be registered. After you are registered, you will receive the link which enables you to attend all the lectures.

Topics of Current Research:

• *The Modern Day Blacksmith,
* Dr Gareth Conduit, 10am Monday 18 January ***Postponed***. Videoconference link: https://meet.google.com/ndi-sdac-smd

• *Breaking the barriers between copper and carbon nanotubes,
* Dr Karolina Milowska, 10am on 8 and 10 February. Videoconference link: https://meet.google.com/cnu-eamk-vsn

• *Topological semimetals and their connection to high-energy theory,
* Dr Jan Behrends, 10am on 1, 3 and 8 March. Videoconference link:
https://us02web.zoom.us/j/8368707576?pwd=M2hjRTE3U0tOM05wYTQyYWdicFQxUT09

• *An Introduction to Topological Order,
* Dr Heidar Moradi, 10am on 9, 10 and 15 March. ***Note that last lecture has been moved from 11 March to 15 March.***
Videoconference link: https://us02web.zoom.us/j/89034493654?pwd=ODI4cmdYZi9jalp0VmJGT09GS3Q2UT09

**Other lectures this term**(Check external links for times and locations.)

•
*Advanced Statistical Mechanics,* Eugene Terentjev

• *Phase Transitions,* Anson Cheung

• *Quantum Information,* Crispin Barnes

## Michaelmas 2020

**TCM graduate lectures**These will run as virtual lectures.

• *Physical Kinetics,* Prof. David Khmelnitskii, 10am Tuesdays and Thursdays, starting 13th
October.

• *Fairy Tales,* Prof. David Khmelnitskii, 10am Fridays, starting 9th
October.

*separately*for KINETICS and the FAIRY TALES in order to be registered. After you are registered, you will receive the link which enables you to attend all the lectures.

** Other lectures this term** (Check external links for times and links.)

Lectures in the
CDT / MPhil in Scientific computing
by TCM staff members include:

• *Foundation Course in QM and Solid State Physics,* Prof. Emilio Artacho

• *Electronic Structure,* Prof. Emilio Artacho

• *Atomistic Modelling of Materials,* Dr Edgar Engel

• *Introduction to Topological Materials,* Dr Bartomeu Monserrat

• *Message Passing Interface,* Dr Michael Rutter

A general course that is very useful for anyone using TCM computers is:

• *Introduction to Linux,* Dr Philip Blakely

Anyone who wishes to attend any of the above lectures will need to contact Ms Samantha Selvini or Dr Philip Blakely so that they can be added into the appropriate part of Teams and/or Moodle.

Relevant Part III Physics lectures include:

• *Theories of Quantum Matter,* Prof. Austen Lamacraft

• *Atomic and Optical Physics,* Prof. Zoran Hadzibabic

• *Advanced Quantum Condensed Matter Physics,* Prof. Crispin Barnes

Relevant Part III Maths lectures include:

• *Non-equilibrium statistical field theory,* Dr Johannes Pausch

You will likely require a key to enrol, which can be obtained by
emailing partiii-secretary@maths.cam.ac.uk.

## Lent 2020

**TCM graduate lectures**(All at 10am in the TCM Seminar Room unless otherwise stated.)

*Physical Kinetics,* Prof. David Khmelnitskii, Tues and Thurs,
21, 23, 28, 30 Jan 4, 6, 11, 13, 18, 20, 25, 27 Feb.

*Fairy Tales,* Prof. David Khmelnitskii, Fridays
17, 24, 31 Jan; 7, 14, 21 Feb.

*Tensor network approaches to the quantum many-body problem,
* Dr Thorsten Wahl, four lectures on 20, 22, 27, 29 Jan.

*Metric mechanics and differential geometry in complex matter,*
Prof. Mark Warner, two lectures on 10, 12 Feb.

*Complex Networks,* Dr Sebastian Ahnert, two lectures on 24, 26 Feb.

*Majorana Fermions in Condensed Matter,* Dr Benjamin Béri, two lectures on 2, 4 Mar.

**Other lectures this term**(Check external links for times and locations.)

Relevant Part III Physics lectures include:

• *Advanced Statistical Mechanics,* Eugene Terentjev

• *Phase Transitions,* Claudio Castelnovo

• *Quantum Information,* Crispin Barnes

## Lecture notes

Some of TCM's staff members have produced some particularly illuminating and engaging course notes for courses presented elsewhere. A selection of these is presented below.

### Fairy Tales

For over twenty years Prof Khmelnitskii has presented his "Fairy Tales." These are stand-alone lectures elucidating a particular topic of mathematical physics. They are given on Friday mornings at 10am, and many remember them for years. They have been appreciated by many, from PhD students through post-docs to professors.

### Ben Simons' lecture notes

Quantum Condensed Matter Physics (Graduate course)

Michaelmas Term 2013, 24 Lectures

Phase Transitions and Collective Phenomena (Part III)

Lent Term 2012, 12 Lectures

Functional Methods in Condensed Matter (Graduate course)

Lent Term 2005: 11 lectures

Quantum Condensed Matter Field Theory (Part III)

Michaelmas Term 2004, 15 lectures

### Michael Rutter's lecture notes

An Introduction to MPI (CDT/MPhil in computational methods / scientific computing), and other computing topics.