Postgraduate Research in TCM

## Supervisors for 2023 entry

[Emilio Artacho](#emilio), [Benjamin Béri](#benjamin), [Claudio Castelnovo](#claudio), [Nigel Cooper](#nigel), [Austen Lamacraft](#austen), [Max McGinley](#max), [Mike Payne](#mike), [Bo Peng](#bo), [Michele Simoncelli](#michele), [Robert-Jan Slager](#robert-jan), ...

- Application info: [www.tcm.phy.cam.ac.uk/vacancies/postgrad.html](https://www.tcm.phy.cam.ac.uk/vacancies/postgrad.html)

- This is an incomplete list of available projects... 
				
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					(»ESC« or »O« for overview mode)
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				##  [Emilio Artacho](https://www.tcm.phy.cam.ac.uk/profiles/ea245)

Research within computational and theoretical condensed matter physics, especially (but not exclusively) developing and using first-principles simulation methods. Recent work includes:

- Nano-confined water in 2D, based on molecular dynamics simulations, both from first principles and empirical. For the former we use the SIESTA linear-scaling density-functional-theory (DFT) method, which we develop and maintain in collaboration with other groups.

- Non-adiabatic processes in forced electronic systems, mostly as affected by a nucleus shooting through them, as happens in radiation-damage processes. We use real-time time-dependent DFT. We recently formulated a Floquet theory for nuclear projectiles shooting through periodic solids.

<figure align="center"> 
					<img src="static/proton-wake-in-diamond.png" alt="wake" width="350" class="center"/>
					<figcaption>
						Proton wake in diamond
					</figcaption>
				</figure>

- Offering projects in:

- Electronic systems strongly out of equilibrium, relating to first principles

- Graphene nanostructures

- First-principles techniques and methods

- Open to other lines within the described context.

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## [Benjamin Béri](https://www.tcm.phy.cam.ac.uk/profiles/bfb26/)

Theory of quantum many-body systems and their quantum computing applications. Directions PhD projects may involve include:
					
				- topologically ordered many-qubit and electronic systems
				- quantum dynamics in isolated and in open systems
				- quantum error correction
				
				These topics can well be in combination: for example, quantum error correction involves open, often topologically ordered, systems and its theory can range from statistical mechanics to novel aspects of quantum dynamics.

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## [Claudio Castelnovo](https://www.tcm.phy.cam.ac.uk/profiles/cc726/)

- Emergent dynamical phenomena in topological magnetic materials, from microscopic modelling to effective theories

- Interplay between topological band structures and quantum spin liquids

- Anomalous noise and transport properties in systems with low-dimensional excitations

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## [Nigel Cooper](https://www.tcm.phy.cam.ac.uk/profiles/nrc25/)

Quantum many-body physics of cold atomic gases and novel electronic materials

- Strongly interacting light-matter systems
				- Topology and symmetry in open quantum systems
				- Collective dynamics in correlated insulators

---
				
				## [Austen Lamacraft](https://www.tcm.phy.cam.ac.uk/profiles/al200/)

- My background is in quantum many-body physics, but I’m also working at the interface of physics and machine learning

- I'm offering projects on (examples below)
					1. Quantum dynamics from [unitary circuits](https://en.wikipedia.org/wiki/Quantum_circuit)
					2. Machine learning in quantum and statistical physics

- I'm also part of the [Accelerate Programme for Scientific Discovery](https://www.cam.ac.uk/research/news/new-programme-to-accelerate-ai-research-capability-at-cambridge)
				
				--

### [Solving Schrödinger Bridges via Max Likelihood](https://www.mdpi.com/1099-4300/23/9/1134)

- A __Schrödinger bridge__ is the most likely stochastic evolution between
				two probability distributions given a prior stochastic evolution

<figure align="center">
					<img src="static/sb1.png" alt="drawing" width="350" class="center"/>
					<img src="static/sb2.png" alt="drawing" width="450" class="center"/>	
					<figcaption>
						Learned Schrödinger Bridge trajectories in a double well experiment.
					</figcaption>
				</figure>

--
				
				### Quantum Circuits

<figure align="center">
					<img src="static/circuit.png" alt="drawing" width="350" class="center"/>			
					<figcaption>
						A "brickwork" quantum circuit.
					</figcaption>
				</figure>

- A model for quantum dynamics inspired by quantum computation
				- How fast can influences propagate in these systems? See [Maximum velocity quantum circuits](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.033032)

---

## [Max McGinley](https://www.tcm.phy.cam.ac.uk/profiles/mm2025/)

- I'm broadly interested in the dynamics of quantum many-body systems, in particular in the context of:
					- Dynamics of quantum information
					- Topological phases and symmetries
					- Measurements, feedback and tomography
					- Open quantum systems
					
				- I like to focus on problems that have potential applications in present-day experimental settings, particularly those where dynamics can be controlled (quantum simulators, quantum computers, etc.)

- Here are some examples of recent work, with links to relevant papers
				
				--

### [Shining a light on anyons](https://arxiv.org/abs/2210.16249)

- __Anyons__ are a novel type of particle that can only exist in strongly correlated 2D systems. They interpolate between bosonic and fermionic statistics

<figure align="center">
					<img src="static/trajectories2.png" alt="drawing" width="400" class="center"/>
					<figcaption>
						Using multiple pulses of light, anyons can be excited and then braided, and their unusual statistics shows up in optical response functions
					</figcaption>
				</figure>
				
				- This could be a useful tool in looking for quantum spin liquids

--
				
				
				### [Time crystals from measurement and feedback](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.090404)
				
				- Just as conventional crystals spontaneously break time-translation symmetry, "time crystals" spontaneously break time-translation symmetry
				
				<figure align="center">
					<img src="static/square_geometry.png" alt="drawing" width="400" class="center"/>
					<figcaption>
						After measuring the state of a many-qubit system, one can provide "feedback" to the system to encourage formation of a time crystal 
					</figcaption>
				</figure>
				
				--
				
				### [Topology in open quantum systems](https://www.nature.com/articles/s41567-020-0956-z)
				
				- Topological phases are expected to be useful for <i>robust</i> quantum information storage, but how robust actually are they?

<figure align="center">
					<img src="static/qshe_fig.png" alt="drawing" width="350" class="center"/>			
					<figcaption>
						A 2D topological system (quantum spin Hall insulator) coupled to external degrees of freedom (a two-level system)
					</figcaption>
				</figure>
				
				- Some topological phases are more fragile than others when it comes to storing information in the presence of an environment

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## [Mike Payne](https://www.tcm.phy.cam.ac.uk/profiles/mcp1/)

### Determining the mechanism of operation of ligand-gated ion channels

Ligand-gated ion channels are transmembrane proteins whose ion channels open on activation by neurotransmitters; this flow of ions is the basis of their physiological action. Our previous work has defined how neurotransmitters activate the ion channel. This project will investigate the mechanical pathway which links the binding of the neurotransmitter and the opening of the ion channel and define necessary and sufficient conditions for opening of the ion channel.

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## [Bo Peng](https://www.tcm.phy.cam.ac.uk/profiles/bp432/)

- My research background is in computational condensed matter physics, and I am offering projects using density functional theory or many-body perturbation theory to predict materials properties.

- The prospective PhD students will work on applications of first principles calculations to emergent new physics in solid state materials, including but not limited to:
				
				--

- Topological properties in various quasiparticles

<figure align="center">
					<img src="static/topological-quasiparticles.png" alt="drawing" width="450" class="center"/>	
					<figcaption>
						Non-Abelian braiding of phonons in monolayer silicate [Bo Peng, Adrien Bouhon, Bartomeu Monserrat & Robert-Jan Slager. <a href="https://www.nature.com/articles/s41467-022-28046-9" target="_blank">Nature Communications 13, 423 (2022)</a>. ESI Top 0.1% Hot Paper]
					</figcaption>
				</figure>
				
				
				--

- Photo-induced phase transitions

<figure align="center">
					<img src="static/photons.png" alt="drawing" width="400" class="center"/>	
					<figcaption>
						Tunable photostriction of halide perovskites through energy dependent photoexcitation [B Peng, et al. <a href="https://journals.aps.org/prmaterials/abstract/10.1103/PhysRevMaterials.6.L082401" target="_blank">Physical Review Materials 6, L082401 (2022)</a>. Editors' Suggestion]
					</figcaption>
				</figure>

<p align="center">
					
				</p>
				
				- Exciton physics

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## [Michele Simoncelli](https://www.tcm.phy.cam.ac.uk/profiles/ms2855/)

- Transport phenomena in solids and liquids — involving e.g. charge, heat, spin, and their interplay — playing a crucial role in technological applications including [thermoelectric energy conversion](https://ceramics.org/ceramic-tech-today/thermal-management/two-materials-one-theory-unified-thermal-transport-formula-describes-heat-flow-in-both-crystals-and-glass), [supercapacitors](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.8.021024), [thermal barriers for aerospace](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.12.041011), and [electronics and phononics](https://nccr-marvel.ch/highlights/2020-01-hydrodynamics).

- We tackle these technology-driven problems relying on quantum statistical physics, coarse-graining techniques, and computational materials science. Specifically, we work on the description of transport at various scales and approximation levels (scroll down for more):

- **Microscopic (quantum) formulations**, based on the [density matrix or Wigner phase-space frameworks](https://www.nature.com/articles/s41567-019-0520-x) and relevant from the fundamental-science viewpoint, as they provide an atomistic quantum-accurate description of transport. 
				<figure align="center">
					<img src="static/1_particle_wave.png" alt="drawing" width="400" class="center"/>	
					<figcaption>
						Phonon mean free paths as a function of energy in the thermal barrier La2Zr2O7 at 1300 K. 
						 (Simoncelli <it>et al.</it>, <a href="https://journals.aps.org/prx/abstract/10.1103/PhysRevX.12.041011" target="_blank">Phys. Rev. X 12 041011, 2022)</a>)
					</figcaption>
				</figure>

- **Mesoscopic formulations,** obtained from microscopic models by aptly integrating out some microscopic degrees of freedom. These have reduced complexity and accuracy compared to microscopic models, but are accurate enough for engineering applications. I have been working on the development of techniques to coarse-grain microscopic models into mesoscopic models, which aim at finding the best trade-off between accuracy and complexity.
				<figure align="center">
					<img src="static/2_hydrodynamics.png" alt="drawing" width="400" class="center"/>	
					<figcaption>
						Left panel, hydrodynamic heat flux in graphite, obtained solving the <a href="https://journals.aps.org/prx/abstract/10.1103/PhysRevX.12.041011" target="_blank">viscous heat equations</a>. Right panel, hydrodynamic heat flux along the section shown on the right (red), and comparison with the predictions from Fourier's diffusive equation (orange).
					</figcaption>
				</figure>

- **Simulation and optimization of devices,** e.g. relying on molecular dynamics to access microscopic quantities unpractical or even impossible to be measured in experiments, thus shed light on the microscopic physics determining the performance of complex devices (the picture shows an example related to a supercapacitor).
				<figure align="center">
					<img src="static/simoncelli-supercapacitor.png" alt="drawing" width="400" class="center"/>	
					<figcaption>
						Molecular dynamics simulation of a supercapacitor used to extract energy from salinity differences (Simoncelli <it>et al.</it>, <a href="https://journals.aps.org/prx/abstract/10.1103/PhysRevX.8.021024" target="_blank">Phys. Rev. X 8 021024, 2018</a>)
					</figcaption>
				</figure>
				
				---

## [Robert-Jan Slager](https://www.tcm.phy.cam.ac.uk/profiles/rjs269/)

- __Multi-gap topology__ in and out of equilibrium. We found that by braiding band nodes in certain setups non-Abelian charges can be defined and converted to render new kinds of topological phases.
				- __Ferroelectric topology__ in multi-layer twisted systems.
				- __Quantum geometry__. We are working on defining some new framework to define more general quantum geometries and how to probe them.
				- __Floquet phases__. Periodic phases and out-of-equilibrium phenomena.
				- __Magnetism__. We have found some new correspondences between topology and certain spin structures in specific cases and are working to extend this.
				- Superfluidity and topology in __multi-layers__ of 2D systems.