I remember that after the first month, I promised to blog every month about my studies here. I admit I had different expectations, so constant change makes it hard to see the reflection of how I feel, perform and what future I see. But now, when my first year had passed in the TU Delft, and I was required to submit my self-reflection for the Go/NoGo meeting, I made a conscious effort on where I stand. Over this time, I have had some unusual thoughts which might form an opinion and recipes posted on my webpage. But for now, about my part of TU delft.

So, my first year in the PhD at TU Delft had passed. During this time, I have had noteworthy, valuable and enjoyable experiences taking roles as a researcher, student and teacher. I have been part of the Weyl disc project which resulted in a fruitful end; I have been educated daily enthusiastically by my college Arpad Lukacs, by the graduate school and by Yuli himself; and notably, I have played a role in quantum transport, where I gave problem-solving sessions and improved the given problem sets.

As with any other PhD candidate, we need to help our supervisors and department with teaching assistance to make their time available for research. Unexpectedly I got teaching assistance duties in the quantum transport course, which I needed to gain prior knowledge. This role's responsibilities were restructuration exercise sets and giving four problem-solving sessions. I knew it would be a challenging task that I could relate to from my previous experiences in doing exercises for Physics Olympiad. But I was confident I could do it and get fresh experiences from the process, after which I am after all. Thus I accepted this challenge from Yuli with great honour and pleasure.

The problem which I tried to address with exercise sets was their cloudiness (feedback I received at the last problem-solving session from a student with nasty exercise), where the characteristics of that are long and unclear exercise formulations and lack of narrative and importance for the exercise questions - as they were made to forcefully question student instead of leading q student to a goal. Now after my corrections and restructuring, the exercise sets are in much better condition than they used to be to train students to apply their knowledge and motivate them to acquire new ones. That also made presentations of exercise solutions much more productive.

Overall we had four problem-solving sessions, with the number of students fluctuating between 3 and 10. Since I had only a little experience in teaching (Previously, I had made one lecture about "Lorentz attractors and Chaos" for bachelor students on a blackboard and a QFT seminar lecture on S-Matrix theory), I stuck to Yuli's advice and used slides as a primary tool for presentations (also the classroom had a tiny whiteboard). Nevertheless, that did not prevent me from breaking down more complicated steps in the solutions on the whiteboard, which I usually did as that gave students time to absorb and to ask questions. By measuring the number of questions I got and answered during problem-solving sessions, I positively impacted helping students learn the course.

Nevertheless, the problem-solving sessions could have gained additional improvement. First, I could have related setups considered in exercises with a broader context which I can now do by being more knowledgeable in quantum transport. Also, the participation of students in solving exercises before the problem-solving sessions could be increased. That can be done by making exercises more engaging and interactive with the great Quantum Transport book. There could be exercises whose solutions would be partly the book's content since derivations tend to be too short and unfocused. Therefore I would greatly appreciate taking responsibility for managing problem-solving sessions next semester to implement such changes.

The teaching assistant duties of the quantum transport course significantly pushed me to learn the content of the course myself. But as I read the book and started participating in work meetings, I missed some fundamental understanding of quantum mechanics. So to broaden my knowledge, I took Yuli's course on advanced quantum mechanics. The book in the course was unusual due to its view of teaching from a condensed matter perspective and its clear, deep and sometimes entertaining storyline. I especially liked the story of how breaking radiation is related to the result of radiation produced by accelerating charge (I had asked such a question during my master years for my QFT lecturer and failed to get an answer to that then).

However, the lectures did not have the same charm. I found chairs, tables, and light annoying for making notes, presentation slides were too bright to look at (a dark theme would be beneficial), and problem-solving sessions were dauntingly useless except for the presentation slides they left afterwards. The idea of making students teach themselves would be great if the listening group were smaller (something like ten students) and the homework could be the presented exercises. That and other parallel duties demotivated me to invest enough time to keep up with the pace to do the homework and the exam. It would be entertaining to take it also next year. Nevertheless, I had a great experience reading the book and have obtained a clearer understanding of how phenomena in condensed matter are being understood.

In the first year, I have not used the opportunity to go to summer school, and I regret missing deadlines due to not understanding my interests. To compensate for this deficiency, I will do two summer schools next year; I will apply to Capri Spring School and Les Houches, where I now see that these could align with my interests. On the bright side, I attended two conferences, one in Veldhoven, where I presented a poster on Weyl Discs and the other in JuliaCon in London under my initiative, funding and time. There I learned I have the necessary social skills and individual abilities to arrange it and effectively participate by asking questions and establishing contacts if I find passion in what people do. Similarly, in the next year, I plan to go to Veldhoven to JuliaCon (if the costs are not too high), and also I will participate in NanoFront Winter Retreat 2019, where I hope to spread new results.

As a researcher, Arpad and I moved the Weyl Disc project to a fruitful end by producing a paper, "Weyl Discs", now under the second review. The project was motivated by the theoretical observation that multi-terminal superconducting junctions would host Weyl points in the Andreev Bound state spectrum in the space of superconducting terminal phases (which leads to quantised conductance), but due to contact effects would be affected by quantum fluctuations. To model the problem, we promoted the superconducting phases, which define the Weyl point to dynamical variables. Those are coupled with external phases by a concave potential which depending on strength, allows us to model hard constraint and soft constraint limits. Independently of how the conjugate variable entered the equation, we saw that behaviour in the energy level spectrum persists - in 2 of 3 directions of the bandstructure are almost degenerate, forming subspaces which we call Weyl discs.

A fascinating application of one such subspace would be in quantum computation. Experimentally, a qubit of Andrew bound states in Josephson junction had already been demonstrated where excitation of the state and readout had already been developed. By changing external superconducting phases on the Weyl disc, one could collect a Berry phase and thus do holonomic computation. Particularly one could consider a circular orbit on the disc. Due to Berry curvature, a phase difference would be acquired between the states. Due to the mixing of the lowest levels, the basis (between which a relative phase would be acquired) would depend on the angular velocity. This effectively allows us to implement any rotation in the Bloch sphere and any single qubit gate (that follows because the time dependence of the Weyl disc Hamiltonian for circular orbit can be factored out as exponentials acting on time independent part). However, it is still unknown how effective (for example, how many Rabbi oscillations one could expect to get) the phase difference collection would be compared with parametric noise (which would also affect decoherence time). That I think could be further addressed in my PhD or as in some master's student projects whom I could supervise.

To sum up, I felt that the Weyl Disc project was particularly well suited for me because it allowed me to explore quantum mechanics from a practical point of view - perturbation theory, quasi-classical approximation, coherent states, quantum harmonic oscillator, Hydrogen atom and the programming of Hamiltonian to get its corresponding eigenstates. The most challenging part of the project was understanding why shifted harmonic oscillator basis was not a good choice for the computation of lowest eigenstates. (The answer was that if we use a simgaz matrix to define a new basis, we change a representation of the sigmay operator in this basis which I mainly explored numerically.) Also, I find a feeling of achievement in implementing hydrogen atoms into coordinate space with the adaptive grid and Richardson's extrapolation. (I also initiated a meeting with Prof. Gijzen, with whom the discussion boosted confidence in reproducing results from his supervised master's thesis.) Also, I participated actively in developing perturbation theory results for the Weyl Disc Hamiltonian and learned a lot from active and enthusiastic discussions with my colleague Arpad Lukacs.

Although I had previous experience writing an article for my master's project, I found the process for this article particularly hard, painful and slow. One of the issues was a lack of confidence that our results would have any practical or fundamental value (a phrase I borrowed from referees), so I was missing what message we should give to the reader. Other differences were that the methods part of this article needed to be more significant. Nevertheless, I had a good experience learning the structure of the PRL article, observing Yuli condensing multiple ideas into single sentences. Also, it allowed me to see what makes a good structure and writing of the article, which I might use as a reference for forthcoming articles. I contributed actively to making figures and captions, discussing what formulas we should write, what to leave in the appendix, and how to think about approximations we use. I actively participated in looking up literature to construct applications for the Weyl discs for computation in the nanostructure and for possible observations of Weyl discs in excitons. Therefore my highest weakness in the process was the actual skills of writing. To improve on that, I plan to take graduate school courses in writing, practice writing in writing blog posts, and read more complex literature. These steps could lead to the skills needed, and I want to be more competent by the end of the current project.

At the moment, we have started a new project which is about understanding how the external circuit affects the topological phase diagram. The setup is the same as with the Weyl Disc project except that now we look at the bandstructure macroscopically and characterise them with order parameters. In the absence of circuit effects, the phase is determined by the emergence of order parameters for the gapless state, that is, the density of states at 0 energy, whereas, for the gaped state, that is the gap energy. Interestingly, there are regions in superconducting phase space where tiny gapless strips separate the two gaped phases. In this project, what would happen to this strip if we considered quantum fluctuations coming from external circuit effects? One could speculate that quantum fluctuations would smear out the gap. But equally possible is that the density of states as an order parameter could also be smeared.

To answer this question, we treat the nanostructure using general quantum circuit theory, for which we write a general action assuming that superconductor phases at the terminals are time-dependent. The frequency of quantum fluctuations for the superconducting phases would be high in the limit where the circuit makes a strong constraint. In contrast, the behaviour of the nanostructure affects the low frequency of internal superconducting phases. Thus we can integrate out higher frequency behaviour (renormalise) to obtain effective action, which would help us understand the topological phase diagram affected by quantum fluctuations. At the moment, Arpad and I are looking to separate high and slow-frequency behaviour for a simpler case we have now stumbled upon. Although we are stuck at the moment, I like the project quite a lot because I see a lot of mathematical concepts coming together in a way I have never seen before. Thus, it is beneficial for the scientific community.

Within my work environment, my colleagues are honest, polite and welcoming. I enjoy morning coffee meetings where we exchange new ideas and views and articulate them, forming an open discussion. And that promotes transparency in faculty drama. Occasionally I also go to work meetings where I enjoy Optics and Cavities section with its creative ideas where in the future, I could participate more actively by asking questions in the meetings. In the future, I could also better integrate with my colleagues by establishing closer relationships and better communicating my experience, expertise and ideas. Unfortunately, not all opinions and views are open for my colleagues to be challenged.

For example, I remember one incident when Joseph (my colleague in the same room) talked with Pjotr (an MSc student) about making his code run faster with Cython and C, an extended period which I recognised as a deep rabbit hole. Seeing that my input would benefit the productivity of Pjotr, we started to look in the code to see how hard it would be to retype in Julia^{[1]}. But then snaps, I got attacks from Joseph, and then my good intentions collapsed. I learned my lesson that to make a change; I would have to deal with Python shaming (due to strong Python binding between colleges) which I do not have time to confront. That was expected because Python and programmer relationships are the same as for a wife with an abusive husband. Everyone recognises you both as a loving couple and gives credit for that. In contrast, at home, he orders you to compile, interface, read C, Cython, and C++, and to do things in a way which do not make him look weak while being asked to follow Pythonic rules which do conflict with the above (object-oriented code is hard to optimise) and within itself due to expression problem.

On the positive side, my expertise and hobby were useful for Yugang, for whom I helped to make his calculation 20 times faster by just retyping from Python to Julia (the performance benefit came from the compiler being able to infer types and inline the code making the assembler free from branching and jump statements). Also, with open discussions, I have inspired Xin to consider Julia due to his slow calculations in Matlab. And with time, my hobby of following how Julia evolves will become more attractive to my colleagues. An open seminar on Julia would introduce some sanity in this world.

To sum up it all, I have had experience rich year. I see multiple fronts where I could improve in writing, teaching, integrating within the community and participating in summer schools and conferences. I am proposing productivity improvements for my colleagues and more effective problem-solving session organisation. I see opportunities to grow, a research project I could supervise, and integrity as the driving force for a greater future in the TU Delft.

[1] | That language is superior and is going to be a mainstream numerical tool, as shown by NumFocus organisation support made of sponsors like Intel, Microsoft, Google, IBM, and Nvidia, who since 2015 have supported Numpy, Scipy, Matplotlib and Jupiter. One of the achievements is the lion's share (more than half)) of Google Summer of code from NumFocus division. That shows it is easier to tackle a problem on Julia; novice users are productive in producing results. At the moment there is the best state of the are a library for mathematical optimisation Jump, for differential equations DiferentialEquation.jl (which has stochastic solvers), Makie for plotting and others http://www.stochasticlifestyle.com/some-state-of-the-art-packages-in-julia-v1-0 |

CC BY-SA 4.0 Janis Erdmanis. Last modified: October 10, 2023. Website built with Franklin.jl and the Julia programming language.