My first year in TU Delft

 2018-10-31
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I remember that after the first month I promissed to make a blog post every month on my studies here. I admit I had different expectations and so being under the constant change makes hard to see the reflection of how I fell, perform and what future I see. But now when my first year had passed in the TU Delft and as I am required to submit my self reflection for the Go/NoGo meeting, I made concious effort on where I actually stand. Over this time I have had some unusual thoughts which might form an opinion and recepies posted in 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, useful and enjoyable experiences for taking role as researcher, student and teacher. I have been part of the Weyl disc project which had resulted in a fruitful end; I have been daily educated enthusiastically by my college Arpad Lukacs, by graduate school and by Yuli himself; and importantly I have played role in quantum transport where I gave problem solving sessions and improved the given problem sets.

As 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 of the quantum transport course of which I had no prior knowledge. The responsibilities for this role were restructurization of exercise sets and giving 4 problem solving sessions. I knew that it would be a hard task which I could relate from my previous experiences for making exercises for Physics Olympiad. But I was confident I can do it and I could get fresh experiences from the process after which I am after all. Thus I accepted challenge from Yuli with great honor and pleasure.

The problem which I tried to address with exercise sets was their cloudiness (a feedback I received at the last problem solving session from a student with particularly bad 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 rather by questioning leading student to a goal. Now after my corrections and restructuring I firmly believe that the exercise sets are in much better condition than they used to be for the goal of training students to apply their knowledge and motivates to acquire new one. That also made presentations of exercise solutions much more productive.

Overall we had 4 problem solving sessions with number of students fluctuating between 3 and 10. Since I had only a little experience of teaching (Previously I had made one lecture about "Lorentz attractors and Chaos" for bachelor students on blackboard and QFT seminar lecture on S-Matrix theory) I sticked to Yuli's advice and used slides as a main tool for presentations (also the classroom had a tiny whiteboard). Nevertheless that did not prevent me from breaking down harder 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 conclude that I made a positive impact on helping students to learn the course.

Nevertheless the problem solving sessions could have gained from additional improvement. First of all, I could have related setups considered in exercises with wider context which I can now do by being more knowledgeable in the quantum transport. Also participation of students to solve exercises before the problem solving sessions could be increased. I think 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 content of the book itself since derivations tends to be too short and unfocused. Therefore I would greatly appreciate to take the responsibility for managing problem solving sessions also next semester to implement such changes.

The teaching assistant duties of the quantum transport course greatly pushed me to learn the content of the course myself. But as I read the book and started to participate into workmeetings, I felt that I missed some fundamental understanding of quantum mechanics. So to broaden my understanding I took Yuli's course on advanced quantum mechanics. The book in the course was unusual due to it's view of teaching from condensed matter perspective and its clear, deep and sometimes entertaining storyline. Especially I liked story how breaking radiation is related to result of radiation produced by accelerating charge (I had asked such question during my master years for my QFT lecturer and failed to get answer to that then). However the lectures did not have such the same charm. I found chairs and 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. Perhaps such idea of making students to teach themselves would be great if the size of group who are listening would be smaller (something like 10 students) and the homework could be the exercises which were presented. That and other parallel duties that demotivated me to invest enough time to keep up with the pace to do the homework and latter the exam. I think it would be entertaining to take it also next year. Nevertheless I had great experience of reading the book and I have obtained clearer understanding on how phenomena in condensed matter is being understood.

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

As researcher, I and Arpad moved the Weyl Disc project to a fruitful end producing a paper "Weyl Discs" which is now under the second review. The project was motivated by theoretical observation that multi terminal superconducting junctions would host Weyl points in Andrev Bound state spectrum in the space of superconducting terminal phases (which leads to quantized conductance), but due to contact effects would be affected by a quantum fluctuations. To model the problem we promoted the superconducting phases which defines 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 limit. Independently of how conjugate variable entered the equation we saw that a behavior in energy level spectrum persists - in 2 of 3 directions of the bandstructure are almost degenerate forming a subspaces which we call a Weyl discs.

A fascinating application of one such subspace would be in quantum computation. Experimentally a qubit of made of Andrew bound states in Jospehson 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 would be able to 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 and due to mixing of the lowest levels, the basis (between which a relative phase would be acquired) would depend on the angular velocity. Thus effectively allowing us to implement any rotation in the Bloch sphere and so any single qubit gate (that follows because 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 collection of phase difference would be in comparison with parametric noise (which would also affect decoherence time). That I think could be further addressed in my PhD or as in some master student project whom I could supervise.

To sum up I felt that 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 hardest parts of the project was understanding why shifted harmonic oscillator basis was not a good choice for computation of lowest eigenstates. (The answer to that was that if we use a simgaz matrix to define new basis we change a representation of sigmay operator in this basis which I particularly explored numerically.) Also I find feeling of achievement in the implementation of hydrogen atom into coordinate space with adaptive grid and Richardson's extrapolation. (There I also initiated meeting with Prof. Gijzen with whom the discussion boosted us in confidence on how to reproduce results from his supervised master 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 in the writing of an article from my master's project, I found the process for this article particularly hard, painful and slow. One of the issues was 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 should we give to the reader. Other differences were that methods part of this article were much less significant. Nevertheless, I had a good experience of learning what is the structure of 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 further might use as a reference for forth coming articles. I contributed actively in making figures and captions, discussing what formulas should we write and what to leave in the appendix, how to think about approximations we use. I actively participated on looking up a 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 were the actual skills of writing. To improve on that I plan to take graduate school course in writing, practice writing in writing blog posts, and read more complex literature. These steps I believe could lead to the skills I need and want for being more competent by the end of the current project.

At the moment we have started a new project which is about understanding how external circuit affects topological phase diagram. The setup is basically the same as with Weyl Disc project except that now we look on the bandstructure macroscopically and characterize them with order parameters. In absence of circuit effects the phase is determined by emergence of order parameters for the gapless state that is density of states at 0 energy whereas for the gaped state that is the gap energy. Interestingly enough there are regions in superconducting phase space where the two gaped phases are separated by infinitesmall gapless strip. In this project we ask what would happen to this strip if we would have taken quantum fluctuations into account coming from external circuit effects? One could speculate that the gap would be smeared out by quantum fluctuations. 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 by means of general quantum circuit theory for which we write a general action assuming that superconductor phases at the terminals are time dependent. In the limit where circuit makes a strong constraint the frequency of quantum fluctuations for the superconducting phases would be high whereas behavior of the nanostructure affects low frequency of internal superconducting phases. Thus we believe we can integrate out higher frequency behavior (renormalize) to obtain effective action which would help us understand the topological phase diagram affected by quantum fluctuations. At the moment I and Arapd are looking on how to separate high and slow frequency behavior for a simpler case with which we have now stumbled upon. Although we are stuck at the moment I like the project quite a lot because I see great deal of mathematical concepts coming together in a way I have never seen before thus in my opinion it is very useful for scientific community.

Within my work environment, I find my colleges honest, polite and welcoming. I enjoy morning coffee meetings where we exchange new ideas, views and articulate on them forming an open discussion. And that in my opinion promotes transparency in faculty drama. Occasionally I also go to workmettings where I particularly enjoy Optics and Cavities section with its creative ideas where in the future I could participate more actively by asking question's in the meetings. In the future I also could do better at integrating within my colleagues by establishing closer relationships and do a better job of communicating my experience, expertise and ideas. Unfortunately not all ideas and views are open by my colleges to be challenged.

As an example, I remember one incident when Joseph (my colleague in the same room) were talking with Pjotr (MSc student) in our room for extended period of making his code rune faster with Cython and C which I recognized 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) with which I do not have time to confront. In a way that was expected because Python and programmer relationships are the same as for a wife with an abusive husband. Everyone recognizes you both as a loving couple and so gives credit for that where as home he orders to compile, interface, read C, Cython, C++ and to do things in a way which do not make him to look weak while being asked to follow Pythonic rules which do conflict with above (object oriented code is hard to optimize) and within itself due to expression problem [1,2]. On the positive side my expertise and hobby was 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 for considering Julia due to his slow calculations in Matlab. And I believe with time my hobby of following how Julia evolve will become more interesting to my colleges. Perhaps 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 community and participating in summer schools and conferences. I am proposing productivity improvements for my colleges, more effective organization of problem solving sessions. I see opportunities to grow, I see a research project which I could supervise and I see integrity as the driving force for greater future in the TU Delft.

Regards from TU Delft Janis

Footnotes:

1

: That language is superior and is going to be mainstream numerical tool is shown by NumFocus organization support made of sponsors like Intel, Microsoft, google, IBM, Nvidia, who since 2015 had supported Numpy, Scipy, Matplotlib and Jupiter. One of the achievements is 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 actually productive on producing results. At the moment there are the best state of the are library for mathematical optimization 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


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