Jekyll2022-06-23T00:01:11+00:00https://alexandrecoates.github.io/feed.xmlSciencishThe PhD website for Alexandre Coates, Theoretical Physicist studying Open Quntum Systems and Quantum Biology.Alexandre CoatesFirst publication out in New Journal of Physics2022-01-10T00:00:00+00:002022-01-10T00:00:00+00:00https://alexandrecoates.github.io/blog/2022/01/10/first-paper-published<p>Happy New Year!</p>
<p>This is just a short update to say that my first paper <strong>Localisation determines the optimal noise rate for quantum transport</strong> is now published in the New Journal of Physics.
This is a nice personal goal for me, I’m a big fan of open access and had long hoped I could get a paper into NJP so this is a double win.</p>
<p>As the journal is fully open-access you can read it online or download it from <a href="https://iopscience.iop.org/article/10.1088/1367-2630/ac3b2c">(<em>the journal page</em>)</a>.
Of course I have updated the manuscript on arXiv if you prefer that format, <a href="https://arxiv.org/abs/2106.12567">(<em>get that here</em>)</a>.
Finally a backup is available <a href="https://alexandrecoates.github.io/assets/documents/Coates,%20Lovett,%20Gauger%20-%202021%20-%20Localisation%20determines%20the%20optimal%20noise%20rate%20for%20quantum%20transport.pdf">(<em>here</em>)</a></p>
<p>It’s been hard doing research in COVID so I’m both happy and lucky to have been able to complete a paper that I’m personally very happy with.
Now I’m in my final PhD year so the goal is to see if I can complete one or two other things in time. Wish me luck!</p>Alexandre CoatesLocalisation determines the optimal noise rate for quantum transport is now available publically in the New Journal PhysicsDigital Poster - Localisation and Optimal Noise Rates2021-08-31T00:00:00+00:002021-08-31T00:00:00+00:00https://alexandrecoates.github.io/blog/2021/08/31/digital-poster-localisation-noise<h2 id="introduction">Introduction</h2>
<p>While I’m waiting to hear back from referees on my first manuscript on localisation and Environment-Assisted Quantum Transport (ENAQT) - <a href="https://arxiv.org/abs/2106.12567">(<em>you can read the preprint here</em>)</a>. I have the opportunity now to present some of my work at <a href="http://quamp2021.iopconfs.org/home">QUAMP 2021</a> as a digital poster made of 4 slides. Along with some additional detail.</p>
<p>So I thought it would be good to show that here as well.</p>
<h1 id="digital-poster---localisation-and-enaqt">Digital Poster - Localisation and ENAQT</h1>
<h2 id="slide-1---relevant-enaqt-mechanisms">Slide 1 - relevant ENAQT mechanisms</h2>
<p><img src="/assets/quamp/Slide1.JPG" alt="Slide 1" /></p>
<p>Here I show 3 relevant ENAQT mechanisms for the paper. They are linewidth broadening, the exclusive subspace, and momentum rejuvenation respectively. The first two are size-independent, being dependent only on a system’s energy differences and the linearity of the eigenbasis (meaning there is always at least 1 eigenstate with 0 presence on a given site).</p>
<p>Meanwhile, momentum rejuvenation is a finite size effect, dependent on the effective size of the system. Which is possible to adjust. Making it a useful probe as we can turn it from present to absent with the right adjustments. For completion’s sake I will note that momentum rejuvenation makes the following claim: a larger system wants <em>less</em> noise for efficient transport. There is a minimum time it takes for fast moving components of any excitation to leave the system $t_{min}$, that time scales with size $N$, and interrupting the system at a rate more frequently than $\frac{1}{t_{min}}$ is inefficient.</p>
<h2 id="slide-2---the-set-up">Slide 2 - the set up</h2>
<p><img src="/assets/quamp/Slide2.JPG" alt="Slide 2" /></p>
<p>This investigation was carried out by modelling thousands of nearest neighbour chains. We generated them with a range of gradients $\eta$, and a range of random on-site disorders $\zeta$, sampled from Normal distributions. By varying the gradients and the width of the Gaussian distributions $\sigma$ we were able to localise the chains in various ways.</p>
<p>The pumping scheme was to pump onto all sites equally (the steady state equivalent of a mixed initial state), and to extract our excitons from one end of the chain. By measuring the steady state current extracted, we could then find the optimal amount of dephasing $\Gamma_{optimal}$ for each chain.</p>
<h2 id="slide-3---effects-of-localisation">Slide 3 - effects of localisation</h2>
<p><img src="/assets/quamp/Slide3.JPG" alt="Slide 3" /></p>
<p>The point here is very directly that, the more localised a system is, the less spread out it’s eigenstates are. In a very direct sense, that is the <em>definition</em> of localisation. To ensure our intuition is general we consider combinations of two localisation methods: one from applying a linear potential (Wannier-Stark) and another from applying random disorders (Anderson), both affect the eigenbasis differently.</p>
<p>The direct implication of localisation being that ENAQT this is that we constrain all of our ENAQT effects. Broadening linewidths does not enable many new transitions, and even more eigenstates will have no presence on any chosen site. From this we get the general tendency that prior research has described: <em>more noise is needed to overcome the effects of more localisation</em>.</p>
<p>The effects are the same, just needing a bit more effort for the same effects as in ordered systems. So we would expect a broad proportionality between the peak noise and the IPR (how many sites the average eigenstate is distributed across), which becomes the power law $\Gamma_{optimal} \propto IPR^\lambda$.</p>
<p>However momentum rejuvenation is a finite size effect, implying that it will disappear in disordered systems. Implying that we need a correction to the above expression.</p>
<p>You can play with interactive sliders below to see how the two kinds of localisation affect the eigenbasis of an $N = 10$ chain. As you can see, when the system is relatively ordered, edge effects become visible, but these disappear as localisation comes to the fore.</p>
<h3 id="interactive-wannier-stark-localisation">Interactive Wannier-Stark Localisation</h3>
<div class="iframe-container">
<iframe src="/assets/wannier-N10.html" title="Wannier-Stark localisation of length 10 chain" height="500" width="100%">
</iframe>
</div>
<h3 id="interactive-anderson-localisation">Interactive Anderson Localisation</h3>
<div class="iframe-container">
<iframe src="/assets/anderson-N10.html" title="Anderson localisation of length 10 chain" height="500" width="100%">
</iframe>
</div>
<h2 id="slide-4---relating-localisation-and-peak-noise-to-a-power-law">Slide 4 - relating localisation and peak noise to a power law</h2>
<p><img src="/assets/quamp/Slide4.JPG" alt="Slide 4" /></p>
<p>Finally we look at chains with different lengths and see how the optimal dephasing rates change across them. We see a very consistent shape that fits very well to our amended curved power law $\Gamma_{optimal} \propto IPR^{\lambda + \kappa \cdot IPR}$, where $\lambda$ corresponds to the size independent effects, and $\kappa$ relates to the size-dependent effects, modelling the influence of momentum rejuvenation.</p>
<p>The far right panel shows the $\Gamma_{opt}$ range for each gradient, on each length of chain considered. Note that the gradient free ($\eta = 0$) bars show a decreasing lower range, as we expect from momentum rejuvenation. Larger systems, lower peak noise rates. However for systems with large gradients ($\eta = 1,10$) the lower limit is relatively constant across lengths, showing size dependence(and thus momentum rejuvenation) is no longer in effect.</p>
<p>So we show that for 1D systems that the optimal noise rate for ENAQT is dependent on the typical eigenstate width (IPR) and can be expressed simply as a power law with both size-independent and size-dependent components. Providing a cohesive, physically intuitive view of how ENAQT functions. For more details, including work applying this to chains at finite temperatures with the nonsecular Bloch Redfield Master equation, <a href="https://arxiv.org/abs/2106.12567">please see the preprint</a>.</p>Alexandre CoatesSharing a short digital poster on my work, made for QuAMP 2021Interactive Localisation, thanks to Bokeh2021-07-22T00:00:00+00:002021-07-22T00:00:00+00:00https://alexandrecoates.github.io/blog/2021/07/22/localisation-interactive-bokeh<h1 id="whats-new">What’s new?</h1>
<p>The latest from me is that I have submitted <a href="https://arxiv.org/abs/2106.12567">my first preprint to ArXiv</a>, <strong>Localisation determines the optimal noise rate for quantum transport</strong>.
It is the result of a few years of fumbling around in the dark until I found a result I ultimately thought was quite neat. Namely, that the eigenstate localisation of a system can tell you a lot about the relative importance of different Environment-Assisted Quantum Transport (ENAQT) effects.
I’m hoping to write a nice popular summary before the referees get back to me, but before that I felt it might be good to stretch myself and try something new.</p>
<p>Namely, I decided to try and make some figure from the paper interactive, to show how different forms of localisation occur, as I think playing around gives a new sense of intuition.
My work focussed on chains of two level systems, coupled to their neighbours, and looked at how localising them changed the importance of different ENAQT effects.</p>
<p>So for these two visualisations we consider a chain of 10 two-level sites, say Calcium ions as experimentalists have done that. For the mathematically minded that would be \(H = \sum_{i = 1}^{N-1} |i>< i+1 | + |i+1>< i|.\) If you were to change the energy linearly across the system by applying a field for example, you would observe Wannier-Stark localisation.
That is, the eigenstates of the system contract, and are spread out over a smaller number of sites. The upshot being, they overlap with fewer of the other system eigenstates. The intuition is quite simple, vary the energy across a system, and in the eigenbasis, the high energy eigenstates will all be at one end, and <em>vice versa</em>.</p>
<h2 id="wannier-stark-localisation">Wannier-Stark Localisation</h2>
<p>You can play around with exactly that effect below. This shows the eigenstates of a length 10 system, and you can vary the difference in energy across the system in terms of the bond strength <em>J</em>, and the sites they are present on. The size of the diamonds are proportional to the propability density of the eigenstate being on that site.
Note how the eigenstates overlap with fewer of their friends as the potential increases.</p>
<div class="iframe-container">
<iframe src="/assets/wannier-N10.html" title="Wannier-Stark localisation of length 10 chain" height="500" width="100%">
</iframe>
</div>
<h2 id="anderson-localisation">Anderson Localisation</h2>
<p>Then here we have Anderson localisation, the one that always pops up in reality because it’s hard to make anything perfect! The intuition is again quite simple, if you add random spikes to the system energy (manufacturing or experimental defects perhaps), then you get lots of destructive interference in the system.
The result is the classic, exponential Anderson localisation. Here for visual clarity one set of random energies has been pulled from a Gaussian distribution, and applied to a degenerate chain. As you increase the anderson disorder, you scale up the size of these spikes and troughs. You should see a much less ordered localisation process.</p>
<div class="iframe-container">
<iframe src="/assets/anderson-N10.html" title="Anderson localisation of length 10 chain" height="500" width="100%">
</iframe>
</div>
<p>These two were made in Bokeh, an open-source and slightly more web-friendly visualisation suite than matplotlib (which I’ve made most of my other figures in). It was a slightly painful learning experience as I had to touch some javascript to make these work.
But it was worthwhile nevertheless, or maybe I’m too easily entertained by little web interactives!</p>
<p>In any case, with this out of the way, the next step is to write a little popular summary - and maybe see if I can justify making any more interactive figures on the way.
If you’re interested in the preprint, do follow the arXiv link at the top, we did our best to make it as readable a paper as possible!</p>
<p>Until the next time, take care.</p>Alexandre CoatesUsing Bokeh I can turn the figures I use to understand localisation into something interactive. More coming soon.A LaTeX Thesis Template - feel free to use it!2021-02-16T00:00:00+00:002021-02-16T00:00:00+00:00https://alexandrecoates.github.io/blog/2021/02/16/latex-thesis-template-hw<p>A quick update here - I have now produced a new and updated LaTeX PhD Thesis template for Heriot-Watt University. If you aren’t at Heriot-Watt feel free to adapt and update it to your needs as well.</p>
<p>I have mainly done this now as I’m approached the 2.5 year mark in my PhD, and have a mean collection of spare figures that aren’t relevant for publication, but <em>are</em> relevant to my research more broadly.</p>
<p>The main updates I’ve implemented are quite simple but nice, especially for students who don’t use much LaTeX:</p>
<ol>
<li>Better University shield for the title page (previous one was a trace, mine is at least a nice crop of an svg)</li>
<li>subfiles support - this means you can now typeset individual parts of chapters of the thesis, without rendering all of it at once. This saves a lot of time for people with Theses particularly full of images</li>
<li>Replaced the glossaries package with the acro package, a simple way to include specialist terms you might have to type repeatedly, like Alloy names, chemicals etc.</li>
<li>Added more maths packages for typesetting</li>
<li>A little bit of context and humour - added a few examples of each bit of functionality, and linked the university guidelines on what a thesis needs, just to make it more self-contained</li>
</ol>
<p>My forked Github repo is public, so you can <a href="https://github.com/AlexandreCoates/HW_LaTex_thesis_template">click here to access it</a>, and download it, then use it in Overleaf or offline in your favourite LaTeX editor.
I have also made the repository a template, meaning you should be able to copy the thing wholesale without any of the commit history. Forking is still possible too of course.</p>
<p>Any comments or wonderful ideas? Feel free to contact me</p>Alexandre CoatesHeriot-Watt University only had one PhD Thesis template, which dated from 2013 and had a shield that looked like it was traced in MS Paint, I've updated it now.Putting Science on a Postcard2020-01-20T00:00:00+00:002020-01-20T00:00:00+00:00https://alexandrecoates.github.io/blog/2020/01/20/sci-art-postcard<p>This is all about how an artist and I produced the image you can see in the header of this post - turning the principles of my work into something visible! A rewarding experience that stretched me to find clearer, and more evocative ways to reduce my work to its fundamental principles. Let’s talk about that.</p>
<h2 id="who-did-it">Who did it?</h2>
<p>‘Art and Science on a Postcard’ was organised by Intersci, a science outreach society at Edinburgh University and ASCUS Art & Science, an art and science charity. The premise was simple:</p>
<blockquote>
<p>Spend two mornings meeting with an artist, talk together, and turn your science into art. One twist, it’s got to fit on a postcard! A second twist: Scientists have to make the art too, no slacking and making the artist do all the work!
<
Simple really. And the outcome were two fields of abstract colour. One blue, one green, both filled with strange shapes and textures. It couldn’t have gone better honestly.</p>
</blockquote>
<h2 id="how-to-explain-abstract-science">How to explain abstract science</h2>
<p>The event started simply, about 8 of us met in a library, 4 artists and 4 scientists. Of the scientists, I was the only one not working in Biology or Biology adjacent fields. So I was faced with a conundrum, my work is more about transport, than any one structure which ‘transports.’ What does movement look like, when it is quantum?
It was by asking these problems that I got the</p>Alexandre CoatesTurning abstract science into abstract art.Quantum Biology: Challenges of a Speculative Science2019-09-26T00:00:00+00:002019-09-26T00:00:00+00:00https://alexandrecoates.github.io/blog/2019/09/26/quantum-biology-post-cm-cdt<p>Part of my work with the <a href="https://cm-cdt.supa.ac.uk/">Scottish Condensed Matter CDT</a> is volunteering to help run the CDT blog.
So recently I wrote a piece on <a href="https://condensed-matters-cmcdt.wp.st-andrews.ac.uk/2019/08/01/quantum-biology-challenges-of-a-speculative-science/">Quantum Biology, and how to justify working in more speculative areas of science</a> for the blog in August.</p>
<p>It is a bit of writing on some of the challenges I face in motivating why I am interested in studying Quantum Biology.
Unlike a lot of areas, things can get a bit speculative, lots of people have doubts about some claims in the field, and these are not unreasonable claims. This post is my attempt to lay out not only what some of the fields claims are, but what is hard to believe about them.</p>
<p>Given that lots of scientific research is speculative or ‘cutting edge’ it isn’t unprecedented to be unsure of the answers, but I felt it would be helpful to put into words some thoughts about honestly asking questions, and honestly receiving results in science.
I hope it’s of interest to people who want to know a bit more about the area, and why I think it is still worth exploring, as long as we approach it in the right ways.</p>
<p>If that sounds like you kind of thing <a href="https://condensed-matters-cmcdt.wp.st-andrews.ac.uk/2019/08/01/quantum-biology-challenges-of-a-speculative-science/">you can click here to read it</a>.
Hopefully with summer over some more pieces will be going up on the ‘Condensed Matters’ Blog soon too, so keep an eye on it for interesting pieces on science and outreach from all of us on the CDT!</p>Alexandre CoatesPart of my work with the Scottish Condensed Matter CDT is volunteering to help run the CDT blog. So recently I wrote a piece on Quantum Biology, and how to justify working in more speculative areas of science for the blog in August.(Good) Changes to UK PhD Sick Leave2019-09-02T00:00:00+00:002019-09-02T00:00:00+00:00https://alexandrecoates.github.io/blog/2019/09/02/sick-leave-changes<p>Some good news, as of a few weeks ago, the rules for sick leave/ medical leave of absence have changed for <strong>many</strong> funded PhD students in the UK. <a href="https://twitter.com/ejnagouse/status/1164909959861145601?s=20">I found out about this from a post by Emma at the University of Sheffield.</a></p>
<p>Above is where I learned about it, so I thought I’d write it up with some more information so people can check their own institutes are aware of it.</p>
<p>So the new UKRI policy is that student can take 13 weeks of leave per 12 months, and receive a full stipend for that time. Not only that, but this money should come from a <em>separate uni pot</em>, and not from the fixed training funds for the candidate. This means candidate deadlines and payment etc should be extended for as long as the leave is taken (up to 13 weeks!), giving them the same amount of time to research once they return.</p>
<p>For reference, the old system was that medical absence was paid from the fixed amount of candidate training money, which forcws students to have less paid research time once they returned! Which was an awful system.</p>
<p>This policy applies right now, and universities should be aware of it already. I emailed my research director and there are meetings happening this week so the University can follow through on this. If you can, check at your university, it’s your right, right now!</p>
<p>To be clear, this applies to anyone funded by a body under UKRI, that being: EPSRC, STFC, AHRC, BBSRC, ESRC, MRC, NERC, Innovate UK or Research England. So if you’re differently funded (for example by the Wellcome Trust or Leverhulme Trust), check what your situation is.</p>
<h3 id="the-official-documents">The Official Documents</h3>
<p>The official guidance is on the <a href="https://www.ukri.org/funding/information-for-award-holders/grant-terms-and-conditions/">UKRI page here</a>
And the specifics about Training Grant Conditions and how these absences are paid for is in sections TGC 6.1.1 and TGC 8.2 of the <a href="https://www.ukri.org/files/funding/ukri-training-grant-terms-and-conditions-jun19-pdf/">second document listed</a></p>
<p>There are other details in the first document too, but the main take away is that this applies now to anyone funded by a body under the UKRI, so that is: EPSRC, STFC, AHRC, BBSRC, ESRC, MRC, NERC, Innovate UK or Research England</p>Alexandre CoatesFor PhD students funded by UKRI, there have been some great improvements to how sick leave is going to be treated going forward.Granada Poster Information2019-08-21T00:00:00+00:002019-08-21T00:00:00+00:00https://alexandrecoates.github.io/blog/2019/08/21/granada-poster-information<p>Thanks for following the QR code to get more information about my poster/work. In case you need a refresher, a small version of my poster is below (right-click to view it full).
Keep scrolling beyond that to see the extra information and animations I couldn’t fit on it, due to the limits of paper.</p>
<p><img src="/assets/Granada_poster_thumbnail.png" alt="Granada Poster - yes I spent a lot of time on this, I wanted a big circle in it." style="width: 596px;" /></p>
<p>If that looks right - then you’re in the right place. If you have any questions or comments about the poster, please let me know at <a href="mailto:ac173@hw.ac.uk">my email</a>.</p>
<h2 id="citation">Citation</h2>
<p>First I must give kudos to the paper that has inspired and directed a lot of this initial work. That is, <strong>Li, Y. et al. (2015). ‘Momentum rejuvenation’ underlies the phenomenon of noise assisted quantum energy flow. New Journal of Physics</strong>. The paper handily describes an underdiscussed mechanism for noise-assisted quantum transport, that being the prospect of pumping excitation states from lower momenta, to higher momenta. In addition to that, it also provides open source code!
The main work I’ve recreates is that shown in Figure 2, that is the transport dynamics of a length 40 chain, for various mixes of quantum and classical transport. Future work may also build off the latter half of the paper to look at driving such a system.</p>
<p><a href="https://iopscience.iop.org/article/10.1088/1367-2630/17/1/013057">Click here for the paper</a></p>
<p><a href="https://figshare.com/articles/Quantum_Classical_Hybrid_Transport_Simulations/1050158">Click here for the code</a></p>
<h2 id="animations">Animations</h2>
<p>As a poster can’t show you animations, here are the central 2D figures, and some additional 1D chains, now in glorious motion. These are a work in progress, but good for showing the physics more visually. Quantitatively the tilted systems function the same as degenerate systems, but transport more slowly, which is due to the limited classical hopping present in the model.
The degenerate animations agree with the physics from the paper described above.</p>
<p>While these demonstrate that the excitations really do move through the systems as described, they also go to show that the current model isn’t sufficient to add in the real directionality one expects of a finite-temperature biased system. That is hopefully what is coming next in my work. Watch this space!</p>
<p>First the flat chain:</p>
<video width="432" height="316" controls="">
<source src="/assets/1by15_flat_granada.mp4" type="video/mp4" />
Your browser does not support the video tag.
</video>
<p>Tilted chain:</p>
<video width="432" height="316" controls="">
<source src="/assets/1by15_slope_granada.mp4" type="video/mp4" />
Your browser does not support the video tag.
</video>
<p>Flat plane:</p>
<video width="432" height="316" controls="">
<source src="/assets/15by15_flat_granada.mp4" type="video/mp4" />
Your browser does not support the video tag.
</video>
<p>Tilted plane:</p>
<video width="432" height="316" controls="">
<source src="/assets/15by15_slope_granada.mp4" type="video/mp4" />
Your browser does not support the video tag.
</video>
<p>Right, that’s everything I could think to include. Thanks for checking the information out.</p>
<p>Have a lovely day,
<em>Alex</em></p>Alexandre CoatesA collection of supplementary information, animations and citations for the poster I presented at the Granada Quantum Matter Summer School.Hello, World! Alex Here2019-08-20T00:00:00+00:002019-08-20T00:00:00+00:00https://alexandrecoates.github.io/blog/2019/08/20/hello-world-alex-here<p>I may have started this unwisely late at night, but now I have a little PhD site and blog to host things. For those curious, this site is run on Jekyll, which runs on top of GitHub pages.
The theme it runs on is <a href="https://mmistakes.github.io/minimal-mistakes/">minimal mistakes</a>. I’m hoping to write something eventually on setting up a free website using Github, but for now you can just follow <a href="https://pages.github.com/">Github’s own advice</a>, or just find a theme you like and fork it!
Anyway, this blog should hopefully act as a little hub for my PhD thoughts, actions and plentiful mistakes.</p>
<p>I look forward to it. Though I say, this is probably a bit too much effort just to have a place to put up extra information for a poster.</p>
<p>Guess I better make good enough use of this to justify the outlay!</p>
<p>Have a lovely day – Alex.</p>Alexandre CoatesHi