And nature does it in real-time

A paper of mine appeared today in Physical Review E.  Called, "Extension of the continuum time-dependent Hartree-Fock method to proton states¹."  As the name suggests, it is a paper about methodology - so it's not going to feature in any press-releases about exciting new physics results.  It's even an extension to an existing method (from our previous paper), which might make it seem all the less exciting.  I think it's still a good paper, and a useful one, hence the blog post.

The method we developed overcomes a problem inherent in many attempts to solve time-dependent equations in physics problems.  From a mathematical point of view, the problem is that the equations that nature seems to have written itself in are differential equations.  By their very nature, such equations have solutions which combine some functional form, along with boundary conditions.  The functional form gives a kind of general prescription of how to solve the equations for absolutely any case at all, and the boundary conditions then shape the details to fit the exact physical situation at hand.  For example, the general solutions to Maxwell's equations describe all (classical) electromagnetic phenomena, but the boundary conditions pin down whether the particular solutions is for a light wave, the electric field round a charge, or the induction in a generator.  

In the case of our paper, we were concerned with the time-dependent Schrödinger equation - the basic equation of quantum mechanics².  In particular, we are interested in solving it for the case of atomic nuclei undergoing some kind of dynamic process.  In mind we have excited wobbling states, or fusion or fission, or some combination of such things.  More or less any case of interest involves the nucleus being excited in such a way that it can decay by breaking up, either into two or more fragments, or by emitting protons or neutrons.  One long-standing problem with solving the time-dependent Schrödinger equation in such cases is that the only simple way of working with boundary conditions is to assume that we can consider the tiny nucleus to be in a little box a bit less tiny than the nucleus, but a box which either reflects back anything emitted from the excited nucleus, or which lets things pass through but then reappear at the other side. This is kinda bad:  Nature doesn't do it that way.  It lets things that decay off of the nucleus travel far away without some artificial box getting in the way.  The reason that these strange unphysical solutions are the easy ones to implement is that they involve pretending that the inside of the box is everything that there is.  If we have stuff in our system, it has to be somewhere in the box.  It's hard to start having by having a bunch of stuff (nucleons in a nucleus) in our calculation, and then to keep calculating how it changes in time, but to stop keeping track of some of it because it's left our system.  It doesn't sound like a hard problem, or even that it should be a problem at all, but it is, on both counts.

So, our paper is about how to deal with this "open quantum system" (search for that phrase, and there are a whole load of hits - it's a field in itself).  Our method is reasonably general, but we've applied it just to vibrational states of nuclei so far.  That was quite a job in itself.  It is the final work from my PhD student Chris Pardi's thesis, from last year.  It took the paper a while to get into print.  We tried first in Physical Review C, where it was felt to concentrate a bit too much on the technical aspects of the algorithm, and not enough on the nuclear physics - a fair enough comment - and so we asked Physical Review E to take a look.  One referee it was sent to was nice enough to write a long report, ending with "In conclusion, I believe that this paper is excellent and very well written." So - thank you anonymous referee.

The title of this post is a reflection of the fact that we have worked hard to solve some equations, along with their proper boundary conditions, using some computational calculations that take a certain time to run.  Not so very long on the scale of things, but still a few tens of seconds.  They describe a process that happens in nature over a few zeptoseconds.  Nature works out what to do so quickly...

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¹ C. I. Pardi, P. D. Stevenson and K. Xu (2014). Extension of the continuum time-dependent Hartree-Fock method to proton states Physical Review E, 89 : 10.1103/PhysRevE.89.033312
² Okay, we could debate what the most basic equation of quantum mechanics is, but calling the Schrödinger equation the basic one is not outrageous.

STAGgering!

A new blog has been set up here at the University of Surrey, on which I have write-access.  I have yet to write anything there, but when I am struck to write something which is a bit more about Higher Education than nuclear physics, then that is probably where it will go.  Other more erudite people than me will also be writing there, and indeed already have started.

The blog is called STAGgering, a fun play on the fact that the University is on a site called Stag Hill, and the stag features in the University's logo.  Ostensibly it's about this particular university, but I expect the there will be lots of stuff about the higher education scene in general, so if that's your thing, then please add it to your list of blogs to follow.

The picture with this post is a rather old one, from the early days of the University.  I think the fence you can see in the background is fencing off some building work of what is now the Guildford Court residence block.  The picture is from the great website uossnaps, set up by a past student to share old photos and memories of the place.  

Welcoming the DIRHB code into the fold

I recently got one of those emails that journals send me announcing recently-published articles.  It came from Computer Physics Communications (CPC), an Elsevier journal that publishes a combination of articles on computational methods and actual computer programs which are made available (to journal subscribers) in a library.  I published a paper there some years ago based on a program I wrote to calculate angular momentum coupling coefficients.  I wrote it in the early stages of my PhD study, because I had very little idea of what I really ought to be doing, and thought it would be a nice excuse to learn some java.  It occurred to me a little later that I could write it up and publish it, as well as having it available on a web page.  It is not a hugely cited paper, though I did notice it appear in the footnote of Rowe and Wood's recentish book.  There's a picture of my name in the footnote attached to this post.  I do get some people coming up to me and telling me how useful they find my program.  More useful than I find it, that's for sure.  I don't think I've needed to evaluate any such coupling coefficients since I've finished my PhD.

Anyway.  Back to that email from CPC.  I noticed that there is a new computer program published by the Zagreb group which performs calculations of nuclei using the relativistic mean field method.  It's quite complementary to the sort of thing I do, and I look forward to downloading it, having a play, and making use of it to throw in the mix of calculations when interpreting data.  So far, the code has not quite made it to the download library, so I haven't played with it.  The paper in CPC is available now, though, and for non-subscribers, the arXiv version is there for all (though with this sort of paper, it's not of so much interest unless you can also play with the code, too).

"Not necessarily the scientific merit"

Following the redesign of the Physical Review C website, they seem to have created a new feature for the front page called "Kaleidoscope".  Phil, my PhD student pointed out to me last night that our most recent paper features there on the front page (though as of right now it's no longer the newest one, so is not quite at the top of the page any more).  

What great aspect of our work got us on the front page?  To quote the PRC website: "Please note that kaleidoscope selections are based on aesthetics and not necessarily the scientific merit of the paper"  Oh well!  At least there is a new route to get your work highlighted on the front page - make sure you include at least one really nice picture in your paper.

End of Fusion'14 and on to NPGP

I am back from Delhi now. Following my last post we had two more days of talks, and one more part of the "cultural programme" (though of course science research is a cultural activity).  This was a musical recital by sitar player Pandit Prateek Chaudhuri.  I enjoyed this very much.  He gave a kind of lesson about the rules and styles in Indian classical music and gave many examples, but did plenty of uninterrupted playing as wells as talking.  A YouTube clip of an earlier performance can't really do justice to a live performance, but I've included one above, and it gives you an idea.

The last couple of days of talks featured a range of theoretical and experimental work on fusion, and I came away from the whole thing with a resewed sense of some of the interesting questions.  My background does not really feature much work in fusion, but enough to justify coming.  I learned a lot from a community for whom it is their main thing and am going to enjoy making some calculations in the upcoming months.

Now, as I write, I am sitting on a train to Reading, where I will pick up a train to Swindon.  It's day one of the Nuclear Physics Grant Panel meeting.  I'm not really looking forward to the job.  I think it's clear from the proposals that there is no "dead wood" in the already well-pruned nuclear physics community, and to have the job of distributing a very limited pot of money won't be a fun one.