| ||||||||
31 August (2020)
Displaced vortices engage their core into a strange and mesmerizing dance (blue dot for the optical field, full-wavefunction for an interacting condensate: both follow a similar phenomenology).
In our latest work arxiv.org/abs/2006.07173 (to appear in Optica) we show how vortex cores can go bananas, escaping the plane on one side and reappearing on the other side, making a detour by infinity with arbitrary high speeds.
At the same time, as topological charges, we'd like to think of them as objects. They remain, after all, clearly identifiable at all times and well-defined like point-like classical particles would be, unlike the wavefunction itself.
In this regard, our equations (16) for the case of a 2D harmonic oscillator, are particularly enigmatic: they relate quantum observables (lhs) to classical Newtonian expressions (rhs) for the core position r꜀ and velocity v꜀, modulo some quantum corrections (hbar terms).
The momenta and energies of whatever the wavefunction describes can thus be wholly accounted for by the core itself, with an effective mass m꜀ different from the mass m of the field (m꜀ is furthermore a negative mass).
These expressions hold when the core doesn't go banana... they otherwise become approximate, and if they can be extended to hold all the time, we didn't figure out yet how.
But in the cases we could pin down, I find this semi-classical link between classical and quantum expressions a perplexing twist on Ehrenfest theorem, showing for instance how the quantum fluctuation energy gets split between the kinetic and potential energy of the core!
There's certainly much more to find, including as librarians, as I'm sure this has been touched upon in the literature. If you know of similar or related results elsewhere, please point them to us. If you don't, you're invited to delve into our text: arxiv.org/pdf/2006.07173….
21 August (2020)
David turning into a Mathematician. t.co/i9KBAOUjQr
Replying to @UtterlyInterest and @DannyDutch
spot on.
I'll give a talk to the Photon2020 webinars (Sept 1) on our recent papers: Laser Photon. Rev., 14:1900279, 2020; Phys. Rev. A, 101:063824, 2020 & arXiv:2005.11800. photon.org.uk
Contributions are pre-recorded. What an agony to have to turn YouTuber, but as I say to students, the worst you do at the start, the highest is your progress. Not sure I can improve very much on my French accent though, that is now broken even in French.
I did the Wave part of this series - youtube.com/playlist?list=… - which, if I'm learning anything, should thus be the worst performance. Let's see how this goes. I'll probably get enough practice to turn into the Physics girl before this online ordeal is over.
19 August (2020)
Par contre faut traverser vite parce que si la voiture peut attendre même à un feu vert, le truc retombe de tout ses 200 kg sur le piéton qui s'attarde.
14 August (2020)