"Clustering-Induced Localization of Quantum Walks on Networks"

One of my papers came out in published form today. Here are some details.

Title: Clustering-Induced Localization of Quantum Walks on Networks

Authors: Lucas Böttcher and Mason A. Porter

Look at Me, I'm 𝞧 sub d...

I am going to have a field day for puns with this new (for me) nugget of information...

Sooo, Max Born, who gave us the statistical interpretation of the quantum mechanical wavefunction, is the grandfather of Olivia Newton-John @olivianj of Grease fame. How did I not know this.

— Michelle Kuchera (@MKizzyy) October 3, 2018

Tales from the ArXiv: "Calculating Spherical Harmonics Without Derivatives"

There is a new paper on the arXiv that apparently includes a new way of calculating spherical harmonics.

A part that some of you may find interesting is the pedagogical discussion at the beginning of Section 5, which starts: "Historically, there are five ways that spherical harmonics can be derived."

The one that is easiest (by far) for me to understand is the oldest method, which is by solving the differential equation. But I am mathematically inclined, and people with more physical intuition may prefer other methods.

(People who are more comfortable than I am with Lie manipulations may also prefer other approaches.)

Anyway, I appreciate the discussion in this paper.

"Scattering of Waves by Impurities in Precompressed Granular Chains"

You may have heard of the Ramsaur–Townsend resonance from scattering problems. The simplest version of it (by examing a particle in a square well) is one of the canonical textbook problems in quantum mechanics.

This is one of the important effects illustrating the need for a notion of wave mechanics.

It turns out that one can also get an RT resonance in a macroscopic, classical system.

The discovery of this classical RT effect (in granular crystals) is the subject of a paper by my collaborators and me, out in final form in Physical Review E today. Here are the details of the article.


Title: "Scattering of Waves by Impurities in Precompressed Granular Chains"

Authors: Alejandro J. Martínez, Hiromi Yasuda, Eunho Kim, P. G. Kevrekidis, Mason A. Porter, and Jinkyu Yang

Abstract: We study scattering of waves by impurities in strongly precompressed granular chains. We explore the linear scattering of plane waves and identify a closed-form expression for the reflection and transmission coefficients for the scattering of the waves from both a single impurity and a double impurity. For single-impurity chains, we show that, within the transmission band of the host granular chain, high-frequency waves are strongly attenuated (such that the transmission coefficient vanishes as the wavenumber k → ±π), whereas low-frequency waves are well-transmitted through the impurity. For double-impurity chains, we identify a resonance—enabling full transmission at a particular frequency—in a manner that is analogous to the Ramsauer–Townsend (RT) resonance from quantum physics. We also demonstrate that one can tune the frequency of the RT resonance to any value in the pass band of the host chain. We corroborate our theoretical predictions both numerically and experimentally, and we directly observe almost complete transmission for frequencies close to the RT resonance frequency. Finally, we show how this RT resonance can lead to the existence of reflectionless modes in granular chains (including disordered ones) with multiple double impurities.

Quantum Chess

I am a bit late to the game in watching the video of Quantum Chess. Go and watch it!

(It is excellent! Not bogus.)

Quantum Mosaic of John Stuart Bell

This mosaic of John Stuart Bell is very cool.

Takes from the ArXiv: Hydrogen π

This paper is cool (though surely someone must have done this before).

It rederives Wallis' formula for π by looking at the spectrum of the quantum-mechanical description of the hydrogen atom. (It does this with a variational computation of the spectrum.)

Quantum Political Science

I love this new article in The Onion.

The headline is "Quantum Political Scientists Hypothesize Country Headed In Both Right And Wrong Directions Simultaneously", and there are also other highly amusing comments in the article.

Rigged Hilbert Spaces

I love the term rigged Hilbert space, which I just encountered from a paper on the arXiv. I was hoping that thinking about probabilities in there would appropriately motivate the name (and maybe that's true in the applications to quantum mechanics), but it isn't immediately obvious to me that this should be the case. I want it to be true, though!

A City Named "Boson"

Note to self: the airport to which I want to fly is in the city of "Boston", not "Boson".

My search will probably be more effective now. And the best news of all is that more than one person can occupy that airport at once.

Commuting

I am commuting more these days.

That's not a bad thing, though. If nothing else, at least it makes me easier to measure accurately. :) (I have always loved this joke.)

Nobel Prize in Physics Awarded for Measurements on Individual Quantum Systems

I should have written a brief blog entry yesterday when the announcement was made, but here it is now.

Serge Haroche and Dave Wineland have won the physics Nobel Prize in 2012 for pioneering experiments that measure single quantum systems. This is important for quantum computing, among other things. John Preskill has described some of their work in this blog entry.

On my end, I'm happy to see a Nobel Prize for this topic (go quantum mechanics!) instead of particle physics and other things of that ilk. :)

One of My Contributions to Physics

The quote "Cycles. Is there anything they can’t do?" certainly sounds like something that I would say or write sarcastically, though I no longer remember when I said (or wrote) this. Anyway, you can find it at the top of Chapter 13 of Chaos: Classical and Quantum.

Schrödinger's Cat Executive Decision Maker

This particular geek toy is pretty damn awesome.

If the shipping cost to get this to the UK weren't so expensive (it costs about the same as the object itself), I would have purchased it. Se la vie.

(Tip of the cap to Jed Yang.)

Models Discussing Quantum Mechanics

This commercial is fantastic.

I would love for some of the academic text I've produced (even if plagiarized, as was the case here) to end up in a commercial like this one.

Tales from the ArXiv: Damping in Quantum Love Affairs

Sometimes, an eye-catching paper gets posted on the arXiv preprint server. Here is one such paper:

Title: Damping in Quantum Love Affairs

Author: Fabio Bagarello

Abstract: In a series of recent papers we have used an operatorial technique to describe stock markets and, in a different context, {\em love affairs} and their time evolutions. The strategy proposed so far does not allow any dumping effect. In this short note we show how, within the same framework, a strictly non periodic or quasi-periodic effect can be introduced in the model by describing in some details a linear Alice-Bob love relation with damping.



One of the things I really like about the title is that 'damping' can be used in both a physical and nonphysical context. Hell, it can be used in at least two different physical contexts! [Rarrrr!] And you know what makes it even more awesome? The fact that the abstract includes a typographical error in which "damping" is inadvertently called "dumping". D'oh!

I have only one question: Shouldn't the author have cited my article on quantum cuteness?

Classical Versus Quantum

Again using Google's new tool, one can see transitions between ordinary English usage and jargon.

Quantum Chaos in Nature

Doug Stone has a News and Views article about quantum chaos in the June 10, 2010 issue of Nature.

In case you don't have full-article access to Nature, you can find the abstract here (it's the second article).

I think I'll try to solve the classical problem first.

In the latest tales from the arXiv, I present quantum dating.

Title: Quantum Dating Market

Authors: O.G. Zabaleta and C.M. Arizmendi

Abstract: We consider the dating market decision problem under the quantum mechanics point of view. Quantum states whose associated amplitudes are modified by men strategies are used to represent women. Grover quantum search algorithm is used as a playing strategy. Success is more frequently obtained by playing quantum than playing classic.


Comment: Um, I think that there is a quantum cuteness paper that really ought to have been cited. :)

Celebrating Number 34

Yesterday was my 34th birthday (with 10:50 pm UK time the time where things turned over, according to my birth certificate), so I had a bunch of friends over to celebrate. We played some games, ate some cake, and generally hung out. The main party started at 7pm, and just before that I went out to dinner with my best friend among the locals.

Now it's very quickly back to the old grind, starting with marking quantum mechanics homework tonight. (My students who are taking this have told me that this is the hardest problem sheet they've seen in the 1.5 years that they've been here. I hope I'm not going to have to do all of these problems from scratch tonight---I'd greatly prefer a calmer marking period where I can wing things. We shall see.)