Monthly Archives: June 2020

List of actions

In the post before the previous one, I advocated for faculty and personnel in physics departments to reflect the make-up of the populace. Here is an excellent concrete list by Professor of Chemistry Kensha Marie Clark of the University of Memphis of actions that your department can undertake (click on the tweet for the whole list or on the unrolled tweet at the link). A lot of this list applies to other underrepresented folks as well:

https://threadreaderapp.com/thread/1268123251978403844.html

Meissner effect as amplified atomic diamagnetism

As you can probably tell from my previous post, I have found the recent activism inspiring and genuinely hopeful of it translating into some form of justice and meaningful action. At the end of this post I share a few videos that I found particularly poignant.

It’s hard to imagine the history of condensed matter physics without both the discovery and theory of superconductivity. Superconductivity has played and continues to play an outsized role in our field, and it is quite easy to understand why this is the case. All one has to do is to imagine what our world would look like with room temperature superconductivity. Besides the potential technological implications, it has also garnered attention because of the wealth of stunning effects associated with it. A few examples include the Josephson effect, flux quantization, persistent superconducting currents, vortex lattices and the Meissner effect.

Now, these effects occur for various reasons, but there are a couple of them that can be viewed to some extent as a microscopic effect on a macroscopic scale. To show what I mean by that, I am going to focus on the Meissner effect and talk about how we can view it as an amplification of atomic diamagnetism. One could also extend the this microscopic to macroscopic amplification picture to the relationship between a Josephson junction in a superconducting ring and the Aharonov-Bohm effect, but I’ll leave that discussion to another day.

To understand what I mean by amplification, let’s first look at atomic diamagnetism. Here we can use a similar logic that led to the Bohr model of the atom. Two conditions are important here — (i) the de Broglie relation \lambda = h/p and (ii) the Bohr quantization condition n\lambda = 2\pi r which states that only integer wavelengths are allowed in a closed loop (such as an atomic orbit). See the image below for a simple picture (click the image for the source).

We can use the classical relation for the momentum p=mv in addition to equations (i) and (ii) above to get mvr = n\hbar, which is what Bohr got in his atomic model. It’s worth noting here that when the atom is in its ground state (i.e. n=0), there is no “atomic current”, meaning that j = ev = 0. Without this current, however, it is not possible to have a diamagnetic response.

So how do we understand atomic diamagnetism? To do so, we need to incorporate the applied field into the deBroglie relation by using the canonical momentum. By making the “Peierls substitution”, we can write that p = mv+eA. Using the same logic as above, our quantization condition is now mvr = n\hbar - eAr. Now, however, something has changed; we do get a non-zero current in the ground state (i.e. j = ev = -e^2A/m for n=0). Qualitatively, this current circulates to screen out the field that is trying to “mess up” the integer-number-of-wavelengths-around-the-loop condition. Note also that we have a response that is strictly quantum mechanical in nature; the current is responding to the vector potential. (I realize that the relation is not strictly gauge invariant, but it makes sense in the “Coulomb gauge”, i.e. when \nabla\cdot A=0 or when the vector potential is strictly transverse). In some sense, we already knew that our answer must look obviously quantum mechanical because of the Bohr-van Leeuwen theorem.

If we examine the equation for the electromagnetic response to a superconductor, i.e. the London equation, we obtain a similar equation j = n_sev = -n_se^2A/m, where n_s is the superfluid density. The resemblance between the two equations is far from superficial. It is this London equation which allows us to understand the origin of the Meissner effect and the associated spectacular diamagnetism. Roughly speaking then, we can understand the Meissner effect as an amplification of an atomic effect that results in a non-zero ground state “screening” current.

I would also like to add that the Meissner effect is also visible in a multiply connected geometry (see below). This time, the magnetic field (for sufficiently small magnetic fields) is forbidden from going through the center of the ring.

What is particularly illuminating about this ring geometry is that you don’t have to have a magnetic field like in the image above. In fact, it is totally possible to have a superconducting ring under so-called Aharonov-Bohm conditions, where a solenoid passes through the center but the ring never sees the magnetic field. Instead, the superconducting ring “feels the vector potential”. In some sense, this latter experiment emphasizes the equation above where the current really responds (in a gauge-invariant way) to a vector potential and not just the magnetic field.

Understanding the Meissner effect in this way helps us divorce the Meissner effect from the at-first-sight similar effect of persistent currents in a superconducting ring. In the Meissner effect, as soon as the magnetic field is turned off, the current dies and goes back to zero. This is because through this entire process, the superconductor remains in its ground state. Only when the superconductor is excited to higher states (i.e. n=1,2,3…) does the current persist in a metastable fashion for a quasi-infinitely long time.

To me, understanding the Meissner effect in this way, which exposes the connection of the microscopic to the macroscopic, harks back to an old post I made about Frank Wilczek’s concept of upward inheritence. The Meissner effect somehow seems clearer through his lens.

Now as promised, here are the couple videos (if the videos don’t play, click on the panel to take you to the twitter website because these videos are worth watching!):

Listening

I am not Black. I am not American. I do not understand the many nuances of American and African-American culture. I do not understand the extra struggle African-American people have to go through each day. But there are some things that are easy to understand. It is easy to understand that the killing of yet another unarmed Black man is due to structural racism. It is easy to understand that the involved police officers did not view George Floyd as a man that was their equal. And it is easy to understand why people are incensed about this.

A lot needs fixing here, and it’s going to take a while for that to happen. But as I write this in Los Angeles with the sound of sirens going by my apartment every few minutes, it is hard not to think of the 1992 L.A. riots. It is hard not to think about what happened in the wake of the acquittal of the officers involved in the brutal beating of Rodney King. When looking at police violence against the Black community, it is easy to feel like very little has changed since then.

This time calls for some reflection about how all of us, in the institutions where we work or participate, can enact some change.

A few months ago, the physics and astronomy department at my new institution, UCLA, invited Sherard Robbins to come and speak about the demographics and minority representation in our department. He asked us to take a look around the room and to see if the representation in the room reflected that of the general population in Los Angeles. This was an embarrassing and shameful exercise. It is shameful because we do not have a single Black faculty member. It is also shameful because women are hugely underrepresented.

Representation matters. It particularly matters in positions of power. It matters because when you see people that look like you and are culturally similar to you in a position you thought was unattainable, you start to believe you can do it. It also matters because people tell stories, and stories are mediators of humanization. When you hear about your culturally different colleague’s weekend with their family at the beach, you see them as a parent, spouse, and human.

I am currently in a position of power. I have been an assistant professor now for almost a year, and because it is so new and fresh, it contrasts strongly with my previous position as a postdoc. I went from having almost no power and social responsibility to being thrust into a position where my words and actions do have an affect on undergraduates, graduate students, postdocs and other faculty members. I know that many of you who read this blog are or will be in similar positions in the future. So when you are afforded the privilege of such a position, it is your responsibility (just as it is now mine) to make sure that conduct in your department changes. It is your responsibility to make sure that the make-up of the department starts to reflect that of the greater population. It is your responsibility to ensure that traditionally underrepresented groups make it into positions of power. And it is your responsibility because if you don’t do it, no one else will.

The activists in the streets deserve tremendous credit for making their voices and anger heard. And it’s important that those in positions of power take actions that say “we hear you”.

I sign off with a rather profound quote adapted from the Talmud for the film Schindler’s List:

Whoever saves one life saves the world entire.