Copasetic Flow

Today's post is a little plain Jane, (as far as I know), in that it's just a review of our classes' derivation of the boundary conditions for the electrical displacement field at an interface between two materials.  Here's a question.  Does anyone know of anything, cool or clever to take away from the following derivation?  At the moment, it seems necessary, but not tantalizing. First, we'll need the Divergence Theorem, (picture 1), stating that the volume integral of the divergence of a vector field is equal to the surface integral of the same field with respect to the normal of the surface that bounds the volume. Given the above tools, and starting with a boundary between two materials, and the typical pillbox, (picture 2), where delta A is the area of the top and bottom of the box, n is the unit vector normal to the top of the pillbox and the pillbox straddles the boundary between the two materials.  In the end we'll let the sides of the pill...

After several lectures in other classes where the use of electron diffraction was described in terms of reciprocal spaces, (the Fourier transform of position as opposed to position itself), I finally saw a great explanation of why we work in the reciprocal space to learn about the structure of crystals and other materials in plain position space.  The diagram shown below, (picture 1 on Google+), sums it all up. Put very simply, there's a very clean relationship for how an electron is diffracted based on the electron's momentum wave which is the Fourier reciprocal of the probability vs. position wave in quantum mechanics.  However, to write this relationship down in its cleanest form, you first have to describe the diffracting media in the reciprocal space as well.  Hence, the emphasis on the reciprocal space even though results are often finally translated back to position space for human consumption. The atoms that form the cell structure in crystals are distribute...

The cool thing I saw in EM yesterday.  So, we all know that you have freedom to choose the vector and scalar potential within a set of rules.  What I hadn't seen before, was the rules written down in a concise form next to each other: If you look at the two right hand terms and then think of the two potentials making a four potential ala special relativity,  you arrive at a much simpler way to memorize the rule for selecting gauges.  You can change either potential by the gradient of a scalar field as long as you compensate the other potential by adjusting the other potential with the negative of the gradient of the scalar field in its 'dimension', (time vs. space/scalar vs. vector). Is there a more fundamental point we should get from this as well? Picture of the Day: From 1/18/13

This starts a new series of posts that will hopefully inspire discussion among folks taking, teaching, and/or using quantum mechanics.  If you're reading this on Google+, the equations are referenced in the album attached to the post. Did you know that DeBroglie came up with the concept of matter waves considering relativistic invariance? I didn't until quantum I lecture yesterday. Does anyone know how the reasoning went? I can see a way to make sense of it. If you look at energy being equal to, (eq. 1) and think about frequency as the reciprocal variable of time in a Fourier transform, then, if you begin to consider momentum, (the other three components of the energy momentum four vector of special relativity), you soon thereafter could arrive at, (eq. 2) where k is the reciprocal variable of the x, y, and z space coordinates in a Fourier transform. In the same lecture, it was mentioned that the simple form of a sound wave could propagate energy but not mass....

This is mostly just a note for myself to help me keep my references straight, but if you're interested in the London moment in superconductors, or the giant atom model of superconductors, you may find this interesting as well. In reading JE Hirsch's articles on the hole theory of superconductivity, I was led to an American Journal of Physics article by R. G. Rystephanic k that had a very nice derivation of the London moment.  In searching for more information on Dr. Rystephanick, I found an article on arxiv that cited him by Hanno Essen .  Dr. Essen's article spoke about the history of the giant atom model of superconductivity which I hadn't realized had been studied so widely in prior years.  JE Hirsch also makes use of the giant atom model in his work. References: AJP article: http://ajp.aapt.org/resource/1/ajpias/v44/i7/p647_s1 Essen paper: http://arxiv.org/abs/cond-mat/0407670 Essen giant atom paper: http://iopscience.iop.org/1402-4896/40/...

So, this is cool!  I've been studying the London moment in superconductors for one of my research projects. It's an effect predicted by Fritz London.  When a superconductor is made to rotate, it generates a magnetic field parallel to its axis of rotation.  The magnetic field is termed the London moment.  London theorized its existence by considering the superconducting electrons to be a viscous fluid. Here's the cool part. I came across an article in the American Journal of Physics where the author R. G. Rystephanick shows that the London moment can be derived simply by considering the assumption that when the superconductor spins, there should be no static force created by the Coriolis effect on the superconducting electrons.  This gives the following very simple derivation References: 1.  Aforementioned AJP article http://dx.doi.org/10.1119%2F1.10326 Rystephanick R.G. (1976). Electromagnetic fields in rotating superconductors, American Jour...

In 1999, R Tao, X. Zhang, X. Tang, PW Anderson, reported that fine paritcles of a Br-Sr-Ca-Cu-O superconductor would clump into a ball when suspended in liquid nitrogen and subjected to an electric field.  The discovery was covered in a physics news update article .  The last author PW Anderson is the Nobel prize winning PW Anderson .  The thoeretical explanation advanced by Tao et al. at the time was, (briefly), This interesting phenomenon directly relates the surface tension to the Josephson coupling energy. I came across this research reading papers authored by JE Hirsch of UCSD.  Dr. Hirsch has advanced and interesting modification of the BCS theory of superconductors, 'the hole theory of superconductivity '.  If the 'Tao effect' was shown to be reproducible, it would help to confirm Hirsch's theory.  Recently however, Ghosh and Hirsch reported that they have observed the Tao effect in non-superconducting particles as well as in ...