Copasetic Flow

My review of the material I mentioned yesterday [1] paid off pretty quickly.  Dr. Hirsch is quick to point out that one of the key differences between his 'hole theory of superconductivity'[4] and the more typical explanation of Cooper pair formation is that his theory predicts kinetic energy lowering after two holes in an energy band pair as opposed to the usual potential energy lowering after two electrons pair . While reading Hirsch's articles, I didn't remember ever coming across kinetic energy lowering pairing before.  It turned out that I had read about it in Dr. Likharev's notes , (see section 2.6, 'Coupled Quantum Wells'), but without an immediate application for the information, I promptly forgot it. Here are the basics 1.  Crystalline materials, (like superconductors, or semiconductors), in which electrons reside can be very roughly modeled as repeated delta function wells, (picture 1)[2] where the delta functions represent the potentia...

G+'er  +Jonah Miller  pointed out yesterday that Unruh had shown that the radiation predicted by Fulling produced a black body thermal spectrum in the same manner as Hawking radiation[1].   For some reason, I had it in my head that Unruh had actually pointed out prior to Hawking, so I wound up on another search through the research.  The necessary papers are usually fairly close at hand since the main thrust of my current theoretical research is looking at the spectrum of particles created, (or not), when an observer is rotating rather than accelerating in a linear fashion, but I digress.  Here's the chronology of papers to the extent I was able to work them out today.  By they way, Jonah was right! Fulling[2] was the first to point out that an event horizon coudl muck with your particle creation and annihilation operators producing what might look like particles to the uniformly accelerating observer. Davies[3] certainly discussed the temperature of th...

After writing about parity violating beta decay a few days I discussed it with a professor here at A&M and he pointed out that the whole thing isn't that odd at all if you look at the correct part of the following diagram based on Cottingham and Greenwood [1]. At first glance, it seemed odd to me that that magnetic field represented by the thick orange-ish arrows above didn't reflect in the mirror.  My professor pointed out, however, that the source of the magnetic field, the small circular current, reflected exactly as you'd expect a directed circle to reflect in a mirror.  Consequently, everything is simple and exactly as it should be if you look at the reflection of the cause rather than the effect. References: 1.  An Introduction to Nuclear Physics http://dx.doi.org/10.1017%2FCBO9781139164405 Cottingham W.N. & Greenwood D.A. An Introduction to Nuclear Physics,  DOI:  10.1017/CBO9781139164405

This was going to be so much longer and more detailed, but as you may or may not be aware, seven month olds occasionally decide of their own volition to pull all nighters, (much like grad students).  So, I leave you with a few somewhat less than scattered thoughts, and an incredible video on the topic of neutrinos. After yesterday's post on the possibility of the variation of radioactive decay rates with neutrino activity from the sun , I spent my free time today reading about beta decay and neutrinos.  The references I mention below are very complete, but this post won't be.  I present to you a series of notes and factoids about beta decay and the history of the neutrino, kind of a backgrounder for cocktail party level discussions of the topic if you will. Beta Decay I wanted to look into beta decay first because it's the type of radioactive decay, (as opposed to alpha or gamma), that involves neutrinos.  It seemed like the natural place to start.  Since...

We interrupt your normal coverage of magnetic monopole searches today to bring you something much more cool from well.. the same location!  I was jazzed to find out yesterday that the next monopole project I was going to write about was done at a stunningly pretty location Gran Sasso, Italy. (picture 1) Then, thanks to +Oliver Thewalt  I found out about a very interesting study done regarding a possible time dependence of the decay rates of radioactive isotopes.  So much for the pretty location I thought, but the science is incredibly interesting.  Then, while reading up on the research this morning I found out that one of the studies[2] was performed at none other than the very same lab in Gran Sasso.  And we're back to where we started and I get to include a pretty picture with the post!  OK, OK enough with the cool coincidences and the small world of science for today. So, here's what's going on in a nutshell.  Radioactive elements decay in a...

In  1961, William Fairbank and Bascomb Deaver experimentally verified that magnetic flux can be quantized.  This week I read an excellent paper on the history of the experiment[1].  For those who aren't close to a library with access to the journal, (and for my own notes), here are a few of the highlights.  For more info on the Fairbank/Deaver experiment see[4] . The Other Experiment The first interesting thing you should know is that there was a similar experiment  performed in Southern Germany by Robert Doll and Martin Näbauer in the same year, (1961)[2].  Their apparatus was different,  instead of  vibrating a superconducting cylinder to determine the value of the magnetic field at had trapped as Deaver and Fairbank did, they used a superconducting cylinder attached to a torsion pendulum (picture 1).  By measuring the amount of time it took the oscillations of the pendulum to die off they were able to determine the strength ...

OK, so let's say you're assigned the problem of determining the mean value, (the expectation value), for n, (the number state), in a harmonic oscillator with a coherent state.  You go back to your favorite coherent state reference by Nieto and Carruthers[1] and get the probability for finding your coherent oscillator in the nth level almost immediately, (picture 1), You're looking for the expectation value for n though, so you need to multiply the probabilty by n and sum the whole mess over all possible values of n, (zero to infinity).  Here's what you get, (excuse my sloppiness in picture 2).  Also, the favored notation for coherent states around here happens to be lambda instead of alpha. So, that looks like a mess. How do you make it more tractable and get down to a single value?  Enter our genius quantum mechanics professor.  He points out that if you just factorize and relabel things a bit, you wind up with (picture 3) Cool! D...

Hans Bethe on spin implied by angular momentum commutator Here's a cool thing about spin and the Dirac equation I hadn't seen until I read Hans Bethe's book "Intermediate Quantum Mechanics".  Commuting the Hamiltonian of the Dirac equation with the orbital angular momentum of a particle indicates that total angular momentum isn't conserved[2]. If you're new to, or not in quantum mechanics, the commutator determines how two quantities behave in a multiplication when the order of the multiply is reversed.  In multiplication with real numbers, A times B is the same as B times A, (the commutative property).  Quantum mechanics uses matrices and in matrix multiplication, A times B is not always the same as B times A.  The commutator, [A,B] just subtracts B times A from A times B.  If the two quantities commute the result will be zero. One last note for the non-QM inclined.  In quantum mechanics, if you take the commutator of an operator matrix with somet...

I think I'm finally hitting my studying stride for finals.  I can tell because my thoughts on quantum mechanics are starting to merge with the text from Jr.'s Little Golden Books[1], (picture 1).  Sure, sure, to some this might mean that I'm studying too much or sleeping too little, but I see it as a sign of some sort of Zen integration of my personal and quantum mechanical lives :) hehehe  Hoo Boy! I hadn't realized it on Friday, but looking back on the whiteboard where my professor kind of wowed me, his solution uses most of the basic tools we were taught this semester in an integrated form rather than as disparate facts which is how they'be been rattling around in my head.  So, in the tone of Jr.'s Sesame Street book on helping each other, here goes the solution of "Show that a time dependent force applied to a harmonic oscillator will produce a coherent state.  Here's the original white board in all it's glory (picture 2).  By th...

Quantum mechanics makes some rather astonishing predictions about how particles behave.  One of the most astonishing to me is that an electron's wave function can interact with a periodic potential, (say from the lattice sites of a crystal), and an applied force,(from a constant electric field for example), to make it behave as though its mass is vastly different, (sometimes even negative), compared to its rest mass in free space.  Semiconductor physicists make use of this property all the time.  It is also this property that Widom and Larsen[ 3 ] utilize in their theory of LENR paper.  The energy of an electron within a crystal depends on its quasi-momentum as shown in picture 1.  The quasi-momentum multiplied by the distance between crystal lattice sites is shown on the x axis and the electron's energy is shown on the y axis.  Notice that the graph includes regions of energy called gaps that the electron does not occupy.  The resgions of energy tha...

Yesterday's Physics Central Physics Buzz Blog [9] post about NASA and LENR, (low energy nuclear reactions), raised a lot of questions for me.  I haven't answered them all yet, so I don't have anything specific to offer, but I thought I'd pass along the following reference list of journal articles, interviews, and videos related to the post in case you wanted to learn more about the physics yourself and form your own thoughts on the matter.  If nothing else, there's a lot of interesting physics at play here including matter waves, Bloch oscillations, and beta decay.  At a minimum, I'll be covering the science behind the controversy soon. References: 1.  NASA video with Joseph Zawodny http://futureinnovation.larc.nasa.gov/view/articles/what/cif-safari.html http://www.youtube.com/watch?feature=player_embedded&v=42hrCRx1JJY 2.  Forbes article on NASA LENR http://www.forbes.com/sites/jeffmcmahon/2013/03/14/tiny-nuclear-reactions-inside-compact-fluores...

I'd hoped I was going to be able to make an authoritative swoop through the oft-mentioned, (here anyway), AJP article by Shubaya and Wulfman[1] wherein they explain how the accidental degeneracy in the hydrogen atom energy solutions can be visualized by looking at the accidental degeneracy in the corresponding two dimensional problem of orbits around a Coulomb potential.  Unfortunately, about half-way through, I realized I'm still not quite there.  Here's what I have so far.  I've cleared up exactly what the definition of the accidental degeneracy is.  There's a more complete grasp on the skeleton of Shubaya and Wulfman's argument here, as well as what 'projection to a +1 dimensional space' actually means. The Accidental Degeneracy  In the hydrogen atom there are two kinds of degeneracy with respect to energy.  The first kind is related to the quantum number m and is expected.  It has to do with...

Today is electricity and magnetism midterm day, so I'm just going to jot down a skeleton of a thought process about the quantum mechanical phase operator research I've been reading for the last few days, and then I have to run. In matrix rperesentation, the derivative of a polynomial can be represented as[1]: for a third degree polynomial and extended for higher degrees.  Integration looks like this[ 2 ]: and can again be extended.  In the article by Nieto [3], he quotes Louisell as saying this about the discrete cosine and sine functions in quantum mechanics. In the Fourier domain where functions are represented by series of sine and cosine functions, derivatives are constructed simply by multiplying by i, (the square root of negative one), times frequency, and integrals are constructed by dividing by i times the frequency. Also, in relation to the EE discrete signal analysis, these two figures from the Nieto RMP article [4], (pictures 4 and 5)...

While searching for journal articles on the Schwinger-Lippmann scattering rule last night, I came across the following. Maybe We Let Quaternions Go A Little Too Easily http://aapt.scitation.org/doi/abs/10.1119/1.1934944 Relation of quaternions to four dimensional rotations [2] If you're into fringe physics, McIntosh worked for RIAS who dabbled in shall we say  'gravity control' in the 1950s. RIAS Inc. of Baltimore [3] RIAS on antigrav [4] McIntosh did a significant amount of group theory work and went on to publish a  survey  of flexagons in 2003 [pdf][5].  This brings us to the really cool flexagon stuff!  First, watch the series of videos on hexaflexagons[10]! Then, go read more about them at the American Mathematical Monthly [6] and Scientific American [7].  They were invented in 1939 and while Feynman didn't come up with the idea, he was involved. from  +Scientific American   Epstein again The author tha...