Recent content by sam_bell

vanhees71 (or should I say Dr. vanhees71), That's a nice set of lecture notes. To clarify: I think I can follow along that a conserved current exists when the action is taken as invariant. In that sense I'm not confused about the formal statement of Noether's theorem. What I have trouble...

Hi, I keep running my brain in circles while trying to get a solid grip on Noether's theorem. (In Peskin and Schroeder they present this as a one-liner.) But I'm having trouble seeing the equivalence between "equations of motion are invariant" and "action is invariant (up to boundary term)"...

I suppose you're right. I see it claimed that the resistance is exactly zero (or close enough that it would exceed the lifetime of the universe to see current decay). It might be difficult to get that out of an entropic argument about occupancies, which might be made in other contexts as well...

Hi just completed a chapter on Superconductivity in a solid-state physics book. I have a few remaining questions. I don't expect they can be easily answered, but I appreciate if someone happens to know. Most of the questions regard how the equations have been motivated. I guess that's kind of...

That was enlightening Davey. One correction, I didn't follow this statement: I believe you need to sum over \mathbf{R} before the theorem is satisfied. VortexLattice, if you forgo choosing a Bravais lattice + basis desc. you will also forgo the opportunity to chose solutions that satisfy...

No, sorry, I would like to understand why the form given the attraction makes sense. It's beginning to make more sense to me. Would it be fair to say .. The interaction U_kk' for k < kFermi is not operative because of the filled Fermi sea, and not for |Ek-Ek'| >> hωD because no phonons are...

Hi All, I am trying to understand why Cooper pairs form. The textbook proof that I am reading (Grosso & Parravicini) starts out as follows: Imagine a 'passive' electron gas filled out to some Fermi sphere kF. Add two 'extra' electrons that interact via a potential U(x-x'). Transform to...

I made some progress. I borrowed a result from the Gambler's Ruin problem: For the finite segment {0,...,n} the probability of being absorbed to x = n starting from x = 1 is 1/n. Knowing this, I can consider the state of the random walk on a circle by how many unique points have been discovered...

Homework Statement Consider a random walk on a circle of N points, labeled {0,1,...,N-1}. Let the initial state be X = 0 and define T to be the first time all points have been visited at least once. Show that the distribution of X[T] (i.e. last unique position visited) is uniform over...

There might be an assumption that the aperture is small compared to the image space (x0,y0). Considering this is a far-field approximation, that tends to make sense.

Hi, I am calculating surface energies for different kinds of defects in a bulk solid (e.g. twins, anti-phase boundaries, etc.) Let's say I get something like (just making this up) 1.0 meV/Angstrom^2. How would I calculate the temperature at which an appreciable number of said defect would be...

I figured it out

Homework Statement Show that because a pure rotational displacement field u(r) has no effect, that the energy of a crystal only depends on the symmetric strain tensor epsilon_ij. Homework Equations As in Ashcroft & Mermin (22.72), the energy of a crystal as a function of displacement field...

I'm reviving an old post here, but I recently started thinking about liberal arts colleges. There is a higher priority there on teaching, good working hours, lower pressure on research, potentially bright students, and good locations. Is this a good possibility for hire if you don't have strong...

Appreciate the help twofish. Thanks, Sam Bell