Saturday, December 18, 2010 links for Dilbert


Thursday, September 30, 2010

"Proton on a string"

In the preprint "Modified string method for finding minimum energy path" (arXiv:1009.5612), Amit Samanta and Weinan E describe a method for finding so-called minimum energy paths (MEP). These paths are the ones with most statistical weight wrt. a transition in configuration space. This could e.g. be a diffusional process, which is shown below for proton conduction in SrTiO3 (Sr, Ti, O and H depicted as green, gray, red and white spheres, respectively; the potential energy surface has been calculated using the Quantum Espresso package), see the preprint for other examples.

I have compared their presented modification of the string method to the nudged elastic band method (NEB). Both methods sample the path using a finite number of images. An initial guess for the path is optimized by gradient following. The two methods differ in how the sliding down of intermediate images from barriers is prevented. For the NEB, this is achieved by introducing virtual spring forces, keeping the images apart. For the string method, the path is iteratively re-parametrized such that the path is evenly sampled.
Both methods perform similarly well. Below are shown the potential energies for MEPs obtained using the string and NEB methods for the above proton diffusion path in SrTiO3, respectively:

The residual gradients in the initial and final configurations seem to be a little too large, therefore the NEB path shows the tendency to have minima away from these configurations. The string method, which is implemented here to fulfill Eq. 6 of the preprint at each optimization step, is more stable against this problem (in the case of the NEB, intermediate configurations at ~0.5 and ~4 Å should be relaxed separately as new boundary configurations).
What is interesting is that the new string method shows a slightly better convergence of the MEP (here optimized using Broyden's method with rank one Quasi-Newton updates):

Instead of plain re-parametrization at each step, the more sophisticated schemes outlined in the preprint might even yield better convergence. Despite the simplicity of what was implemented here, this seems to be basically as good as the NEB method.

Tuesday, September 7, 2010

Random numbers out of vacuum

In a letter to Nature Photonics Gabriel et al. have generated truly random numbers (as opposed to pseudo random numbers) by measuring continuous vacuum state quadratures (i.e. E-field noise) in a homodyne setup. Random number data sets can be downloaded from their website: They are even planning on a random number live stream you can directly feed into your Quantum Monte Carlo calculations.

Thursday, March 18, 2010

"Backfolding" of Fermi surfaces revisited

Folding the paper model up is easiest beginning from the bottom of the sketch below. Which noble metal does this Fermi surface belong to?

Saturday, January 2, 2010

|→ Quasiparticles

Quasiparticle models allow for a solution of certain many-particle problems and may also provide descriptive pictures. Examples in solid state physics are
  • composite Fermions with a mean field approximation related to the attached flux
  • effective-mass Hamiltonians, where the energetic dispersion is reproduced
  • Kohn-Sham Hamiltonians, where an effective potential is adjusted such that a given density is obtained (self-consistently)
In the case of non-interacting quasiparticles, an efficient solution of the corresponding many-particle problem is possible. Furthermore, infinite interaction strength can be considered instead (or in addition to zero interaction strength in terms of interpolation; see e.g. Seidl, Perdew, Kurth, PRL 84, 5070 (2000)). Although Kohn-Shamions are often over-interpreted as single electrons, I'd still say that they are neat quasiparticles since it's the best you can generally do with a single Slater determinant. Would be cool to have solvable, not low-dimensional models for Coulomb systems at finite interaction strength (not only for a KS Hamiltonian). Are there any?

Really awesome is/would be the emergence of a Fermi liquid from the Anti-de-Sitter/Conformal Field Theory correspondence — here, quasiparticle shape and position in the spectral function are approximately reproduced [Cubrovic, Zaanen, Schalm, arXiv:0904.1993, Science 325, 439 (2009)] (in the AdS/CFT correspondence itself, the product of string coupling and number of D-branes is kept fixed — quasi2 ...). [For composite Fermions ↔ gravity, have a look at Bak, Rey, arXiv:0912.0939.]