Problems looking for collaborators:


In this page you will find a list of interesting problems from a broad range of topics that now or in the past I have studied but that I could not fully understand. My feeling is that additional expertise is needed so help is welcome. Some of these problems are very difficult (maybe almost imposssible). Others, I suspect, are easy or maybe are already known. In any case it is more fun if I do not give them to you organized by topic or difficulty:
  1. Correlations of the Calogero Sutherland model at finite temperature at least for the values of the coupling related to random matrix theory: Do you know how to carry out the integrals over Jack polynomials and evaluate explicitly (in the large N limit) the resulting combinatorial factor?

  2. Including confinement in the instanton liquid model: Standard (not the more general refined solutions found by Van Baal) instanton liquid model do not describe confinenement mainly because the short distance interaction is chosen more or less by hand in order to keep the stability of the ensemble. Is it possible to modify this short distance in such a way that confinement is reproduced?

  3. In recent experiments in sonoluminiscence it has been observed that in a certain range of frequencies the radiation is similar to that of a blackbody at high temperature (thousands of Kelvins). The reason for that it is not fully understood. In a recent paper I study finite size corrections to the blackbody radiation. With the appropiate modifications these results should be applicable to these experiments. I would like to talk to an experimentalist expert on that.

  4. A test quark is moving through the quark gluon plasma. Assuming that in a certain range of energies and/or masses the test quark undergoes some kind of diffusion. How important are interference effects?. Is is possible to find a region such that the mean free path is comparable to the thermal de Broglie wavelength of the quark?. Is it possible an analytical calculation using AdS-CFT techniques?.

  5. Assume you prepare experimentally a cloud of cold atoms with the lowest temperature and density possible such that to a good approximation the system is described by the Schroedinger equation. If we measure some observable and compare the results with the prediction of the Schroedinger equation, up to what precision can we test the validity of the Schroedinger equation?

  6. Assume you study experimentally superconductivity in nano grain in the line of the experiments of Tinkham and collaborators in the 90's. Is it possible to really determine the effect of the Coulomb interaction in these results?. Is there any analytical framework to include them in the BCS formalism?. Using cold atoms, is it possible to produce the BCS phase but with the unwanted additional interactions?. If so, how easy is it to modify the confining potential?

  7. Again about superconductivity but this time easier. Assume you have a clean superconducting nano grain in a constant magnetic field. An important element in order to solve the BCS gap equation in this case are the matrix elements (density-density) of the one body hamiltonian. These elements will depend on the magnetic field. The question is, for magnetic fields as weak as we wish, is it a good approximation to neglect the imaginary part of these matrix elements?

  8. Can you diagonalize the full (I mean all the eigenvalues for a given lattice size) lattice QCD Dirac operator?. An interesting project is to look at the spectral and eigenstates correlation of the Dirac operator. In the region close to the origin (E~0) it is well known that, at least for suffciently small volumes, the spectrum is correlated according to random matrix theory. The bulk of the spectrum has been studied in a few papers but there is not yet a conclusive answer. If the correlations are again random matrix in the bulk then it is possible an analytical (though somehow phenomenological) evaluation of mesonic correlation function.

  9. Spectral correlations in a disordered metal and at the metal-insualtor transition are supossed to be universal and described by random matrix theory. Is it possible to rederive these results by using just the effective conformal symmetry of the spectrum for distance much longer than the mean level spacing?.

  10. It is well known that 1d kicked rotors can be studied experimentally by using cold atoms techniques. The question is, is it possible to extend these techniques to the 2d and 3d case. If so I would be really interested to know more since I have many theoretical predictions to test.