arXiv subjects
Publications and source records attributed to M. Gaudin.
We study a set of static solutions of the Einstein equations in presence of a massless scalar field and establish their connection to the Kantowski-Sachs cosmological solutions based on some kind of duality transformations. The physical properties of the limiting case of an empty hyperbolic spacetime (pseudo-Schwarzschild geometry) are analyzed in some detail.
In the context of the fractional quantum Hall effect, we investigate Laughlin's celebrated ansatz for the groud state wave function at fractional filling of the lowest Landau level. Interpreting its normalization in terms of a one component plasma, we find the effect of an additional quadrupolar field on the free energy, and derive estimates for the thermodynamically equivalent spherical plasma. In a second part, we present various methods for expanding the wave function in terms of Slater determinants, and obtain sum rules for the coefficients. We also address the apparently simpler question of counting the number of such Slater states using the theory of integral polytopes.
We consider the $ su(n) $ spin chains with long range interactions and the spin generalization of the Calogero-Sutherland models. We show that their properties derive from a transfer matrix obeying the Yang-Baxter equation. We obtain the expression of the conserved quantities and we diagonalize them.