A note on the heat kernel method applied to fermions

The spectrum of the fermionic operators depending on external fields is an important object in Quantum Field Theory. In this paper we prove, using transition to the alternative basis for the $\gamma$-matrices, that this spectrum does not depend on the sign of the fermion mass, up to a constant factor. This assumption has been extensively used, but usually without proof. As an illustration, we calculated the coincidence limit of the coefficient $a_2(x,x^\prime)$ on the general metric background, vector and axial vector fields.Comment: 5 pages, LaTeX, no figures. Revised versio

Composition-induced structural transitions in mixed rare-gas clusters

The low-energy structures of mixed Ar--Xe and Kr--Xe Lennard-Jones clusters are investigated using a newly developed parallel Monte Carlo minimization algorithm with specific exchange moves between particles or trajectories. Tests on the 13- and 19- atom clusters show a significant improvement over the conventional basin-hopping method, the average search length being reduced by more than one order of magnitude. The method is applied to the more difficult case of the 38-atom cluster, for which the homogeneous clusters have a truncated octahedral shape. It is found that alloys of dissimilar elements (Ar--Xe) favor polytetrahedral geometries over octahedra due to the reduced strain penalty. Conversely, octahedra are even more stable in Kr--Xe alloys than in Kr_38 or Xe_38, and they show a core-surface phase separation behavior. These trends are indeed also observed and further analysed on the 55-atom cluster. Finally, we correlate the relative stability of cubic structures in these clusters to the glassforming character of the bulk mixtures.Comment: 14 pages, 8 figures, 5 tables PRB vol 70, in pres

Comment on "Thermal Lifshitz force between an atom and a conductor with a small density of carriers"

We demonstrate that the generalization of the Lifshitz theory proposed by L. P. Pitaevskii arXiv:0801.0656 [Phys. Rev. Lett. v.101, 163202 (2008)] violates the Nernst heat theorem for many dielectric materials and is experimentally inconsistent.Comment: 2 pages, 1 figure; minor revisions are made in accordance with the text accepted for publication in Phys. Rev. Let