Some new expressions are found, concerning the one-loop effective action of four dimensional massive and massless Dirac fermions in the presence of general uniform electric and magnetic fields, with ~ E · ~ H 6= 0 and ~ E2 6= ~ H2. The rate of pairproduction is computed and briefly discussed. Non-renormalizable effective field theories turn out to be quite useful in the description of physics b...

Fermi surfaces are basic objects in solid state physics and in the spectral theory of periodic operators. We define several measures connected to Fermi surfaces and study their measure theoretic properties. From this we get absence of singular continuous spectrum and of singular continuous components in the density of states for symmetric periodic elliptic differential operators acting on vecto...

Fermi surfaces are basic objects in solid state physics and in the spectral theory of periodic operators. We deene several measures connected to Fermi surfaces and study their measure theoretic properties. From this we get absence of singular continuous spectrum and of singular continuous components in the density of states for symmetric periodic elliptic diierential operators acting on vector ...

Rational Chebyshev approximations are given for the complete Fermi-Dirac integrals of orders — \, \ and f. Maximal relative errors vary with the function and interval considered, but generally range down to 10~9 or less.

We announce a proof of an asymptotic formula for the ground{state energy of a large atom. The early work of Thomas{Fermi, Hartree{Fock, Dirac and Scott predicted

The effect of charge-carrier screening on the transport properties of a neutral graphene sheet is studied by directly probing its electronic structure. We find that the Fermi velocity, Dirac point velocity, and overall distortion of the Dirac cone are renormalized due to the screening of the electron-electron interaction in an unusual way. We also observe an increase of the electron mean free p...

The Dirac spin liquid was proposed to be the ground state of the spin-1/2 kagomé antiferromagnets. In a magnetic field B, we show that the state with Fermi pocket is unstable to the Landau level (LL) state. The LL state breaks the spin rotation around the axis of the magnetic field. We find that the LL state has an in-plane 120 degrees q=0 magnetization M which scales with the external field M ...

It is proposed that the presence of a tilted and anisotropic Dirac cone can be verified using the interlayer magnetoresistance in the layered Dirac fermion system, which is realized in quasi-two-dimensional organic compound α-(BEDT-TTF)2 I3. Theoretical formula for the interlayer magnetoresistance is derived using the analytic Landau level wave functions and assuming local tunneling of electron...

We consider the best entropic estimation to a unknown density x, given some of its algebraic or trigonometric moments. A uniform convergence theorem is established in this paper for such problems using Fermi-Dirac type entropic objectives .