Finite temperature properties of the Dirac operator with bag boundary   conditions
  We study the finite temperature free energy and fermion number for Dirac fields in a one-dimensional spatial segment, under local boundary conditions compatible with the presence of a spectral asymmetry. We discuss in detail the contribution of this part of the spectrum to the determinant. We evaluate the finite temperature properties of the theory for arbitrary values of the chemical potential. 
C.G. Beneventano and E.M. Santangelo