Terahertz emission from lithium doped silicon under continuous wave interband optical excitation

We report on experimental observation and study of terahertz emission from lithium doped silicon crystals under continuous wave band-to-band optical excitation. It is shown that radiative transitions of electrons from 2P excited states of lithium donor to the 1S(A1) donor ground state prevail in the emission spectrum. The terahertz emission occurs due to capture of nonequilibrium electrons to charged donors, which in turn are generated in the crystal as a result of impurity assisted electron-hole recombination. Besides the intracentre radiative transitions the terahertz emission spectrum exhibits also features at about 12.7 and 15.27 meV, which could be related to intraexciton transitions and transitions from the continuum to the free exciton ground state

Spectral action for torsion with and without boundaries

We derive a commutative spectral triple and study the spectral action for a rather general geometric setting which includes the (skew-symmetric) torsion and the chiral bag conditions on the boundary. The spectral action splits into bulk and boundary parts. In the bulk, we clarify certain issues of the previous calculations, show that many terms in fact cancel out, and demonstrate that this cancellation is a result of the chiral symmetry of spectral action. On the boundary, we calculate several leading terms in the expansion of spectral action in four dimensions for vanishing chiral parameter $\theta$ of the boundary conditions, and show that $\theta=0$ is a critical point of the action in any dimension and at all orders of the expansion.Comment: 16 pages, references adde