On Distance-Regular Graphs with Smallest Eigenvalue at Least −m-m

A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer $m\geq 2$, there are only finitely many non-geometric distance-regular graphs with smallest eigenvalue at least $-m$, diameter at least three and intersection number $c_2 \geq 2$

Effective potential for composite operators and for an auxiliary scalar field in a Nambu-Jona-Lasinio model

We derive the effective potentials for composite operators in a Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in each case they are equivalent to the corresponding effective potentials based on an auxiliary scalar field. The both effective potentials could lead to the same possible spontaneous breaking and restoration of symmetries including chiral symmetry if the momentum cutoff in the loop integrals is large enough, and can be transformed to each other when the Schwinger-Dyson (SD) equation of the dynamical fermion mass from the fermion-antifermion vacuum (or thermal) condensates is used. The results also generally indicate that two effective potentials with the same single order parameter but rather different mathematical expressions can still be considered physically equivalent if the SD equation corresponding to the extreme value conditions of the two potentials have the same form.Comment: 7 pages, no figur

Nonlocal explanation of stationary and nonstationary regimes in cascaded soliton pulse compression

We study soliton pulse compression in materials with cascaded quadratic nonlinearities, and show that the group-velocity mismatch creates two different temporally nonlocal regimes. They correspond to what is known as the stationary and nonstationary regimes. The theory accurately predicts the transition to the stationary regime, where highly efficient pulse compression is possible.Comment: 3 pages, 2 figures, published verison in Optics Letters. Contains revised equations, including an updated mode

Are there nodes in LaFePO, BaFe2_2(AsP)2_2, and KFe2_2As2_2 ?

We reexamined the experimental evidences for the possible existence of the superconducting (SC) gap nodes in the three most suspected Fe-pnictide SC compounds: LaFePO, BaFe$_2$(As$_{0.67}$P$_{0.33}$)$_2$, and KFe$_2$As$_2$. We showed that while the $T$-linear temperature dependence of the penetration depth $\lambda(T)$ of these three compounds indicate extremely clean nodal gap superconductors, the thermal conductivity data $\lim_{T,H \rightarrow 0} \kappa_S (H,T)/T$ unambiguously showed that LaFePO and BaFe$_2$(As$_{0.67}$P$_{0.33}$)$_2$ are extremely dirty, while KFe$_2$As$_2$ can be clean. This apparently conflicting experimental data casts a serious doubt on the nodal gap possibility on LaFePO and BaFe$_2$(As$_{0.67}$P$_{0.33}$)$_2$.Comment: 11 pages, 5 figures A new section "4. Remark on the quantum oscillation (QO) experiments" is adde