Gate-voltage dependence of Kondo effect in a triangular quantum dot

We study the conductance through a triangular triple quantum dot, which are connected to two noninteracting leads, using the numerical renormalization group (NRG). It is found that the system shows a variety of Kondo effects depending on the filling of the triangle. The SU(4) Kondo effect occurs at half-filling, and a sharp conductance dip due to a phase lapse appears in the gate-voltage dependence. Furthermore, when four electrons occupy the three sites on average, a local S=1 moment, which is caused by the Nagaoka mechanism, is induced along the triangle. The temperature dependence of the entropy and spin susceptibility of the triangle shows that this moment is screened by the conduction electrons via two separate stages at different temperatures. The two-terminal and four-terminal conductances show a clear difference at the gate voltages, where the SU(4) or the S=1 Kondo effects occurring.Comment: 4 pages, 4 figs: typos just below (4) are corrected, results are not affecte

Strong Lefschetz elements of the coinvariant rings of finite Coxeter groups

For the coinvariant rings of finite Coxeter groups of types other than H$_4$, we show that a homogeneous element of degree one is a strong Lefschetz element if and only if it is not fixed by any reflections. We also give the necessary and sufficient condition for strong Lefschetz elements in the invariant subrings of the coinvariant rings of Weyl groups.Comment: 18 page

Chlorine Isotopes: As a Possible Tracer of Fluid/Bio-Activities on Mars and a Progress Report on Chlorine Isotope Analysis by TIMs

Significantly large mass fractionations between chlorine isotopes (Cl-35, Cl-37) have been reported for terrestrial materials including both geological samples and laboratory materials. Also, the chlorine isotopic composition can be used as a tracer for early solar system processes. Moreover, chlorine is ubiquitous on the Martian surface. Typical chlorine abundances in Gusev soils are approx.0.5 %. The global surface average chlorine abundance also is approx.0.5 %. Striking variations among outcrop rocks at Meridiani were reported with some chlorine abundances as high as approx.2%. Characterizing conditions under which chlorine isotopic fractionation may occur is clearly of interest to planetary science. Thus, we have initiated development of a chlorine isotopic analysis technique using TIMS at NASA-JSC. We present here a progress report on the current status of development at JSC and discuss the possible application of chlorine isotopic analysis to Martian meteorites in a search for fluid- and possibly biological activity on Mars

A bijective proof of a factorization formula for Macdonald polynomials at roots of unity

We give a combinatorial proof of the factorization formula of modified Macdonald polynomials $\widetilde{H}_{\lambda} (X;q,t)$ when $t$ is specialized at a primitive root of unity. Our proof is restricted to the special case where $\lambda$ is a two columns partition. We mainly use the combinatorial interpretation of Haiman, Haglund and Loehr giving the expansion of $\widetilde{H}_{\lambda} (X;q,t)$ on the monomial basis