Two-Loop Superstrings in Hyperelliptic Language III: the Four-Particle Amplitude

We compute explicitly the four-particle amplitude in superstring theories by using the hyperelliptic language and the newly obtained chiral measure of D'Hoker and Phong. Although the algebra of the intermediate steps is a little bit involved, we obtain a quite simple expression for the four-particle amplitude. As expected, the integrand is independent of all the insertion points. As an application of the obtained result, we show that the perturbative correction to the $R^4$ term in type II superstring theories is vanishing point-wise in (even) moduli space at two loops.Comment: v1, LaTex file, 33 pages; v2, 34 pages, add references and minor correction

Comments on Two-Loop Four-Particle Amplitude in Superstring Theory

It is shown that the four-particle amplitude of superstring theory at two loops obtained in [1,2] is equivalent to the previously obtained results in [3,4,5]. Here the ${\bf Z}_2$ symmetry in hyperelliptic Riemann surface plays an important role in the proof.Comment: 10 pages, Latex fil

Positive-partial-transpose distinguishability for lattice-type maximally entangled states

We study the distinguishability of a particular type of maximally entangled states -- the "lattice states" using a new approach of semidefinite program. With this, we successfully construct all sets of four ququad-ququad orthogonal maximally entangled states that are locally indistinguishable and find some curious sets of six states having interesting property of distinguishability. Also, some of the problems arose from \cite{CosentinoR14} about the PPT-distinguishability of "lattice" maximally entangled states can be answered.Comment: It's rewritten. We deleted the original section II about PPT-distinguishability of three ququad-ququad MESs. Moreover, we have joined new section V which discuss PPT-distinguishability of lattice MESs for cases $t=3$ and $t=4$ . As a result, the sequence of the theorems in our article has been changed. And we revised the title of our articl

Polyoxometalate intercalated MXene with enhanced electrochemical stability

Altres ajuts: ICN2 is funded by the CERCA programme/Generalitat de Catalunya. This work has been carried out within the framework of the doctoral program (PhD) of Material Science (Department of Physics) of Universitat Autonoma de Barcelona (UAB).MXene/polyoxometalate (POM) hybrids are useful target materials for a variety of applications. Yet, the goal of preparing simple binary hybrids by intercalation of POMs into MXene has not been achieved. We propose and demonstrate here a method to intercalate POMs (phosphotungstate, PW12) into TiCT MXene through the interaction between POM anions and pre-intercalated surfactant cations. A variety of quaternary ammonium cations have been used to expand TiCT interlayer spacing. Cetyltrimethylammonium cations (CTA) lead to an expansion of 2 nm while allowing intercalation of a considerable load (10 wt%) thanks to their tadpole-like shape and size. CTAPW12 has a layered structure compatible with TiCT. The CTA-delaminated TiCT keeps the large interlayer spacing after being coupled with PW12. The PW12 clusters are dispersed and kept isolated thanks to CTA surfactant and the confinement into TiCT layers. The redox reactions in CTA-delaminated TiCT/PW12 are diffusion-controlled, which proves the well-dispersed PW12 clusters are not adsorbed on the surface of TiCT particles but within TiCT layers. The CTA- delaminated TiCT/PW12 shows superior electrochemical stability (remaining redox active after 5000 cycles) over the other MXene/POM hybrids prepared in this work (inactive after 500 cycles). We associate this improved stability to the effective intercalation of PW12 within TiCT layers helped by the CTA cations, as opposed to the external aggregation of PW12 clusters into micro or nanocrystals taking place for the other cations. The results provide a solid guide to help develop high-performance MXene/POM hybrid materials for a variety of applications