It is known that a lattice path matroid polytope can be associated with two given noncrossing lattice paths on $\mathbb{Z}\times\mathbb{Z}$ with the same end points. In this short note we give explicit formulae for the $f$-vector, toric $f$- and $g$-polynomials of a lattice path matroid polytope when two boundary paths enclose a hook shape.

Sen-Peng Eu Yuan-Hsun Lo Ya-Lun Tsai

Let $E/F$ be a quadratic extension of $p$-adic fields and $\textrm{U}_{2r+1}$ be the unitary group associated with $E/F$. We prove the following local converse theorem for $\textrm{U}_{2r+1}$: given two irreducible generic supercuspidal representations $\pi,\pi_0$ of $\textrm{U}_{2r+1}$ with the same central character, if $\gamma(s,\pi\times \tau,\psi)=\gamma(s,\pi_0\times \tau,\psi)$ for all irreducible generic representation $\tau$ of $\textrm{GL}_n(E)$ and for all $n$ with $1\le n\le r$, then $\pi\cong \pi_0$. The proof depends on analysis of the local integrals which define local gamma factors and uses certain properties of partial Bessel functions developed by Cogdell-Shahidi-Tsai recently.

Qing Zhang

In this article, we focus on the stability of dark solitons for a general one-dimensional nonlinear Schr\"odinger equation. More precisely, we prove the orbital stability of a chain of travelling waves whose speeds are well ordered, taken close to the speed of sound c s and such that the solitons are initially localized far away from each other. The proof relies on the arguments developed by F. B\'ethuel, P. Gravejat and D. Smets and first introduced by Y. Martel, F. Merle and T.-P. Tsai.

Jordan Berthoumieu

We present exact analytical and numerical results for the electronic spectra and the Friedel oscillations around a substitutional impurity atom in a graphene lattice. A chemical dopant in graphene introduces changes in the on-site potential as well as in the hopping amplitude. We employ a T-matrix formalism and find that disorder in the hopping introduces additional interference terms around the impurity that can be understood in terms of bound, semi-bound, and unbound processes for the Dirac electrons. These interference effects can be detected by scanning tunneling microscopy.

N. M. R. Peres F. D. Klironomos S. -W. Tsai J. R. Santos J. M. B. Lopes dos Santos A. H. Castro Neto

In this report, we investigate the effect of low coefficient of thermal expansion (CTE) metals on the operating speed of hafnium-based oxide capacitance. We found that the cooling process of low CTE metals during rapid thermal annealing (RTA) generates in-plane tensile stresses in the film, This facilitates an increase in the volume fraction of the o-phase and significantly improves the domain switching speed. However, no significant benefit was observed at electric fields less than 1 MV/cm. This is because at low voltage operation, the defective resistance (dead layer) within the interface prevents electron migration and the increased RC delay. Minimizing interface defects will be an important key to extending endurance and retention.

Y. -T. Tsai C. -R. Liu Y. -T. Chen S. -M. Wang Z. -K. Chen C. -S. Pai Z. -R. Haung F. -S. Chang Z. -X. Li K. -Y. Hsiang M. -H. Lee Y. -T. Tang

Two of the major obstacles to achieve quantum computing (QC) are (i) scalability to many qubits and (ii) controlled connectivity between any selected qubits. Using Josephson charge qubits, here we propose an experimentally realizable method to efficiently solve these two central problems. Since any two charge qubits can be effectively coupled by an experimentally accessible inductance, the proposed QC architecture is scalable. In addition, we formulate an efficient and realizable QC scheme that requires only one (instead of two or more) two-bit operation to implement conditional gates.

J. Q. You J. S. Tsai Franco Nori

To verify the hypothesis about the common origin of the low frequency 1/f noise and the quantum f noise recently measured in the Josephson charge qubits, we study temperature dependence of the 1/f noise and decay of coherent oscillations. T^2 dependence of the 1/f noise is experimentally demonstrated, which supports the hypothesis. We also show that dephasing in the Josephson charge qubits off the electrostatic energy degeneracy point is consistently explained by the same low frequency 1/f noise that is observed in the transport measurements.

O. Astafiev Yu. A. Pashkin Y. Nakamura T. Yamamoto J. S. Tsai

We have carried out spectroscopic measurements of a system of three strongly coupled four-junction flux qubits. The samples studied cover a wide range of parameters with the coupling energy between neighboring qubits varying between 0.75 GHz and 6.05 GHz. The observed complicated spectra agree well with eight-level theory. The experiments are relevant for the realization of a tunable coupling between qubits.

A. O. Niskanen K. Harrabi F. Yoshihara Y. Nakamura J. S. Tsai

Two different types of Cooper pair transistors, with Al and Nb islands, have been investigated in a tunable electromagnetic environment. The device with an Al island demonstrates gate charge modulation with 2e-periodicity in a wide range of environmental impedances at bath temperatures below 340 mK. Contrary to the results of the Al sample, we were not able to detect 2e-periodicity under any conditions on similar samples with Nb island. We attribute this to the material properties of Nb.

A. M. Savin M. Meschke J. P. Pekola Yu. A. Pashkin T. F. Li H. Im J. S. Tsai

We present simultaneous operation of ten single-electron turnstiles leading to one order of magnitude increase in current level up to 100 pA. Our analysis of device uniformity and background charge stability implies that the parallelization can be made without compromising the strict requirements of accuracy and current level set by quantum metrology. In addition, we discuss how offset charge instability limits the integration scale of single-electron turnstiles.

V. F. Maisi Yu. A. Pashkin S. Kafanov J. S. Tsai J. P. Pekola