Crepant resolutions of a Slodowy slice in a nilpotent orbit closure in slN(C)\mathfrak{sl}_N(\mathbb{C})

One of our results of this article is that every (projective) crepant resolution of a Slodowy slice in a nilpotent orbit closure in $\mathfrak{sl}_N(\mathbb{C})$ can be obtained as the restriction of some crepant resolution of the nilpotent orbit closure. We also show that there is a decomposition of the Slodowy slice into other Slodowy slices with good properties. From this decomposition, one can count the number of crepant resolutions.Comment: 22 page

Fundamental quantum limits for practical devices

We present experimentally testable quantum limitations on the phase-insensitive linear amplification and phase conjugation with respect to the transformation of a Gaussian distributed set of coherent states following the footing to assess the success of continuous-variable quantum teleportation and quantum memory devices. The results enable us to compare the real device with the quantum limited device via feasible input of coherent states.Comment: 4 pages, RevTeX

A remark on the Wiener-Ikehara Tauberian theorem

In this paper we point out that the proof of Kable's extension of the Wiener-Ikehara Tauberian theorem can be applied to the case where the Dirichlet series has a pole of order "$l / m$" without much modification (Kable proved the case $l = 1$).Comment: 9 page

Specialization orders on atom spectra of Grothendieck categories

We introduce systematic methods to construct Grothendieck categories from colored quivers and develop a theory of the specialization orders on the atom spectra of Grothendieck categories. We show that any partially ordered set is realized as the atom spectrum of some Grothendieck category, which is an analog of Hochster's result in commutative ring theory. We also show that there exists a Grothendieck category which has empty atom spectrum but has nonempty injective spectrum.Comment: 39 page