arXiv subjects

Ryo Takahashi

Publications and source records attributed to Ryo Takahashi.

At least 127 records · Page 7Linked to original sources

arXiv2017

Spinless hourglass nodal-line semimetals

Nodal-line semimetals, one of the topological semimetals, have degeneracy along nodal lines where the band gap is closed. In many cases, the nodal lines appear accidentally, and in such cases it is impossible to determine whether the nodal lines appear or not, only from the crystal symmetry and the electron filling. In this paper, for spinless systems, we show that in specific space groups at $4N+2$ fillings ($8N+4$ fillings including the spin degree of freedom), presence of the nodal lines is required regardless of the details of the systems. Here, the spinless systems refer to crystals where the spin-orbit coupling is negligible and the spin degree of freedom can be omitted because of the SU(2) spin degeneracy. In this case the shape of the band structure around these nodal lines is like an hourglass, and we call this a spinless hourglass nodal-line semimetal. We construct a model Hamiltonian as an example and we show that it is always in the spinless hourglass nodal-line semimetal phase even when the model parameters are changed without changing the symmetries of the system. We also establish a list of all the centrosymmetric space groups, under which spinless systems always have hourglass nodal lines, and illustrate where the nodal lines are located. We propose that Al$_3$FeSi$_2$, whose space-group symmetry is Pbcn (No. 60), is one of the nodal-line semimetals arising from this mechanism.

cond-mat.mtrl-sci↗

arXiv2017

FOREST Unbiased Galactic plane Imaging survey with the Nobeyama 45-m telescope (FUGIN) I: Project Overview and Initial Results

The FOREST Unbiased Galactic plane Imaging survey with the Nobeyama 45-m telescope (FUGIN) project is one of the legacy projects using the new multi-beam FOREST receiver installed on the Nobeyama 45-m telescope. This project aims to investigate the distribution, kinematics, and physical properties of both diffuse and dense molecular gas in the Galaxy at once by observing 12CO, 13CO, and C18O J=1-0 lines simultaneously. The mapping regions are a part of the 1st quadrant (10d < l < 50d, |b| < 1d) and the 3rd quadrant (198d < l <236d, |b| < 1d) of the Galaxy, where spiral arms, bar structure, and the molecular gas ring are included. This survey achieves the highest angular resolution to date (~20") for the Galactic plane survey in the CO J=1-0 lines, which makes it possible to find dense clumps located farther away than the previous surveys. FUGIN will provide us with an invaluable dataset for investigating the physics of the galactic interstellar medium (ISM), particularly the evolution of interstellar gas covering galactic scale structures to the internal structures of giant molecular clouds, such as small filament/clump/core. We present an overview of the FUGIN project, observation plan, and initial results, which reveal wide-field and detailed structures of molecular clouds, such as entangled filaments that have not been obvious in previous surveys, and large-scale kinematics of molecular gas such as spiral arms.

astro-ph.GA↗

arXiv2017

Thick tensor ideals of right bounded derived categories

Let $R$ be a commutative noetherian ring. Denote by $D^-(R)$ the derived category of cochain complexes $X$ of finitely generated $R$-modules with $H^i(X)=0$ for $i\gg0$. Then $D^-(R)$ has the structure of a tensor triangulated category with tensor product $-\otimes_R^L-$ and unit object $R$. In this paper, we study thick tensor ideals of $D^-(R)$, i.e., thick subcategories closed under the tensor action by each object in $D^-(R)$, and investigate the Balmer spectrum $Spc\,D^-(R)$ of $D^-(R)$, i.e., the set of prime thick tensor ideals of $D^-(R)$. First, we give a complete classification of the thick tensor ideals of $D^-(R)$ generated by bounded complexes, establishing a generalized version of the Hopkins-Neeman smash nilpotence theorem. Then, we define a pair of maps between the Balmer spectrum $Spc\,D^-(R)$ and the Zariski spectrum $Spec\,R$, and study their topological properties. After that, we compare several classes of thick tensor ideals of $D^-(R)$, relating them to specialization-closed subsets of $Spec\,R$ and Thomason subsets of $Spc\,D^-(R)$, and construct a counterexample to a conjecture of Balmer. Finally, we explore thick tensor ideals of $D^-(R)$ in the case where $R$ is a discrete valuation ring.

math.AC↗

arXiv2017

Structure of irreducible homomorphisms to/from free modules

The primary goal of this paper is to investigate the structure of irreducible monomorphisms to and irreducible epimorphisms from finitely generated free modules over a noetherian local ring. Then we show that over such a ring, self-vanishing of Ext and Tor for a finitely generated module admitting such an irreducible homomorphism forces the ring to be regular.

math.AC↗

arXiv2017

On radial two-species Onsager vortices near the critical temperature

We compare two mean field equations describing hydrodynamic turbulence in equilibrium, which are derived under a deterministic vs.\ stochastic assumption on the variable vortex intensity distribution. Mathematically, such equations correspond to non-local Liouville type problems, and the critical temperature corresponds to the optimal Moser-Trudinger constant. We consider the radial case and we assume that the inverse temperature is near its critical value. Under these assumptions we show that, unlike previously existing results, the qualitative properties of the solution set in the deterministic case is more similar to the single vortex intensity case than the stochastic case. Some new variational interpretations of the value explicit values of the critical temperature are also provided.

math.AP↗

arXiv2017

Associated Primes and Syzygies of Linked Modules

Motivated by the notion of geometrically linked ideals, we show that over a Gorenstein local ring $R$, if a Cohen-Macaulay $R$-module $M$ of grade $g$ is linked to an $R$-module $N$ by a Gorenstein ideal $c$, such that $Ass_R(M)\cap Ass_R(N)=\emptyset$, then $M\otimes_RN$ is isomorphic to direct sum of copies of $R/a$, where $a$ is a Gorenstein ideal of $R$ of grade $g+1$. We give a criterion for the depth of a local ring $(R,m,k)$ in terms of the homological dimensions of the modules linked to the syzygies of the residue field $k$. As a result we characterize a local ring $(R,m,k)$ in terms of the homological dimensions of the modules linked to the syzygies of $k$.

math.AC↗

arXiv2017

Fabrication and magnetic control of Y3Fe5O12 cantilevers

We have fabricated ferrite cantilevers in which their vibrational properties can be controlled by external magnetic fields. Submicron-scale cantilever structures were made from Y3Fe5O12 (YIG) films by physical etching combined with use of a focused ion beam milling technique. We found that the cantilevers exhibit two resonance modes which correspond to horizontal and vertical vibrations. Under external magnetic fields, the resonance frequency of the horizontal mode increases, while that of the vertical mode decreases, quantitatively consistent with our numerical simulation for magnetic forces. The changes in resonance frequencies with magnetic fields reach a few percent, showing that efficient magnetic control of resonance frequencies was achieved.

cond-mat.mes-hall↗

arXiv2017

On the vanishing of self extensions over Cohen-Macaulay local rings

The celebrated Auslander-Reiten Conjecture, on the vanishing of self extensions of a module, is one of the long-standing conjectures in ring theory. Although it is still open, there are several results in the literature that establish the conjecture over Gorenstein rings under certain conditions. The purpose of this article is to obtain extensions of such results over Cohen-Macaulay local rings that admit canonical modules. In particular, our main result recovers theorems of Araya, and Ono and Yoshino simultaneously.

math.AC↗

arXiv2016

Gorenstein modifications and $\mathbb{Q}$-Gorenstein rings

Let $R$ be a Cohen--Macaulay normal domain with a canonical module $ω_R$. It is proved that if $R$ admits a noncommutative crepant resolution (NCCR), then necessarily it is $\mathbb{Q}$-Gorenstein. Writing $S$ for a Zariski local canonical cover of $R$, then a tight relationship between the existence of noncommutative (crepant) resolutions on $R$ and $S$ is given. A weaker notion of Gorenstein modification is developed, and a similar tight relationship is given. There are three applications: non-Gorenstein quotient singularities by connected reductive groups cannot admit an NCCR, the centre of any NCCR is log-terminal, and the Auslander--Esnault classification of two-dimensional CM-finite algebras can be deduced from Buchweitz--Greuel--Schreyer.

math.RT↗

arXiv2016

On the ideal case of a conjecture of Auslander and Reiten

A celebrated conjecture of Auslander and Reiten claims that a finitely generated module $M$ that has no extensions with $M\oplus Λ$ over an Artin algebra $Λ$ must be projective. This conjecture is widely open in general, even for modules over commutative Noetherian local rings. Over such rings, we prove that a large class of ideals satisfy the extension condition proposed in the aforementioned conjecture of Auslander and Reiten. Along the way we obtain a new characterization of regularity in terms of the injective dimensions of certain ideals.

math.AC↗

arXiv2016

Noncommutative resolutions using syzygies

Given a noether algebra with a noncommutative resolution, a general construction of new noncommutative resolutions is given. As an application, it is proved that any finite length module over a regular local or polynomial ring gives rise, via suitable syzygies, to a noncommutative resolution.

math.RT↗

arXiv2016

Renormalization Group Improved Higgs Inflation with a Running Kinetic Term

We study a Higgs inflation model with a running kinetic term, taking account of the renormalization group evolution of relevant coupling constants. Specifically we study two types of the running kinetic Higgs inflation, where the inflaton potential is given by the quadratic or linear term potential in a frame where the Higgs field is canonically normalized. We solve the renormalization group equations at two-loop level and calculate the scalar spectral index and the tensor-to-scalar ratio. We find that, even if the renormalization group effects are included, the quadratic inflation is ruled out by the CMB observations, while the linear one is still allowed.

hep-ph↗

arXiv2016

Singularity categories and singular equivalences for resolving subcategories

Let $\X$ be a resolving subcategory of an abelian category. In this paper we investigate the singularity category $\ds(\underline\X)=\db(\mod\underline\X)/\kb(\proj(\mod\underline\X))$ of the stable category $\underline\X$ of $\X$. We consider when the singularity category is triangle equivalent to the stable category of Gorenstein projective objects, and when the stable categories of two resolving subcategories have triangle equivalent singularity categories. Applying this to the module category of a Gorenstein ring, we characterize simple hypersurface singularities of type $(\a_1)$ as complete intersections over which the stable categories of resolving subcategories have trivial singularity categories. We also generalize several results of Yoshino on totally reflexive modules.

math.AC↗

arXiv2016

Perfect linkage of Cohen--Macaulay modules over Cohen--Macaulay rings

In this paper, we introduce and study the notion of linkage by perfect modules, which we call perfect linkage, for Cohen-Macaulay modules over Cohen--Macaulay local rings. We explore perfect linkage in connection with syzygies, maximal Cohen-Macaulay approximations and Yoshino-Isogawa linkage. We recover a theorem of Yoshino and Isogawa, and analyze the structure of double perfect linkage. Moreover, we establish a criterion for two Cohen-Macaulay modules of codimension one to be perfectly linked, and apply it to the classical linkage theory for ideals. We also construct various examples of linkage of modules and ideals.

math.AC↗

arXiv2016

Ulrich ideals and almost Gorenstein rings

The structure of the complex $\operatorname{\mathbf{R}Hom}_R(R/I,R)$ is explored for an Ulrich ideal $I$ in a Cohen-Macaulay local ring $R$. As a consequence, it is proved that in a one-dimensional almost Gorenstein but non-Gorenstein local ring, the only possible Ulrich ideal is the maximal ideal. It is also studied when Ulrich ideals have the same minimal number of generators.

math.AC↗

arXiv2016

When are n-syzygy modules n-torsionfree?

Let R be a commutative noetherian ring. We consider the question of when n-syzygy modules over R are n-torsionfree in the sense of Auslander and Bridger. Our tools include Serre's condition and certain conditions on the local Gorenstein property of R. Our main result implies the converse of a celebrated theorem of Evans and Griffith.

math.AC↗

arXiv2016

Gauge coupling unification in a classically scale invariant model

There are a lot of works within a class of classically scale invariant model, which is motivated by solving the gauge hierarchy problem. In this context, the Higgs mass vanishes at the UV scale due to the classically scale invariance, and is generated via the Coleman-Weinberg mechanism. Since the mass generation should occur not so far from the electroweak scale, we extend the standard model only around the TeV scale. We construct a model which can achieve the gauge coupling unification at the UV scale. In the same way, the model can realize the vacuum stability, smallness of active neutrino masses, baryon asymmetry of the universe, and dark matter relic abundance. The model predicts the existence vector-like fermions charged under $SU(3)_C$ with masses lower than $1\,{\rm TeV}$, and the SM singlet Majorana dark matter with mass lower than $2.6\,{\rm TeV}$.

hep-ph↗

arXiv2015

A model realizing inverse seesaw and resonant leptogenesis

We construct a model realizing the inverse seesaw mechanism. The model has two types of gauge singlet fermions in addition to right-handed neutrinos. A required Majorana mass scale (keV scale) for generating the light active neutrino mass in the conventional inverse seesaw can be naturally explained by a "seesaw" mechanism between the two singlet fermions in our model. We find that our model can decrease the magnitude of hierarchy among the mass parameters by $\mathcal{O}(10^4)$ from that in the conventional inverse seesaw model. We also show that a successful resonant leptogenesis occurs for generating the baryon asymmetry of the universe in our model. The desired mass degeneracy for the resonant leptogenesis can also be achieved by the "seesaw" between the two singlet fermions.

hep-ph↗