arXiv subjects

Kentaro Nakamura

Publications and source records attributed to Kentaro Nakamura.

33 records · Page 2Linked to original sources

arXiv2019

Remarks on Kato's Euler systems for elliptic curves with additive reduction

Extending the former work for the good reduction case, we provide a numerical criterion to verify a large portion of the "Iwasawa main conjecture without $p$-adic $L$-functions" for elliptic curves with additive reduction at an odd prime $p$ over the cyclotomic $\mathbb{Z}_p$-extension. We also deduce the corresponding $p$-part of the Birch and Swinnerton-Dyer formula for elliptic curves of rank zero from the same numerical criterion. We give explicit examples at the end and specify our choice of Kato's Euler system in the appendix.

math.NT↗

arXiv2018

Fiber-optic cascaded forward Brillouin scattering seeded by backward stimulated Brillouin scattering: conceptual proposal and experimental validation

We propose a method for generating cascaded forward Brillouin scattering (CFBS), based on a counter-propagated pump-probe technique, utilizing backward stimulated Brillouin scattering as its seed. The CFBS, induced by forward stimulated Brillouin scattering (FSBS), is generated via the energy transfer from the probe light to other acoustic resonance frequencies. Experimental results for the CFBS generated in a 390-m-long highly nonlinear fiber indicate that it has a high signal-to-noise ratio (SNR) and that the center frequencies of its acoustic resonance peaks agree with theoretical values. The sensing properties of the generated CFBS were also verified.

physics.optics↗

arXiv2016

Local epsilon-isomorphisms for rank two p-adic representations of Gal(overline{Q}_p/Q_p) and a functional equation of Kato's Euler system

In this article, we prove (many parts of) the rank two case of the Kato's local epsilon-conjecture using the Colmez's p-adic local Langlands correspondence for GL_2(Q_p). We show that a Colmez's pairing defined in his study of locally algebraic vectors gives us the conjectural epsilon-isomorphisms for (almost) all the families of p-adic representations of Gal(overline{Q}_p/Q_p) of rank two, which satisfy the desired interpolation property for the de Rham and trianguline case. For the de Rham and non trianguline case, we also show this interpolation property for the "critical" range of Hodge-Tate weights using the Emerton's theorem on the compatibility of classical and p-adic local Langlands correspondence. As an application, we prove that the Kato's Euler system associated to any Hecke eigen new form satisfies a functional equation which has the same form as predicted by the Kato's global epsilon-conjecture.

math.NT↗

arXiv2015

High-speed optical correlation-domain reflectometry without using acousto-optic modulator

To achieve a distributed reflectivity measurement along an optical fiber, we develop a simplified cost-effective configuration of optical correlation- (or coherence-) domain reflectometry based on a synthesized optical coherence function by sinusoidal modulation. By excluding conventional optical heterodyne detection (practically, without using an acousto-optic modulator) and by exploiting the foot of the Fresnel reflection spectrum, the electrical bandwidth required for signal processing is lowered down to several megahertz. We evaluate the basic system performance and demonstrate its high-speed operation (10 ms for one scan) by tracking a moving reflection point in real time.

physics.optics↗

arXiv2015

A generalization of Kato's local epsilon-conjecture for (phi,Gamma)-modules over the Robba ring

The aim of this article is to generalize Kato's (commutative) p-adic local epsilon-conjecture [Ka93b] for families of (phi,Gamma)-modules over the Robba ring. In particular, we prove the generalized local epsilon-conjecture for rank one (phi,Gamma)-modules, which is a generalization of Kato's theorem [Ka93b] for rank one Galois representations. The key ingredients are the recent results of Kedlaya-Pottharst-Xiao [KPX12] on the finiteness of cohomology of (phi,Gamma)-modules and the theory of Bloch-Kato's exponential map for (phi,Gamma)-modules developed in [Na13].

math.NT↗

arXiv2014

Alternative implementation of simplified Brillouin optical correlation-domain reflectometry

We developed an alternative configuration of simplified Brillouin optical correlation-domain reflectometry, which can overcome the drawbacks of the original configuration. This system uses, as reference light, the light that is Fresnel reflected at a partial reflection point artificially produced near an optical circulator. We show that the influence of the 0th correlation peak fixed at the partial reflection point can be suppressed by replacing the nearby fibers with other fibers having different Brillouin frequency shift values (here, multi-mode fibers are used). Finally, we demonstrate a distributed measurement for detecting a 1.46-m-long strained section with a high signal-to-noise ratio.

physics.optics↗

arXiv2014

Brillouin scattering in multi-core optical fibers

We measure the Brillouin gain spectra in two cores (the central core and one of the outer cores) of a ~3-m-long, silica-based, 7-core multi-core fiber (MCF) with incident light of 1550 nm wavelength, and investigate the Brillouin frequency shift (BFS) and its dependence on strain and temperature. The BFSs of both the cores are ~10.92 GHz, and the strain- and temperature-dependence coefficients of the BFS in the central core are 484.8 MHz/% and 1.08 MHz/K, respectively, whereas those in the outer core are 516.9 MHz/% and 1.03 MHz/K. All of these values are not largely different from those in a silica single-mode fiber, which is expected because the cores are composed of the same material (silica). The difference in the BFS dependence of strain between the two cores may originate from the difference in structural deformation when strain is applied to the fiber, which is a unique characteristic to MCFs. The future prospect on distributed strain and temperature sensing based on Brillouin scattering in MCFs is finally presented.

physics.optics↗

arXiv2014

Fiber-Optic Interferometry Using Narrowband Light Source and Electrical Spectrum Analyzer: Influence on Brillouin Measurement

We observe an interference pattern using a simple fiber-optic interferometer consisting of an electrical spectrum analyzer and a narrowband light source, which is commonly employed for observing the Brillouin gain spectrum. This interference pattern expands well beyond the frequency range corresponding to the Brillouin frequency shift in silica fibers (approximately 11 GHz at 1550 nm). Using both silica single-mode and polymer optical sensing fibers, we then experimentally prove that the distinctive noise in a self-heterodyne-based Brillouin measurement with an unoptimized polarization state originates from the interference between the reference light and the Fresnel-reflected light. This noise can be almost completely suppressed by employing a delay line that is longer than the coherence length of the light source and by artificially applying a high loss near the open end of the sensing fiber.

physics.optics↗

arXiv2014

Simplified configuration of Brillouin optical correlation-domain reflectometry

We develop a simple and cost-efficient configuration of Brillouin optical correlation-domain reflectometry (BOCDR), the setup of which does not include an additional reference path used in standard BOCDR systems. The Fresnel-reflected light from an open end of a sensing fiber is used as reference light. The limitations of spatial resolution, measurement range, and their ratio are theoretically clarified, and then a distributed strain measurement with a < 100-mm spatial resolution and a 4.1-m measurement range is demonstrated with a high signal-to-noise ratio.

physics.optics↗

arXiv2013

Deformations of trianguline B-pairs and Zariski density of two dimensional crystalline representations

The aim of this article is to study deformation theory of trianguline B-pairs for any p-adic field. For benign B-pairs, a special good class of trianguline B-pairs, we prove a main theorem concerning tangent spaces of these deformation spaces. These are generalizations of Bellaiche-Chenevier's and Chenevier's works in the Q_p case, where they used (ϕ,Γ)-modules over the Robba ring instead of using B-pairs. As an application of this theory, in the final chapter, we prove a theorem concerning Zariski density of two dimensional crystalline representations for any p-adic field, which is a generalization of Colmez and Kisin's results in the Q_p case.

math.NT↗

arXiv2013

Zariski density of crystalline representations for any p-adic field

The aim of this article is to prove Zariski density of crystalline representations in the rigid analytic space associated to the universal deformation ring of a d-dimensional mod p representation of Gal(\bar{K}/K) for any d and for any p-adic field K. This is a generalization of the results of Colmez, Kisin (d=2, K=Q_p), of the author (d=2, any K), of Chenevier (any d, K=Q_p). A key ingredient for the proof is to construct a p-adic family of trianguline representations. In this article, we construct (an approximation of) this family by generalizing Kisin's theory of finite slope subspace X_{fs} for any d and for any K.

math.NT↗

arXiv2013

Polymer optical fiber fuse

Although high-transmission-capacity optical fibers are in demand, the problem of the fiber fuse phenomenon needs to be resolved to prevent the destruction of fibers. As polymer optical fibers become more prevalent, clarifying their fuse properties has become important. Here, we experimentally demonstrate a fuse propagation velocity of 21.9 mm/s, which is 1 to 2 orders of magnitude slower than that in standard silica fibers. The achieved threshold power density and proportionality constant between the propagation velocity and the power density are respectively 1/186 of and 16.8 times the values for silica fibers. An oscillatory continuous curve instead of periodic voids is formed after the passage of the fuse. An easy fuse termination method is presented herein, along with its potential plasma applications.

physics.optics↗

arXiv2012

Iwasawa theory of de Rham (ϕ,Γ)-modules over the Robba rings

The aim of this article is to study Bloch-Kato's exponential map and Perrin-Riou's "big" exponential map purely in terms of (ϕ,Γ)-modules over the Robba ring. We first generalize the definition of Bloch-Kato's exponential map for all the (ϕ,Γ)-modules without using Fontaine's rings B_{cris}, B_{dR} of p-adic periods and then we generalize the construction of Perrin-Riou's "big" exponential map for all the de Rham (ϕ,Γ)-modules and prove that this map interpolates our Bloch-Kato's exponential map and the dual exponential map. Finally, we prove a theorem concerning to the determinant of our "big" exponential map, which is a generalization of Perrin-Riou's δ(V)-conjecture. The key ingredients for our study are Pottharst's theory of analytic Iwasawa cohomology and Berger's construction of p-adic differential equations associated to de Rham (ϕ,Γ)-modules.

math.NT↗

arXiv2010

Deformations of trianguline B-pairs

The aim of this article is to study deformation theory of trianguline B-pairs for any p-adic field. For benign B-pairs, a special good class of trianguline B-pairs, we prove a main theorem concerning tangent spaces of these deformation spaces. These are generalizations of Bellaiche-Chenevier's and Chenevier's works in the case of K=Q_p, where they used (phi,Gamma)-modules over Robba ring instead of using B-pairs. The main theorem, the author hopes, will play crucial roles in some problems of Zariski density of modular points or of crystalline points in deformation spaces of global or local p-adic Galois representations.

math.NT↗

arXiv2008

Classification of two dimensional split trianguline representations of $p$-adic fields

The aim of this paper is to classify two dimensional split trianguline representations of $p$-adic fields. This is a generalization of a result of Colmez who classified two dimensional split trianguline representations of $\mathrm{Gal}(\bar{\mathbb{Q}}_p/\mathbb{Q}_p)$ by using $(ϕ,Γ)$-modules over Robba ring. In this paper, we classify two dimensional split trianguline representations of $\mathrm{Gal}(\bar{K}/K)$ for general $p$-adic field $K$ by using $B$-pairs defined by Berger.

math.NT↗