Massive Graviton Geons

We find vacuum solutions such that massive gravitons are confined in a local spacetime region by their gravitational energy in asymptotically flat spacetimes in the context of the bigravity theory. We call such self-gravitating objects massive graviton geons. The basic equations can be reduced to the Schr\"odinger-Poisson equations with the tensor "wavefunction" in the Newtonian limit. We obtain a non-spherically symmetric solution with $j=2,\ell=0$ as well as a spherically symmetric solution with $j=0,\ell=2$ in this system where $j$ is the total angular momentum quantum number and $\ell$ is the orbital angular momentum quantum number, respectively. The energy eigenvalue of the Schr\"odinger equation in the non-spherical solution is smaller than that in the spherical solution. We then study the perturbative stability of the spherical solution and find that there is an unstable mode in the quadrupole mode perturbations which may be interpreted as the transition mode to the non-spherical solution. The results suggest that the non-spherically symmetric solution is the ground state of the massive graviton geon. The massive graviton geons may decay in time due to emissions of gravitational waves but this timescale can be quite long when the massive gravitons are non-relativistic and then the geons can be long-lived. We also argue possible prospects of the massive graviton geons: applications to the ultralight dark matter scenario, nonlinear (in)stability of the Minkowski spacetime, and a quantum transition of the spacetime.Comment: 16 pages, 7 tables, 3 figures; v2: references added, improved discussion, published versio

A supersolutions perspective on hypercontractivity

The purpose of this article is to expose an algebraic closure property of supersolutions to certain diffusion equations. This closure property quickly gives rise to a monotone quantity which generates a hypercontractivity inequality. Our abstract argument applies to a general Markov semigroup whose generator is a diffusion and satisfies a curvature condition.Comment: 7 page

Superfluidity of liquid 4He confined to one-dimensional straight nanochannel structures

Superfluidity of liquid 4He confined in one-dimensional (1D) nanometer-size channels has been studied by means of a torsional oscillator. When the channel is larger than 2.8 nm in diameter, liquid 4He becomes superfluid at low temperatures and a dissipation due to quantized vortex is observed. The superfluid onset temperature is 1.8 K at 0.14 MPa for the 4.7 nm channel and 0.89 K at 0.01 MPa for the 2.8 nm channel. For the latter, it is suppressed strongly under the application of pressure, and continuously approaches zero at around 2.1 MPa at absolute zero, which suggests a quantum phase transition between the superfluid and nonsuperfluid states in the 1D channel

尿中Nerve Growth Factorは、過活動膀胱症状を呈する患児の治療効果の予測因子になる

Objective: To assess urinary nerve growth factor (NGF) in children with overactive bladder (OAB) and to investigate the relationship between urinary NGF/creatinine (Cr) levels and OAB. Patients and methods: Thirty-five children (27 boys and 8 girls) with OAB and 11 children (6 boys and 5 girls) without OAB or any other urinary symptoms, who served as controls, were included in this study. Urinary NGF levels were measured using enzyme-linked immunosorbent assay. The total urinary NGF levels were adjusted with the concentration of urinary creatinine (NGF/Cr level). Refractory OAB was defined as little improvement in OAB symptoms despite at least 3 months of urotherapy and anticholinergic agent treatment. Urinary NGF/Cr was compared between the children with OAB and the controls. The relationship between urinary NGF/Cr and treatment outcomes was also evaluated. Results: Urinary NGF/Cr was significantly higher in the children with OAB when compared with those in the control group (0.65 ± 0.82 vs 0.11 ± 0.09, P = .0007). Improvement of OAB symptoms was observed in 26 out of 35 children (74%). The remaining 9 children showed refractory OAB symptoms (the refractory group). Urinary NGF/Cr was significantly higher in the refractory group than in the improved group (1.28 ± 1.34 vs 0.44 ± 0.39, P = .027). Conclusion: Urinary NGF/Cr was significantly higher in the children with OAB than in the controls, and was significantly higher in the refractory group than in the improved group. Urinary NGF/Cr could not only be a potential biomarker for children with OAB, but also a predictor of therapeutic efficacy in children with OAB.博士（医学）・乙第1454号・令和2年3月16日Copyright © 2017 Elsevier Inc. All rights reserved