Variations on theorems of Mertens
We present variations on theorems of Mertens as special cases of Density Hypothesis. Moreover, we study a Serre's estimate concerning Lang-Weil estimate.
math.NT↗
arXiv subjects
Hidekazu Tanaka
Publications and source records attributed to Hidekazu Tanaka.
Field-orientation dependence of quantum phase transitions in the S=1/2 triangular-lattice antiferromagnet Ba$_3$CoSb$_2$O$_9$
Ba$_3$CoSb$_2$O$_9$ approximates the two-dimensional spin-1/2 triangular-lattice Heisenberg antiferromagnet. This compound displays magnetic-field-induced quantum phase transitions, including the 1/3-magnetization-plateau, but its magnetization processes for the magnetic field $H$ parallel and perpendicular to the $c$ axis are different due to the weak easy-plane anisotropy and the weak interlayer antiferromagnetic exchange interaction. To elucidate how the quantum phase transitions change between these two field directions, we measured the field-angle dependence of the magnetization process in Ba$_3$CoSb$_2$O$_9$ using pulsed high magnetic fields. We compared obtained magnetic field-field angle phase diagram with those obtained by the large-size cluster mean-field method combined with a scaling scheme and the semiclassical theory. We also found a narrow 1/3-magnetization plateau and a high-field transition with a small magnetization jump for $H\,{\parallel}\,c$, not observed in the previous studies.
cond-mat.str-el↗
Impacts of viscous dissipation on collisional growth and fragmentation of dust aggregates
Understanding the collisional behavior of dust aggregates consisting of submicron-sized grains is essential to unveiling how planetesimals formed in protoplanetary disks. It is known that the collisional behavior of individual dust particles strongly depends on the strength of viscous dissipation force; however, impacts of viscous dissipation on the collisional behavior of dust aggregates have not been studied in detail, especially for the cases of oblique collisions. Here we investigated the impacts of viscous dissipation on the collisional behavior of dust aggregates. We performed numerical simulations of collisions between two equal-mass dust aggregates with various collision velocities and impact parameters. We also changed the strength of viscous dissipation force systematically. We found that the threshold collision velocity for the fragmentation of dust aggregates barely depends on the strength of viscous dissipation force when we consider oblique collisions. In contrast, the size distribution of fragments changes significantly when the viscous dissipation force is considered. We obtained the empirical fitting formulae for the size distribution of fragments for the case of strong dissipation, which would be useful to study the evolution of size and spatial distributions of dust aggregates in protoplanetary disks.
astro-ph.EP↗
Structures of magnetic excitations in the spin-1/2 kagome-lattice antiferromagnets Cs$_2$Cu$_3$SnF$_{12}$ and Rb$_2$Cu$_3$SnF$_{12}$
We show the structures of magnetic excitations in spin-1/2 kagome-lattice antiferromagnets Cs$_2$Cu$_3$SnF$_{12}$ and Rb$_2$Cu$_3$SnF$_{12}$ investigated by inelastic neutron scattering in wide energy and momentum ranges. For Cs$_2$Cu$_3$SnF$_{12}$, four single-magnon excitation modes were observed. Low-energy three modes are assigned to be transverse modes and the high-energy fourth mode is suggested to be an amplitude mode. It was found that the broad excitation continuum without a marked structure spreads in a wide energy range from $0.15J$ to approximately $2.5J$ in contrast to the clearly structured excitation continuum observed in the spin-1/2 triangular-lattice Heisenberg antiferromagnet. These findings strongly suggest spinon excitations as elementary excitations in Cs$_2$Cu$_3$SnF$_{12}$. In Rb$_2$Cu$_3$SnF$_{12}$, singlet-triplet excitations from the pinwheel VBS state and their ghost modes caused by the enlargement of the chemical unit cell were clearly confirmed. It was found that the excitation continuum is structured in the low-energy region approximately below $J_{\mathrm{avg}}$ and the almost structureless high-energy excitation continuum extends to approximately $2.6J_{\mathrm{avg}}$. The characteristics of the high-energy excitation continuum are common to both Cs$_2$Cu$_3$SnF$_{12}$ and Rb$_2$Cu$_3$SnF$_{12}$, irrespective of their ground states. The experimental results strongly suggest that the spin liquid component remains in the ground state as quantum fluctuations in Cs$_2$Cu$_3$SnF$_{12}$ and Rb$_2$Cu$_3$SnF$_{12}$.
cond-mat.str-el↗
Contrasting Magnetic Structures in SrLaCuSbO$_{6}$ and SrLaCuNbO$_{6}$: Spin-1/2 Quasi-Square-Lattice $J_1 {-} J_2$ Heisenberg Antiferromagnets
We report the magnetic properties of the double perovskites SrLaCuSbO$_6$ (SLCSO) and SrLaCuNbO$_6$ (SLCNO). The temperature dependence of the magnetic susceptibilities of both compounds shows a broad maximum characteristic of an $S\,=\,1/2$ square lattice Heisenberg antiferromagnet. Magnetic ordering occurs at $T_{\rm N}\,{=}\,13.6$ and 15.7 K for SLCSO and SLCNO, respectively. Neutron powder diffraction measurements reveal contrasting spin structures in both compounds. The spin structures of SLCSO and SLCNO below $T_{\rm N}$ are Néel antiferromagnetic and collinear antiferromagnetic, respectively. This result demonstrates that the nearest-neighbor interaction is dominant in SLCSO, whereas the next-nearest-neighbor interaction is dominant in SLCNO. The magnitude of the ordered moment was evaluated at 3.5 K to be $m\,{=}\,0.39(3)\,μ_{\rm B}$ for SLCSO and $0.37(1)\,μ_{\rm B}$ for SLCNO, which are significantly smaller than those calculated using linear spin wave theory. We infer that the small ordered moment is caused by the effect of exchange bond randomness arising from the site disorder of Sr and La ions.
cond-mat.str-el↗
Can stellar-mass black hole growth disrupt disks of active galactic nuclei? The role of mechanical feedback
Stellar-mass BHs (sBHs) are predicted to be embedded in active galactic nuclei (AGN) disks due to gravitational drag and in-situ star formation. However, we find that due to a high gas density in an AGN disk environment, compact objects may rapidly grow to intermediate-mass BHs and deplete matter from the AGN disk unless accretion is suppressed by some feedback process(es). These consequences are inconsistent with AGN observations and the dynamics of the Galactic center. Here we consider mechanical feedback mechanisms for the reduction of gas accretion. Rapidly accreting sBHs launch winds and/or jets via the Blandford-Znajek mechanism, which produce high-pressure shocks and cocoons. Such a shock and cocoon can spread laterally in the plane of the disk, eject the outer regions of a circum-sBH disk (CsBD) and puncture a hole in the AGN disk with horizontal size comparable to the disk scale-height. Since the depletion timescale of the bound CsBD is much shorter than the resupply timescale of gas to the sBH, the time-averaged accretion rate onto sBHs is reduced by this process by a factor of $\sim 10$--$100$. This feedback mechanism can therefore help alleviate the sBH over-growth and AGN-disk depletion problems. On the other hand, we find that cocoons of jets can unbind a large fraction of the gas accreting in the disks of less massive SMBHs, which may help explain the dearth of high-Eddington ratio AGNs with SMBH mass $\lesssim10^5{\rm M_\odot}$.
astro-ph.HE↗
Magnons and Spinons in $\mathrm{Ba}_2\mathrm{CoTeO}_6 $: A Composite System of Isolated Spin-$1/2$ Triangular Heisenberg-like and Frustrated Honeycomb Ising-like Antiferromagnets
We report the neutron scattering results on magnetic orderings and excitations in $\mathrm{Ba}_2\mathrm{CoTeO}_6$ composed of two almost isolated subsystems A and B, which are described as an $S\,{=}\,1/2$ triangular Heisenberg-like antiferromagnet and a frustrated honeycomb Ising-like antiferromagnet, respectively. Stripy ordering of subsystem B was confirmed below $T_{\rm N1}\,{=}\,12.0$ K, whereas sharp streaks were observed along $(1/3, 1/3, L)$ and $(2/3, 2/3, L)$ at 0.3 K (${\ll}\,T_{\rm N2}\,{=}\,3.0$ K). This indicates the two-dimensional nature of ordering in subsystem A. It was found that the excitation spectra of both subsystems are well separated and independent of each other. The excitation spectrum of subsystem A is composed of two single-magnon branches with roton-like minima at the M point and a clearly structured intense continuum, as similarly observed in $\mathrm{Ba}_3\mathrm{CoSb}_2\mathrm{O}_9$, which is strongly indicative of spinon excitations. Dispersion curves for subsystem B can be described by linear spin wave theory within the third-neighbor exchange interaction.
cond-mat.str-el↗
Eccentric gap induced by a super-Jupiter mass planet
A giant planet embedded in a protoplanetary disk opens a gap by tidal interaction, and properties of the gap strongly depend on the planetary mass and disk parameters. Many numerical simulations of this process have been conducted, but detailed simulations and analysis of gap formation by a super-Jupiter mass planet have not been thoroughly conducted. We performed two-dimensional numerical hydrodynamic simulations of the gap formation process by a super-Jupiter mass planet and examined the eccentricity of the gap. When the planet is massive, the radial motion of gas is excited, causing the eccentricity of the gap's outer edge to increase. Our simulations showed that the critical planetary mass for the eccentric gap was $\sim3~M_{\rm J}$ in a disk with $α=4.0\times10^{-3}$ and $h/r=0.05$, a finding that was consistent with that reported in a previous work. The critical planetary mass for the eccentric gap depends on the viscosity and the disk scale height. We found that the critical mass could be described by considering a dimensionless parameter related to the gap depth. The onset of gap eccentricity enhanced the surface density inside the gap, shallowing the gap more than the empirical relation derived in previous studies for a planet heavier than the critical mass. Therefore, our results suggest that the mass accretion rate, which strongly depends on the gas surface density in the gap is also enhanced for super-Jupiter mass planets. These results may substantially impact the formation and evolution processes of super-Jupiter mass planets and population synthesis calculations.
astro-ph.EP↗
Rapid formation of Gas Giant Planets via Collisional Coagulation from Dust Grains to Planetary Cores
Gas-giant planets, such as Jupiter, Saturn and massive exoplanets, were formed via the gas accretion onto the solid cores each with a mass of roughly ten Earth masses. However, rapid radial migration due to disk-planet interaction prevents the formation of such massive cores via planetesimal accretion. Comparably rapid core growth via pebble accretion requires very massive protoplanetary disks because most pebbles fall into the central star. Although planetesimal formation, planetary migration, and gas-giant core formation have been studied with much effort, the full evolution path from dust to planets are still uncertain. Here we report the result of full simulations for collisional evolution from dust to planets in a whole disk. Dust growth with realistic porosity allows the formation of icy planetesimals in the inner disk (> 10 au), while pebbles formed in the outer disk drift to the inner disk and there grow to planetesimals. The growth of those pebbles to planetesimals suppresses their radial drift and supplies small planetesimals sustainably in the vicinity of cores. This enables rapid formation of sufficiently massive planetary cores within 0.2-0.4 million years, prior to the planetary migration. Our models shows first gas giants form at 2-7 au in rather common protoplanetary disks, in agreement with the exoplanet and solar systems.
astro-ph.EP↗
Dust rings as a footprint of planet formation in a protoplanetary disk
Relatively large dust grains (referred to as pebbles) accumulate at the outer edge of the gap induced by a planet in a protoplanetary disk, and a ring structure with a high dust-to-gas ratio can be formed. Such a ring has been thought to be located right outside of the planet orbit. We examined the evolution of the dust ring formed by a migrating planet, by performing two-fluid (gas and dust) hydrodynamic simulations. We found that the initial dust ring does not follow the migrating planet and remains at the initial location of the planet in the cases with a low viscosity of $α\sim 10^{-4}$. The initial ring is gradually deformed by viscous diffusion, and a new ring is formed in the vicinity of the migrating planet, which developes from the trap of the dust grains leaking from the initial ring. During this phase, two rings co-exist outside the planet orbit. This phase can continue over $\sim 1$~Myr for a planet migrating from 100~au. After the initial ring disappears, only the later ring remains. This change in the ring morphology can provide clues as to when and where the planet was formed, and is the footprint of the planet. We also carried out simulations with a mass-growing planet. These simulations show more complex asymmetric structures in the dust rings. The observed asymmetric structures in the protoplanetary disks may be related to a migrating and mass-growing planet.
astro-ph.EP↗
Continuous control of classical-quantum crossover by external high pressure in the coupled chain compound CsCuCl$_3$
In solid materials, the parameters relevant to quantum effects, such as the spin quantum number, are basically determined and fixed at the chemical synthesis, which makes it challenging to control the amount of quantum correlations. We propose and demonstrate a method for active control of the classical-quantum crossover in magnetic insulators by applying external pressure. As a concrete example, we perform high-field, high-pressure measurements on CsCuCl$_3$, which has the structure of weakly-coupled spin chains. The magnetization process experiences a continuous evolution from the semi-classical realm to the highly-quantum regime with increasing pressure. Based on the idea of "squashing" the spin chains onto a plane, we characterize the change in the quantum correlations by the change in the value of the local spin quantum number of an effective two-dimensional model. This opens a way to access the tunable classical-quantum crossover of two-dimensional spin systems by using alternative systems of coupled-chain compounds.
cond-mat.str-el↗
Infinite products of absolute zeta functions
We study some infinite products of absolute zeta functions. Especially, we consider the convergence and the rationality of them.
math.NT↗
First ESR Detection of Higgs Amplitude Mode and Analysis with Extended Spin-Wave Theory in Dimer System KCuCl$_3$
KCuCl$_3$ is known to show a quantum phase transition from the disordered to antiferromagnetically ordered phases by applying pressure. There is a longitudinal excitation mode (Higgs amplitude mode) in the vicinity of the quantum critical point in the ordered phase. To detect the Higgs amplitude mode, high-pressure ESR measurements are performed in KCuCl$_3$. The experimental data are analyzed by the extended spin-wave theory on the basis of the vector spin chirality. We report the first ESR detection of the Higgs amplitude mode and the important role of the electric dipole described by the vector spin chirality.
cond-mat.str-el↗
Electrostatic potential measurement at the Pt/TiO$_2$ interface using electron holography
The interface of Pt/TiO$_2$ plays an essential role in device engineering and chemical reactions. Here, we report the electrostatic potential distribution of a Pt/TiO$_2$ interface by electron holography. The decrease of the electrostatic potential exists at TiO$_2$ in the vicinity of the interface, indicating the presence of negative charge due to electron transfer from TiO$_2$ and Pt. The decrease of the electrostatic potential can be understood in the difference in work functions between Pt and TiO$_2$. This study reveals the interplay between Pt and TiO$_2$ and the usefulness of electron holography for probing the potential in nanoscale interfaces.
cond-mat.mtrl-sci↗
Collisional Growth and Fragmentation of Dust Aggregates with Low Mass Ratios. I: Critical Collision Velocity for Water Ice
We investigated fundamental processes of collisional sticking and fragmentation of dust aggregates by carrying out N-body simulations of submicron-sized icy dust monomers. We examined the condition for collisional growth of two colliding dust aggregates in a wide range of the mass ratio, 1-64. We found that the mass transfer from a larger dust aggregate to a smaller one is a dominant process in collisions with a mass ratio of 2-30 and impact velocity of \approx 30-170 m s^-1. As a result, the critical velocity, v_fra, for fragmentation of the largest body is considerably reduced for such unequal-mass collisions; v_fra of collisions with a mass ratio of 3 is about half of that obtained from equal-mass collisions. The impact velocity is generally higher for collisions between dust aggregates with higher mass ratios because of the difference between the radial drift velocities in the typical condition of protoplanetary disks. Therefore, the reduced v_fra for unequal-mass collisions would delay growth of dust grains in the inner region of protoplanetary disks.
astro-ph.EP↗
Spin injection into vanadium dioxide films from a typical ferromagnetic metal, across the metal-insulator transition of the vanadium dioxide films
A vanadium dioxide VO2 film shows metal-insulator transition (MIT) induced by changing environmental temperature. We report the temperature dependence of electromotive force properties generated in VO2/Ni80Fe20 bilayer junctions under the ferromagnetic resonance (FMR) of the Ni80Fe20 layer. An electromotive force generated in a VO2/Ni80Fe20 bilayer junction under the FMR showed a small change across the MIT temperature of the VO2 film, while the VO2 film resistance drastically changed. This behavior was not only explained with the temperature dependence of the electromotive force property generated in the Ni80Fe20 film itself under the FMR, but also with the generated electromotive forces due to the inverse spin-Hall effect (ISHE) in the VO2 film under the FMR of the Ni80Fe20 film. That is, we successfully demonstrated the spin injection from a Ni80Fe20 film into a VO2 film across the MIT temperature of the VO2 film.
cond-mat.mtrl-sci↗
Ring formation by coagulation of dust aggregates in early phase of disk evolution around a protostar
Ring structures are observed by (sub-)millimeter dust continuum emission in various circumstellar disks from early stages of Class 0 and I to late stage of Class II young stellar objects (YSOs). In this paper, we study one of the possible scenarios of such ring formation in early stage, which is coagulation of dust aggregates. The dust grains grow in an inside-out manner because the growth timescale is roughly proportional to the orbital period. The boundary of the dust evolution can be regarded as the growth front, where the growth time is comparable to the disk age. With radiative transfer calculations based on the dust coagulation model, we find that the growth front can be observed as a ring structure because dust surface density is sharply changed at this position. Furthermore, we confirm that the observed ring positions in the YSOs with an age of $\lesssim1$ Myr are consistent with the growth front. The growth front could be important to create the ring structure in particular for early stage of the disk evolution such as Class 0 and I sources.
astro-ph.EP↗
Coupled spin-1/2 antiferromagnetic chain Cs$_2$LiRuCl$_6$ with partially disordered crystal lattice
We determined the crystal structure of Cs$_2$LiRuCl$_6$, which was synthesized first in this work, and investigated its magnetic properties. Cs$_2$LiRuCl$_6$ has a hexagonal structure composed of linear chains of face-sharing RuCl$_6$ and LiCl$_6$ octahedra. In two-thirds of the structural chains, Ru$^{3+}$ and Li$^+$ sites are almost ordered, while in the other chains their sites are disordered. This situation is analogous to the ground state of the antiferromagnetic Ising model on a triangular lattice. Using electron paramagnetic resonance, we evaluated the $g$ factors of Ru$^{3+}$ with effective spin-1/2 as $g_c\,{=}\,2.72$ and $g_{ab}\,{=}\,1.50$ for magnetic fields $H$ parallel and perpendicular to the $c$ axis, respectively. Magnetization curves for $H\,{\parallel}\,c$ and $H\,{\perp}\,c$ are highly anisotropic. However, these magnetization curves approximately coincide when normalized by the $g$ factors. It was found from the magnetization and specific heat results that Cs$_2$LiRuCl$_6$ can be described as a coupled one-dimensional $S\,{=}\,1/2$ Heisenberg-like antiferromagnet with $J/k_{\rm B}\,{\simeq}\,3.7$ K. Three-dimensional ordering occurs at $T_{\rm N}\,{=}\,0.48$ K. A magnetic phase diagram for $H\,{\parallel}\,c$ is also presented.
cond-mat.str-el↗