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Global dynamics below excited solitons for the nonlinear Schrödinger equation with a potentialApr 24 2015Feb 10 2016Consider the nonlinear Schr\"odinger equation (NLS) with a potential with a single negative eigenvalue. It has solitons with negative small energy, which are asymptotically stable, and, if the nonlinearity is focusing, then also solitons with positive ... More

On the boundary Strichartz estimates for wave and Schrödinger equationsMay 03 2018We consider the $L_t^2L_x^r$ estimates for the solutions to the wave and Schr\"odinger equations in high dimensions. For the homogeneous estimates, we show $L_t^2L_x^\infty$ estimates fail at the critical regularity in high dimensions by using stable ... More

Global dynamics above the first excited energy for the nonlinear Schrödinger equation with a potentialMar 08 2016Consider the focusing nonlinear Schr\"odinger equation with a potential with a single negative eigenvalue. It has solitons with negative small energy, which are asymptotically stable, and solitons with positive large energy, which are unstable. We classify ... More

Global dynamics above the ground state energy for the cubic NLS equation in 3DJul 22 2010Mar 04 2011We extend our previous result on the nonlinear Klein-Gordon equation to the nonlinear Schrodinger equation with the focusing cubic nonlinearity in three dimensions, for radial data of energy at most slightly above that of the ground state. We prove that ... More

The Zakharov system in 4D radial energy space below the ground stateOct 13 2018We prove dynamical dichotomy into scattering and blow-up (in a weak sense) for all radial solutions of the Zakharov system in the energy space of four spatial dimensions that have less energy than the ground state, which is written using the Aubin-Talenti ... More

Randomized final-data problem for Systems of Nonlinear Schrödinger Equations and the Gross-Pitaevskii EquationMay 15 2018We consider the final-data problem for systems of nonlinear Schr\"odinger equations with $L^2$ subcritical nonlinearity. An asymptotically free solution is uniquely obtained for almost every randomized asymptotic profile in $L^2(\mathbb{R}^d)$, extending ... More

Failure of scattering to solitary waves for long-range nonlinear Schrödinger equationsJun 05 2019We consider nonlinear Schr\"odinger equations with either power-type or Hartree nonlinearity in the presence of an external potential. We show that for long-range nonlinearities, solutions cannot exhibit scattering to solitary waves or more general localized ... More

Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumptionOct 31 2010We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy at most slightly above that of the ground state.

Global dynamics above the ground state energy for the focusing nonlinear Klein-Gordon equationMay 26 2010Jul 04 2010We study the focusing, cubic, nonlinear Klein-Gordon equation in 3D with large radial data in the energy space. This equation admits a unique positive stationary solution, called the ground state. In 1975, Payne and Sattinger showed that solutions with ... More

Invariant manifolds around soliton manifolds for the nonlinear Klein-Gordon equationFeb 28 2011We construct center-stable and center-unstable manifolds, as well as stable and unstable manifolds, for the nonlinear Klein-Gordon equation with a focusing energy sub-critical nonlinearity, associated with a family of solitary waves which is generated ... More

Small energy scattering for the Zakharov system with radial symmetryMar 18 2012Jan 23 2013We prove small energy scattering for the 3D Zakharov system with radial symmetry. The main ingredients are normal form reduction and the radial-improved Strichartz estimates.

Global dynamics above the ground state for the energy-critical Schrodinger equation with radial dataOct 15 2015Consider the focusing energy critical Schrodinger equation in three space dimensions with radial initial data in the energy space. We describe the global dynamics of all the solutions of which the energy is at most slightly larger than that of the ground ... More

Non-ideal behavior of intramolecular structure factor of dilute polymers in a theta solventSep 11 2009We study the configurational properties of single polymers in a theta solvent by Monte Carlo simulation of the bond fluctuation model. The intramolecular structure factor at the theta point is found to be distinctively different from that of the ideal ... More

Global dynamics away from the ground state for the energy-critical nonlinear wave equationOct 19 2010We study global behavior of radial solutions for the nonlinear wave equation with the focusing energy critical nonlinearity in three and five space dimensions. Assuming that the solution has energy at most slightly more than the ground states and gets ... More

Sharp global regularity for the 2+1-dimensional equivariant Faddeev modelJul 17 2013The aim of this article is to prove that for the 2+1-dimensional equivariant Faddeev model, which is a quasilinear generalization of the corresponding nonlinear sigma model, small initial data in critical Besov spaces evolve into global solutions which ... More

Global dynamics above the ground state energy for the one-dimensional NLKG equationNov 08 2010In this paper we obtain a global characterization of the dynamics of even solutions to the one-dimensional nonlinear Klein-Gordon (NLKG) equation on the line with focusing nonlinearity |u|^{p-1}u, p>5, provided their energy exceeds that of the ground ... More

Center-stable manifold of the ground state in the energy space for the critical wave equationMar 11 2013We construct a center-stable manifold of the ground state solitons in the energy space for the critical wave equation without imposing any symmetry, as the dynamical threshold between scattering and blow-up, and also as a collection of solutions which ... More

Trudinger-Moser inequality on the whole plane with the exact growth conditionOct 08 2011Trudinger-Moser inequality is a substitute to the (forbidden) critical Sobolev embedding, namely the case where the scaling corresponds to $L^\infty$. It is well known that the original form of the inequality with the sharp exponent (proved by Moser) ... More

Scattering for the 3D Gross-Pitaevskii equationNov 24 2016Jan 10 2017We study the Cauchy problem for the 3D Gross-Pitaevskii equation. The global well-posedness in the natural energy space was proved by G\'erard \cite{Gerard}. In this paper we prove scattering for small data in the same space with some additional angular ... More

Small energy scattering for the Klein-Gordon-Zakharov system with radial symmetryAug 08 2012We prove small energy scattering for the 3D Klein-Gordon-Zakharov system with radial symmetry. The idea of proof is the same as the Zakharov system studied in \cite{GN}, namely to combine the normal form reduction and the radial-improved Strichartz estimates ... More

Global dynamics of the nonradial energy-critical wave equation above the ground state energyDec 23 2011Mar 04 2013In this paper we establish the existence of certain classes of solutions to the energy critical nonlinear wave equation in dimensions 3 and 5 assuming that the energy exceeds the ground state energy only by a small amount. No radial assumption is made. ... More

Scattering for the 3D Gross-Pitaevskii equationNov 24 2016We study the Cauchy problem for the 3D Gross-Pitaevskii equation. The global well-posedness in the natural energy space was proved by G\'erard \cite{Gerard}. In this paper we prove scattering for small data in the same space with some additional angular ... More

Threshold phenomenon for the quintic wave equation in three dimensionsSep 03 2012Sep 05 2012For the critical focusing wave equation $\Box u = u^5$ on $\R^{3+1}$ in the radial case, we establish the role of the "center stable" manifold $\Sigma$ constructed in \cite{KS} near the ground state $(W,0)$ as a threshold between type I blowup and scattering ... More

Exponential Energy Decay for Damped Klein-Gordon Equation with Nonlinearities of Arbitrary GrowthJan 01 2010We derive a uniform exponential decay of the total energy for the nonlinear Klein-Gordon equation with a damping around spatial infinity in the whole space or in the exterior of a star shaped obstacle.

Scattering threshold for the focusing nonlinear Klein-Gordon equationJan 10 2010Jun 14 2010We show scattering versus blow-up dichotomy below the ground state energy for the focusing nonlinear Klein-Gordon equation, in the spirit of Kenig-Merle for the $H^1$ critical wave and Schr\"odinger equations. Our result includes the $H^1$ critical case, ... More

Errata: Scattering threshold for the focusing nonlinear Klein-Gordon equationJun 20 2015This article resolves some errors in the paper "Scattering threshold for the focusing nonlinear Klein-Gordon equation", Analysis & PDE 4 (2011) no. 3, 405-460. The errors are in the energy-critical cases in two and higher dimensions.

Global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial caseApr 12 2013We consider the global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case; and obtain the dichotomy between scattering and finite time blow up.

Global dynamics below the ground state energy for the Zakharov system in the 3D radial caseJun 12 2012We consider the global dynamics below the ground state energy for the Zakharov system in the 3D radial case. We obtain dichotomy between the scattering and the growup.

Asymptotic Stability and Completeness in the Energy Space for Nonlinear Schrödinger Equations with Small Solitary WavesAug 06 2003In this paper we study a class of nonlinear Schr\"odinger equations which admit families of small solitary wave solutions. We consider solutions which are small in the energy space $H^1$, and decompose them into solitary wave and dispersive wave components. ... More

Threshold solutions in the case of mass-shift for the critical Kline-Gordon equationOct 08 2011We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove that the solutions ... More

Tropicalization method in cluster algebrasOct 25 2011Mar 17 2012This is a brief survey on the recently developing tropicalization method in cluster algebras and its applications to the periodicities of Y-systems and the associated dilogarithm identities.

Dilogarithm identities for conformal field theories and cluster algebras: simply laced caseSep 30 2009Nov 15 2010The dilogarithm identities for the central charges of conformal field theories of simply laced type were conjectured by Bazhanov, Kirillov, and Reshetikhin. Their functional generalizations were conjectured by Gliozzi and Tateo. They have been partly ... More

Fusion, mass, and representation theory of the Yangian algebraMay 31 1994May 13 2014Based on the formulation of Drinfel'd, Chari, and Pressley, a technique to analyze the structure of tensor products of the Yangian algebra representations is presented. We then apply the results to the $S$-matrix theory of the $G\otimes G$-invariant nonlinear ... More

Quantum generalized cluster algebras and quantum dilogarithms of higher degreesOct 02 2014Jul 21 2015We extend the notion of the quantization of the coefficients of the ordinary cluster algebras to the generalized cluster algebras by Chekhov and Shapiro. In parallel to the ordinary case, it is tightly integrated with certain generalizations of the ordinary ... More

Regularization and conformal transformations of the power spectrum in general single field inflationJun 11 2015The regularization of the CMB power spectrum is an important issue of cosmology. Most approaches assume that there is no need to regularize the power spectrum, while Parker advocated the new regularization approach for the power spectrum in 2007: the ... More

Lame operators with projective octahedral and icosahedral monodromiesNov 08 2004Nov 18 2004We show that there exists a Lame operator $L_n$ with projective octahedral monodromy for each $n\in{1/2}(\mathbf{N}+{1/2})\cup{1/3}(\mathbf{N}+{1/2}) $, and with projective icosahedral monodromy for each $n\in{1/3}(\mathbf{N}+{1/2})\cup{1/5}(\mathbf{N}+{1/2}) ... More

Spectra of Linearized Operators for NLS Solitary WavesNov 15 2006Nonlinear Schr\"odinger (NLS) equations with focusing power nonlinearities have solitary wave solutions. The spectra of the linearized operators around these solitary waves are intimately connected to stability properties of the solitary waves, and to ... More

Global well-posedness and scattering for Skyrme wave mapsJun 28 2011We study equivariant maps corresponding to the classical Skyrme model and the Adkins-Nappi model, for which we prove global existence and scattering in critical Sobolev-Besov spaces.

Non-uniqueness for an energy-critical heat equation on $\mathbb{R}^2$Mar 15 2019We construct a singular solution of a stationary nonlinear Schr\"{o}dinger equation on $\mathbb{R}^2$ with square-exponential nonlinearity having linear behavior around zero. In view of Trudinger-Moser inequality, this type of nonlinearity has an energy-critical ... More

Radio broadband visualization of global three-dimensional magneto-hydrodynamical simulations of spiral galaxies I. Faraday rotation at 8GHzNov 07 2018Observational study of galactic magnetic fields is hampered by the fact that the observables only probe various projections of the magnetic fields. Comparison with numerical simulations is helpful to understand the real structures, and observational visualization ... More

Generalized Strichartz estimates and scattering for 3D Zakharov systemMay 14 2013We obtain scattering for the 3D Zakharov system with non-radial small data in the energy space with angular regularity of degree one. The main ingredient is a generalized Strichartz estimate for the Schr\"odinger equation in the space of $L^2$ angular ... More

Codimension one threshold manifold for the critical gKdV equationFeb 16 2015We construct the 'threshold manifold' near the soliton for the mass critical gKdV equation, completing results obtained in arXiv:1204.4625 and arXiv:1204.4624. In a neighborhood of the soliton, this C1 manifold of codimension one separates solutions blowing ... More

Finite-time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric DynamicsOct 27 2012In an earlier work we have shown the global (for all initial data and all time) well-posedness of strong solutions to the three-dimensional viscous primitive equations of large scale oceanic and atmospheric dynamics. In this paper we show that for certain ... More

Well-posedness and scattering for the Zakharov system in four dimensionsApr 05 2015The Cauchy problem for the Zakharov system in four dimensions is considered. Some new well-posedness results are obtained. For small initial data, global well-posedness and scattering results are proved, including the case of initial data in the energy ... More

Small solutions of nonlinear Schrödinger equations near first excited statesAug 20 2010Consider a nonlinear Schr\"odinger equation in $R^3$ whose linear part has three or more eigenvalues satisfying some resonance conditions. Solutions which are initially small in $H^1 \cap L^1(R^3)$ and inside a neighborhood of the first excited state ... More

Energy scattering for 2D critical wave equationJun 19 2008We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schr\"odinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on the value of ... More

Sharp threshold nonlinearity for maximizing the Trudinger-Moser inequalitiesFeb 03 2019We study existence of maximizer for the Trudinger-Moser inequality with general nonlinearity of the critical growth on $R^2$, as well as on the disk. We derive a very sharp threshold nonlinearity between the existence and the non-existence in each case, ... More

Complex distribution and velocity field of molecular gas in NGC 1316 as revealed by Morita Array of ALMAMay 27 2019We present the results of $^{12}$CO($J$=1-0) mosaicing observations of the cD galaxy NGC 1316 at kpc-resolution performed with the Morita Array of the Atacama Large Millimeter/submillimeter Array (ALMA). We reveal the detailed distribution of the molecular ... More

Bethe Equation at q=0, Moebius Inversion Formula, and Weight Multiplicities: II. X_n caseAug 06 2000Jan 16 2001We study a family of power series characterized by a system of recursion relations (Q-system) with a certain convergence property. We show that the coefficients of the series are expressed by the numbers which formally count the off-diagonal solutions ... More

Thermopower of a Quantum Dot in a Coherent RegionNov 20 2006Thermoelectric power due to coherent electron transmission through a quantum dot is theoretically studied. In addition to the known features related to resonant peaks, we show that a novel significant structure appears between the peaks. This structure ... More

Fluid dynamics and jamming in a dilatant fluidOct 25 2010We present a phenomenological fluid dynamics model for a dilatant fluid, i.e. a severe shear thickening fluid, by introducing a state variable. The Navier-Stokes equation is coupled with the state variable field, which evolves in response to the local ... More

Notes on Unfair Papers by Mebarki et al. on ``Quantum Nonsymmetric Gravity''Dec 06 1999It is pointed out that the essential parts of some recent papers by Mebarki {\it et al.} (hep-th/9911045, hep-th/9911046, hep-th/9911048, hep-th/9911049, dated 6 Nov.1999) are taken from a book written by Nakanishi and Ojima, published in 1990.

Rolling Tachyon with Electromagnetic Field in Linear Dilaton BackgroundDec 13 2003Apr 08 2004Rolling tachyon in linear dilaton background is examined by using an effective field theory with gauge field on an unstable D-brane in bosonic string theory. Several solutions are identified with tachyon matter equipped with constant electromagnetic field ... More

Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network DynamicsJun 03 2016Control of nonlinear large-scale dynamical networks, e.g., collective behavior of agents interacting via a scale-free connection topology, is a central problem in many scientific and engineering fields. For the linear version of this problem, the so-called ... More

Origin of a bottom-heavy stellar initial mass function in elliptical galaxiesNov 07 2013We investigate the origin of a bottom-heavy stellar initial mass function (IMF) recently observed in elliptical galaxies by using chemical evolution models with a non-universal IMF. We adopt the Kroupa IMF with the three slopes (alpha_1, alpha_2, and ... More

Formation of massive globular clusters with heavy element abundance spread in the Galactic building blocksDec 16 2011A growing number of recent observations have revealed that the Galactic globular cluster (GC) omega Cen is not the only GC that shows abundance spread in heavy elements (e.g., Fe). In order to understand the origin of the Galactic GCs with heavy element ... More

Merging between a Central Massive Black Hole and a Compact Stellar System: A Clue to the Origin of M31'S NucleusDec 16 2000The central bulge of M31 is observed to have two distinct brightness peaks with the separation of $\sim$ 2 pc. Tremaine (1995) recently proposed a new idea that the M31's nucleus is actually a single thick eccentric disk surrounding the central super-massive ... More

Gas fueling and nuclear disk formation in merging between a central black hole and a gas clumpDec 14 2000We numerically investigate dynamical evolution of a merger between a central massive black hole (MBH) and a gas clump with the mass of $10^6$ $-$ $10^7$ $M_{\odot}$ in the central tens pc of a galactic bulge. We found that strong tidal gravitational field ... More

Formation of emission line dots and extremely metal-deficient dwarfs from almost dark galaxiesSep 14 2015Recent observations have discovered a number of extremely gas-rich very faint dwarf galaxies possibly embedded in low-mass dark matter halos. We investigate star formation histories of these gas-rich dwarf ("almost dark") galaxies both for isolated and ... More

Simulating galaxy evolution with a non-universal stellar initial mass functionSep 16 2013We consider that the stellar initial mass function (IMF) depends on physical properties of star-forming molecular clouds in galaxies and thereby investigate how such a non-universal IMF (NUIMF) influences galaxy evolution. We incorporate a NUIMF model ... More

Evolution of the Small Magellanic CloudJul 31 2007Based on the results of N-body simulations on the last 2.5 Gyr evolution of the Large and Small Magellanic Clouds (LMC and SMC, respectively) interacting with the Galaxy, we firstly show when and where the leading arms (LAs) of the Magellanic stream (MS) ... More

Formation of a polar-ring galaxy in a galaxy mergerApr 22 1998We numerically investigate stellar and gas dynamics in star-forming and dissipative galaxy mergers between two disk galaxies with specific orbital configurations. We find that violent relaxation combined with gaseous dissipation in galaxy merging transforms ... More

Critical surface in hot and dense QCD with the vector interactionSep 18 2008Nov 05 2008We discuss the chiral phase transition of hot and dense quark matter. We illustrate that the first-order phase transition is generally favored at high baryon density and the repulsive vector-vector interaction weakens the first-order phase transition. ... More

Initial fields and instability in the classical model of the heavy-ion collisionApr 26 2007May 22 2007Color Glass Condensate (CGC) provides a classical description of dense gluon matter at high energies. Using the McLerran-Venugopalan (MV) model we calculate the initial energy density \epsilon(\tau) in the early stage of the relativistic nucleus-nucleus ... More

Characterizing the Larkin-Ovchinnikov-Fulde-Ferrel phase induced by the chromomagnetic instabilityMar 26 2006Apr 04 2006We discuss possible destinations from the chromomagnetic instability in color superconductors with Fermi surface mismatch $\delta\mu$. In the two-flavor superconducting (2SC) phase we calculate the effective potential for color vector potentials $A_\alpha$ ... More

Deconfinement and Chiral Restoration in Hot and Dense MatterSep 13 2004We propose a picture that the chiral phase transition at zero quark mass and the deconfinement transition at infinite quark mass are continuously connected. This gives a simple interpretation on the coincidence of the pseudo-critical temperatures observed ... More

Phase diagram of hot and dense QCD constrained by the Statistical ModelJun 14 2010Jun 30 2010We propose a prescription to constrain the chiral effective model approach to the QCD phase diagram using the thermal Statistical Model, which is a description consistent with the experimental data at the freeze-out. In the transition region where thermal ... More

Chiral effective model with the Polyakov loopOct 09 2003Apr 11 2004We discuss how the simultaneous crossovers of deconfinement and chiral restoration can be realized. We propose a dynamical mechanism assuming that the effective potential gives a finite value of the chiral condensate if the Polyakov loop vanishes. Using ... More

Algebra of Kodaira-Spencer Gravity and Deformation of Calabi-Yau ManifoldNov 12 2016We study the algebraic structure of the configuration space of the Kodaira-Spencer gravity theory on a Calabi-Yau threefold. We then investigate the deformation problem of the Kodaira-Spencer gravity at the classical level using the algebraic tools obtained ... More

On the symmetry of commuting differential operators with singularities along hyperplanesSep 03 2003Feb 14 2004We study the commutants of a Schr\"{o}dinger operator whose potential function possesses inverse square singularities along some hyperplanes passing through the origin. It is shown that the Weyl group symmetry of the potential function and the commutants ... More

Deformations of reducible SL(n,C) representations of fibered 3-manifold groupsSep 24 2015Sep 27 2015Let $M_\phi$ be a surface bundle over a circle with monodromy $\phi:S \rightarrow S$. We study deformations of certain reducible representations of $\pi_1(M_\phi)$ into $\text{SL}(n,\mathbb{C})$, obtained by composing a reducible representation into $\text{SL}(2,\mathbb{C})$ ... More

Kernel method for corrections to scalingOct 14 2014Jul 07 2015Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are corrections to ... More

Bayesian Inference in the Scaling Analysis of Critical PhenomenaFeb 21 2011Nov 18 2011To determine the universality class of critical phenomena, we propose a method of statistical inference in the scaling analysis of critical phenomena. The method is based on Bayesian statistics, most specifically, the Gaussian process regression. It assumes ... More

Cosmic evolution of dust in galaxies: Methods and preliminary resultsDec 03 2014We investigate the redshift (z) evolution of dust properties, its dependences on initial conditions of galaxy formation, and physical correlations between dust, gas, and stellar contents at different z based on our original chemodynamical simulations ... More

Secondary star formation within massive star clusters: Origin of multiple stellar populations in globular clustersNov 27 2010We numerically investigate whether and how gaseous ejecta from AGB stars can be converted into new stars within originally massive star clusters (MSCs) in order to understand the origin of multiple stellar populations in globular clusters (GCs). We adopt ... More

Formation of a giant HI bridge between M31 and M33 from their tidal interactionJul 08 2008Recent observations have discovered a giant HI bridge that appears to connect between the outer halo regions of M31 and M33. We propose that this HI bridge can be formed as a result of the past interaction between M31 and M33 based on test particle simulations ... More

Imprint of galaxy formation and evolution on globular cluster propertiesMay 13 2006We discuss the origin of physical properties of globular cluster systems (GCSs) in galaxies in terms of galaxy formation and evolution processes. Based on numerical simulations of dynamical evolution of GCSs in galaxies, we particularly discuss (1) the ... More

Origin of companion galaxies in QSO hostsApr 03 1999Recent morphological studies of QSO host galaxies by the Hubble Space Telescope (HST) have revealed that a sizable fraction of QSO host galaxies possess close small companion galaxies. It is however not clear why and how these companion galaxies are physically ... More

On interpretation of recent proper motion data for the Large Magellanic CloudFeb 08 2011Recent observational studies using the Hubble Space Telescope (HST) have derived the center-of-mass proper motion (CMPM) of the Large Magellanic Cloud (LMC). Although these studies carefully treated both rotation and perspective effects in deriving the ... More

Unequal-mass galaxy mergers and the creation of cluster S0 galaxiesJun 08 1998It is a longstanding and remarkable problem when and how red S0 galaxies were formed in clusters of galaxies. We here propose that the major mechanism for the S0 creation is galaxy merging between two spirals with unequal mass. Our numerical simulations ... More

$N=2$ super $W$ algebra in half-twisted Landau-Ginzburg modelJul 06 1993We investigate $N=2$ extended superconformal symmetry, using the half-twisted Landau-Ginzburg models. The first example is the $D_{2n+2}$ -type minimal model. It has been conjectured that this model has a spin $n$ super $W$ current. We checked this by ... More

$SO(3)$-Floer homology of 3-manifolds with boundary 1Jun 03 2015In this paper the author discuss the relation between Lagrangian Floer homology and Gauge-theory (Donaldson theory) Floer homology. It can be regarded as a version of Atiyah-Floer type conjecture in the case of $SO(3)$-bundle with non-trivial second Stiefel-Whitney ... More

Views of the Chiral Magnetic EffectSep 23 2012Oct 09 2012My personal views of the Chiral Magnetic Effect are presented, which starts with a story about how we came up with the electric-current formula and continues to unsettled subtleties in the formula. There are desirable features in the formula of the Chiral ... More

Magnetic-field Induced Screening Effect and Collective ExcitationsMar 23 2011Apr 03 2011We explicitly construct the fermion propagator in a magnetic field background B to take the lowest Landau-level approximation. We analyze the energy and momentum dependence in the polarization tensor and discuss the collective excitations. We find there ... More

Relation between color-deconfinement and chiral restorationSep 05 2003We discuss the relation between the Polyakov loop and the chiral order parameter at finite temperature by using an effective model. We clarify why and how the pseudo-critical temperature associated with the Polyakov loop should coincide with that of the ... More

Spectral representation of the particle production out of equilibrium - Schwinger mechanism in pulsed electric fieldsFeb 12 2014We develop a formalism to describe the particle production out of equilibrium in terms of dynamical spectral functions, i.e. Wigner transformed Pauli-Jordan's and Hadamard's functions. We take an explicit example of a spatially homogeneous scalar theory ... More

QCD matter in extreme environmentsAug 15 2011Oct 25 2011We review various theoretical approaches to the states of QCD matter out of quarks and gluons in extreme environments such as the high-temperature states at zero and finite baryon density and the dimensionally reduced state under an intense magnetic field. ... More

Chiral Symmetry and Heavy-Ion CollisionsJun 02 2008I revisit the phase structure of hot and dense matter out of quarks and gluons with some historical consideration on the color deconfinement and chiral phase transitions. My goal is to make clear which part of the QCD phase diagram is under theoretical ... More

Quark description of the Nambu-Goldstone bosons in the color-flavor locked phaseMar 09 2004Sep 05 2004We investigate the color-singlet order parameters and the quark description of the Nambu-Goldstone (NG) bosons in the color-flavor locked (CFL) phase. We put emphasis on the NG boson (phason) called ``H'' associated with the $\mathrm{U_B(1)}$ symmetry ... More

Thermodynamic limit of the canonical partition function with respect to the quark number in QCDApr 26 2002Jul 14 2003We investigate QCD in the canonical ensemble with respect to the quark number. We reveal that the canonical description in which the quark number is fixed would be reduced to the grand canonical description under the thermodynamic limit. Since the grand ... More

Lectures on Factorization of Birational MapsFeb 11 2000This is an expanded version of the notes for the lectures given by the author at RIMS in the summer of 1999 to give a detailed account of the proof for the (weak) factorization theorem of birational maps by Abramovich-Karu-Matsuki-W{\l}odarczyk.

Black Hole Graybody Factor and Black Hole EntropyJul 22 1998Mar 19 1999We have proposed the entropy formula of the black hole which is constructed by the intersecting D1-brane and D5-brane with no momentum, whose compactification radii are constrained by the surface gravities in ten-dimensions. We interpret the entropy of ... More

Deep Learning without Poor Local MinimaMay 23 2016Aug 22 2016In this paper, we prove a conjecture published in 1989 and also partially address an open problem announced at the Conference on Learning Theory (COLT) 2015. With no unrealistic assumption, we first prove the following statements for the squared loss ... More

Socle filtrations of the standard Whittaker (g,K)-modules of Spin(r,1)Mar 18 2013Studied are the composition series of the standard Whittaker (g,K)-modules. For a generic infinitesimal character, the structures of these modules are completely understood, but if the infinitesimal character is integral, then there are not so many cases ... More

Non-extremal Stringy Black HoleNov 13 1996Dec 15 1997We construct a four-dimensional BPS saturated heterotic string solution from the Taub-NUT solution. It is a non-extremal black hole solution since its Euler number is non-zero. We evaluate its black hole entropy semiclassically. We discuss the relation ... More

D0-D4 system and QCD_{3+1}Jan 11 2000Jan 30 2001We consider a $(3+1)$-dimensional QCD model using a dual supergravity description with a non-extremal $D0$-$D4$ brane background. We calculate the spectrum of glueball masses and Wilson loops in the background. The mass spectrum is shown to coincide with ... More

Black hole entropy as T-duality invariantDec 24 1997Jul 06 1998We study the Euler numbers and the entropies of the non-extremal intersecting D-branes in ten-dimensions. We use the surface gravity to constrain the compactification radii. We correctly obtain the integer valued Euler numbers for these radii. Moreover, ... More

On a q-difference Painlevé III equation: II. Rational solutionsMay 29 2002Mar 13 2004Rational solutions for a $q$-difference analogue of the Painlev\'e III equation are considered. A Determinant formula of Jacobi-Trudi type for the solutions is constructed.

Quantum World-line Monte Carlo Method with Non-binary Loops and Its ApplicationAug 03 2006A quantum world-line Monte Carlo method for high-symmetrical quantum models is proposed. Firstly, based on a representation of a partition function using the Matsubara formula, the principle of quantum world-line Monte Carlo methods is briefly outlined ... More

Numerical study of incommensurability of the spiral state on spin-1/2 spatially anisotropic triangular antiferromagnets using entanglement renormalizationAug 21 2012Nov 16 2012The ground state of an S=1/2 antiferromagnetic Heisenberg model on a spatially anisotropic triangular lattice, which is an effective model of Mott insulators on a triangular layer of organic charge transfer salts or Cs2CuCl4, is numerically studied. We ... More