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Yang-Mills theory on noncommutative space: does it exist?Apr 15 2016Aug 02 2016I revisit a basic question about the noncommutative Yang-Mills theory: if it exists or not, or more precisely, whether a nonperturbative formulation exists. As the most promising approach, I consider a formulation based on matrix models. It is explained ... More

Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 superchargesSep 30 2011Jan 05 2012In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills (SYM) theory and deform it by a mass parameter M with keeping all supercharges. We further add another mass parameter m in a manner to respect two of the eight supercharges and ... More

What lattice theorists can do for superstring/M-theoryApr 19 2016Jul 23 2016The gauge/gravity duality provides us with nonperturbative formulation of superstring/M-theory. Although inputs from gauge theory side are crucial for answering many deep questions associated with quantum gravitational aspects of superstring/M-theory, ... More

Gauged And Ungauged: A Nonperturbative TestFeb 08 2018We study the thermodynamics of the `ungauged' D0-brane matrix model by Monte Carlo simulation. Our results appear to be consistent with the conjecture by Maldacena and Milekhin.

A proposal of a fine tuning free formulation of 4d N=4 super Yang-MillsSep 05 2010Nov 07 2011Recently, a nonperturbative formulation of 4d N=4 super Yang-Mills theory which does not require fine tuning at least to all order in perturbation theory has been proposed by combining two-dimensional lattice and matrix model techniques. In this paper ... More

A proposal of the gauge theory description of the small Schwarzschild black hole in AdS$_5\times$S$^5$Aug 10 2016Aug 17 2016Based on 4d ${\cal N}=4$ SYM on $\mathbb{R}^{1}\times$S$^3$, a gauge theory description of a small black hole in AdS$_5\times$S$^5$ is proposed. The change of the number of dynamical degrees of freedom associated with the emission of the scalar fields' ... More

Cascade of Gregory-Laflamme Transitions and U(1) Breakdown in Super Yang-MillsJun 01 2007Sep 01 2007In this paper we consider black p-branes on square torus. We find an indication of a cascade of Gregory-Laflamme transitions between black p-brane and (p-1)-brane. Through AdS/CFT correspondence, these transitions are related to the breakdown of the U(1) ... More

Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-NJul 28 2009We study two-dimensional N=(2,2) SU(N) super Yang-Mills theory on Euclidean two-torus using Sugino's lattice regularization. We perform the Monte-Carlo simulation for N=2,3,4,5 and then extrapolate the result to N = infinity. With the periodic boundary ... More

Universality of phase diagrams in QCD and QCD-like theoriesNov 14 2011We show the universality of phase diagrams in QCD and QCD-like theories through the large-N_c equivalence. The whole phase diagrams are identical between QCD at finite isospin chemical potential and SO(2N_c) and Sp(2N_c) gauge theories at finite baryon ... More

Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on latticeOct 14 2010Jan 12 2011We show that N=(2,2) SU(N) super Yang-Mills theory on lattice does not have sign problem in the continuum limit, that is, under the phase-quenched simulation phase of the determinant localizes to 1 and hence the phase-quench approximation becomes exact. ... More

Universality of Phases in QCD and QCD-like TheoriesMar 28 2011Mar 06 2012We argue that the whole or the part of the phase diagrams of QCD and QCD-like theories should be universal in the large-N_c limit through the orbifold equivalence. The whole phase diagrams, including the chiral phase transitions and the BEC-BCS crossover ... More

Orbifold equivalence and the sign problem at finite baryon densitySep 08 2010Apr 18 2011We point out that SO(2N_{c}) gauge theory with N_{f} fundamental Dirac fermions does not have a sign problem at finite baryon number chemical potential \mu_{B}. One can thus use lattice Monte Carlo simulations to study this theory at finite density. The ... More

On a new type of orbifold equivalence and M-theoretic AdS4/CFT3 dualitySep 28 2011Mar 11 2012We consider the large-N limit of \mathcal{N}=6 U(N) \times U(N) superconformal Chern-Simons (ABJM) theory with fixed level k, which is conjectured to be dual to M-theory on AdS4\times (S^7/Z_k) background. We point out that the so-called orbifold equivalence ... More

Phase quenching in finite-density QCD: models, holography, and latticeOct 08 2012Nov 04 2012Finite-density QCD is difficult to study numerically because of the sign problem. We prove that, in a certain region of the phase diagram, the phase quenched approximation is exact to O(Nf/Nc). It is true for any physical observables. We also consider ... More

Large Nc volume reduction and chiral random matrix theoryDec 31 2012Motivated by recent progress on the understanding of the Eguchi-Kawai (EK) volume equivalence and growing interest in conformal window, we simultaneously use the large-Nc volume reduction and Chiral Random Matrix Theory (chRMT) to study the chiral symmetry ... More

A microscopic description of black hole evaporation via holographyMar 09 2016Jul 03 2016We propose a description of how a large, cold black hole (black zero-brane) in type IIA superstring theory evaporates into freely propagating D0-branes, by solving the dual gauge theory quantitatively. The energy spectrum of emitted D0-branes is parametrically ... More

Two-dimensional lattice for four-dimensional N=4 supersymmetric Yang-MillsApr 30 2010Aug 30 2011We construct a lattice formulation of a mass-deformed two-dimensional N=(8,8) super Yang-Mills theory with preserving two supercharges exactly. Gauge fields are represented by compact unitary link variables, and the exact supercharges on the lattice are ... More

Sign problem and phase quenching in finite-density QCD: models, holography, and latticeMay 04 2012Oct 24 2012The effect of the complex phase of the fermion determinant is a key question related to the sign problem in finite-density QCD. Recently it has been shown that ignoring the complex phase -- the phase quenching -- does not change physics in a certain region ... More

Taming the pion condensation in QCD at finite baryon densityOct 27 2014In the Monte Carlo study of QCD at finite baryon density based upon the phase reweighting method, the pion condensation in the phase-quenched theory and associated zero-mode prevent us to go to the low-temperature high-density region. We propose a method ... More

On Matrix Model Formulations of Noncommutative Yang-Mills TheoriesJun 19 2008Dec 01 2008We study stability of noncommutative spaces in matrix models and discuss the continuum limit which leads to noncommutative Yang-Mills theories (NCYM). It turns out that most of noncommutative spaces in bosonic models are unstable. This indicates perturbative ... More

Creating and probing the Sachdev-Ye-Kitaev model with ultracold gases: Towards experimental studies of quantum gravityJun 08 2016We suggest that the holographic principle, combined with recent technological advances in atomic, molecular, and optical physics, can lead to experimental studies of quantum gravity. As a specific example, we consider the Sachdev-Ye-Kitaev (SYK) model, ... More

Instanton dynamics in finite temperature QCD via holographyMay 18 2015Jun 08 2015We investigate instantons in finite temperature QCD via Witten's holographic QCD. To study the deconfinement phase, we use the setup proposed in [1] (arXiv:1107.4048). We find that the sizes of the instantons are stabilized at certain values both in the ... More

A new large-N limit and the planar equivalence outside the planar limitMay 04 2012Jul 30 2012We consider a new large-N limit, in which the 't Hooft coupling grows with N. We argue that a class of large-N equivalences, which is known to hold in the 't Hooft limit, can be extended to this very strongly coupled limit. Hence this limit may lead to ... More

Deconfinement transition as black hole formation by the condensation of QCD stringsMay 07 2014Jul 31 2014We argue that the deconfinement transition of large-N Yang-Mills theory is the condensation of very long and self-intersecting chromo-electric flux strings (QCD string), which is analogous to the formation of a black hole in string theory. We do this ... More

Describing Curved Spaces by MatricesAug 27 2005May 09 2006It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions on the principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can be described in terms ... More

Generating new dualities through the orbifold equivalence: a demonstration in ABJM and four-dimensional quiversOct 17 2011Nov 03 2011We show that the recently proposed large $N$ equivalence between ABJM theories with Chern-Simons terms of different rank and level, U(N_1)_{k_1}\times U(N_1)_{-k_1} and U(N_2)_{k_2}\times U(N_2)_{-k_2}, but the same value of N' =N_1 k_1=N_2 k_2, can be ... More

Quantum Black Hole Formation in the BFSS Matrix ModelMar 18 2015We study the various head-on collisions of two bunches of D0-branes and their real-time evolution in the BFSS matrix model in classical limit. For a various matrix size N respecting the 't Hooft scaling, we find quantitative evidence for the formation ... More

Non-lattice simulation for supersymmetric gauge theories in one dimensionJun 12 2007Lattice simulation of supersymmetric gauge theories is not straightforward. In some cases the lack of manifest supersymmetry just necessitates cumbersome fine-tuning, but in the worse cases the chiral and/or Majorana nature of fermions makes it difficult ... More

Large-$N_c$ gauge theory and chiral random matrix theoryFeb 14 2013We discuss how the $1/N_c$ expansion and the chiral random matrix theory ($\chi$RMT) can be used in the study of large-$N_c$ gauge theories. We first clarify the parameter region in which each of these two approaches is valid: while the fermion mass $m$ ... More

Curved Superspaces and Local Supersymmetry in Supermatrix ModelFeb 21 2006May 09 2006In a previous paper, we introduced a new interpretation of matrix models, in which any d-dimensional curved space can be realized in terms of d matrices, and the diffeomorphism and the local Lorentz symmetries are included in the ordinary unitary symmetry ... More

From the planar limit to M-theoryOct 12 2012Apr 29 2013The large-N limit of gauge theories has been playing a crucial role in theoretical physics over the decades. Despite its importance, little is known outside the planar limit where the 't Hooft coupling $\lambda=g_{YM}^2N$ is fixed. In this Letter we consider ... More

Large-N reduced models of supersymmetric quiver, Chern-Simons gauge theories and ABJMJul 28 2009Aug 10 2009Using the Eguchi-Kawai equivalence, we provide regularizations of supersymmetric quiver and Chern-Simons gauge theories which leave the supersymmetries unbroken. This allow us to study many interesting theories on a computer. As examples we construct ... More

Four-dimensional N=1 super Yang-Mills from matrix modelMay 19 2009Nov 12 2009We consider a supersymmetric matrix quantum mechanics. This is obtained by adding Myers and mass terms to the dimensional reduction of 4d N=1 super Yang-Mills theory to one dimension. Using this model we construct 4d N=1 super Yang-Mills theory in the ... More

Chaos in Matrix Models and Black Hole EvaporationFeb 03 2016Mar 17 2016Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question ---especially aspects of this question such as a black hole's negative specific heat---we consider the real-time dynamics of a solitonic object in ... More

Numerical tests of the gauge/gravity duality conjecture for D0-branes at finite temperature and finite NMar 02 2016Apr 06 2016According to the gauge/gravity duality conjecture, the thermodynamics of gauge theory describing D-branes corresponds to that of black branes in superstring theory. We test this conjecture directly in the case of D0-branes by applying Monte Carlo methods ... More

Putting M theory on a computerJan 28 2008We propose a non-lattice simulation for studying supersymmetric matrix quantum mechanics in a non-perturbative manner. In particular, our method enables us to put M theory on a computer based on its matrix formulation proposed by Banks, Fischler, Shenker ... More

Recent progress of lattice and non-lattice super Yang-MillsNov 08 2011We report recent progress of non-perturbative formulation of supersymmetric Yang-Mills. Although lattice formulations of two-dimensional theories which are fine tuning free to all order in perturbation theory are known for almost ten years, however, there ... More

Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperatureJul 30 2007We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature. The recently proposed non-lattice simulation enables us to include the effects of fermionic matrices in a transparent ... More

Holographic realization of large-Nc orbifold equivalence with non-zero chemical potentialJan 18 2012Recently, it has been suggested that large-Nc orbifold equivalences may be applicable to certain theories with chemical potentials, including QCD, in certain portions of their phase diagram. When valid, such an equivalence offers the possibility of relating ... More

Chaos in Classical D0-Brane MechanicsNov 30 2015Jan 13 2016We study chaos in the classical limit of the matrix quantum mechanical system describing D0-brane dynamics. We determine a precise value of the largest Lyapunov exponent, and, with less precision, calculate the entire spectrum of Lyapunov exponents. We ... More

Phase structure of the large-N reduced gauge theory and generalized Weingarten modelApr 10 2006Mar 19 2007We study a generalization of Weingarten model reduced to a point, which becomes the large-N reduced U(N) gauge theory in a special limit. We find that the U(1)^d symmetry is broken one by one, and restored simultaneously as U(1)^d -> U(1)^{d-1} -> ... ... More

Large-N reduction in QCD-like theories with massive adjoint fermionsJun 03 2010Dec 13 2010Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four- and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, center symmetry ... More

Worldsheet Analysis of Gauge/Gravity DualitiesDec 08 2008Dec 29 2008Gauge/gravity dualities are investigated from the worldsheet point of view. In [arXiv:0706.1163] and [arXiv:0708.2463], a duality between 4d SYM and supergravity on AdS_5xS^5 has been partly explained by using an anisotropic scale invariance of worldsheet ... More

Phase structure of twisted Eguchi-Kawai modelNov 13 2007Dec 13 2007Twisted Eguchi-Kawai model is a useful tool for studying the large-N gauge theory. It can also provide a nonperturbative formulation of the gauge theory on noncommutative spaces. Recently it was found that the Z_N^4 symmetry in this model, which is crucial ... More

Field Equations of Massless Fields in the New Interpretation of the Matrix ModelNov 08 2006Recently, some of the authors have introduced a new interpretation of matrix models in which covariant derivatives on any curved space can be expressed by large-N matrices. It has been shown that the Einstein equation follows from the equation of motion ... More

Fuzzy Torus in Matrix ModelDec 27 2004We have calculated the free energy up to two loop to compare T^2 with T^4 in IIB matrix model. It turns out that T^2 has smaller free energy than T^4. We have also discussed the generation of the gauge group by considering k-coincident fuzzy tori and ... More

Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanicsNov 19 2008Mar 09 2009We perform a direct test of the gauge-gravity duality associated with the system of N D0-branes in type IIA superstring theory at finite temperature. Based on the fact that higher derivative corrections to the type IIA supergravity action start at the ... More

Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanicsNov 13 2008In the string/gauge duality it is important to understand how the space-time geometry is encoded in gauge theory observables. We address this issue in the case of the D0-brane system at finite temperature T. Based on the duality, the temporal Wilson loop ... More

On the shape of a D-brane bound state and its topology changeJan 26 2009As is well known, coordinates of D-branes are described by NxN matrices. From generic non-commuting matrices, it is difficult to extract physics, for example, the shape of the distribution of positions of D-branes. To overcome this problem, we generalize ... More

Nonperturbative studies of supersymmetric matrix quantum mechanics with 4 and 8 supercharges at finite temperatureDec 14 2010Feb 18 2011We investigate thermodynamic properties of one-dimensional U(N) supersymmetric gauge theories with 4 and 8 supercharges in the planar large-N limit by Monte Carlo calculations. Unlike the 16 supercharge case, the threshold bound state with zero energy ... More

Multi-matrix models and emergent geometryMay 30 2008Nov 20 2008Encouraged by the AdS/CFT correspondence, we study emergent local geometry in large N multi-matrix models from the perspective of a strong coupling expansion. By considering various solvable interacting models we show how the emergence or non-emergence ... More

Holographic description of quantum black hole on a computerNov 21 2013The discovery of the fact that black holes radiate particles and eventually evaporate led Hawking to pose the well-known information loss paradox. This paradox caused a long and serious debate since it claims that the fundamental laws of quantum mechanics ... More

Phase structure of twisted Eguchi-Kawai modelOct 15 2007We study the phase structure of the four-dimensional twisted Eguchi-Kawai model using numerical simulations. This model is an effective tool for studying SU(N) gauge theory in the large-N limit and provides a nonperturbative formulation of the gauge theory ... More

A new look at instantons and large-N limitJul 02 2013We analyze instantons in the very strongly coupled large-$N$ limit ($N\to\infty$ with $g^2$ fixed) of large-$N$ gauge theories, where the effect of the instantons remains finite. By using the exact partition function of four-dimensional ${\cal N}=2^*$ ... More

Monte Carlo studies of 3d N=6 SCFT via localization methodNov 29 2012We perform Monte Carlo study of the 3d N=6 superconformal U(N)*U(N) Chern-Simons gauge theory (ABJM theory), which is conjectured to be dual to M-theory or type IIA superstring theory on certain AdS backgrounds. Our approach is based on a localization ... More

Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constantFeb 23 2012Mar 21 2012We show that the ABJM theory, which is an N=6 superconformal U(N)*U(N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory ... More

Precision lattice test of the gauge/gravity duality at large-$N$Jun 15 2016We pioneer a systematic, large-scale lattice simulation of D0-brane quantum mechanics. The large-$N$ and continuum limits of the gauge theory are taken for the first time at various temperatures $0.4 \leq T \leq 1.0$. As a way to directly test the gauge/gravity ... More

Supergravity from D0-brane Quantum MechanicsJun 15 2016The gauge/gravity duality conjecture claims the equivalence between gauge theory and superstring/M-theory. In particular, the one-dimensional gauge theory of D0-branes and type IIA string theory should agree on properties of hot black holes. Type IIA ... More

Mutual Entropy in Quantum Information and Information GeneticsJun 30 2004After Shannon, entropy becomes a fundamental quantity to describe not only uncertainity or chaos of a system but also information carried by the system. Shannon's important discovery is to give a mathematical expression of the mutual entropy (information), ... More

Proposed experiment to test the non-locality hypothesis in transient light-interference phenomenaJul 31 2006May 20 2008The transient phenomena of the Mach-Zender interferometer are discussed. To test the non-locality hypothesis, a single mode laser with a large coherence length is used. The behavior of a photon and its wave packets in the paths of the interferometer are ... More

Odd number and Trapezoidal numberApr 16 2015In this paper, we give a bijective proof of the reduced lecture hall partition theorem. It is possible to extend this bijection in lecture hall partition theorem. And refined versions of each theorems are also presented.

Duality of Weights, Mirror Symmetry and Arnold's Strange DualityFeb 06 1995A notion of duality of weight systems which corresponds to Batyrev's toric mirror symmetry is given. Explicit duality on the (1,1)-cohomology of K3 surfaces which are minimal models of toric hypersurfaces is constructed using monomial divisor mirror map ... More

Quasiparticles of spatially anisotropic triangular antiferromagnets in a magnetic fieldSep 23 2009Nov 05 2009The spectral properties of the spin-1/2 Heisenberg antiferromagnet on an anisotropic triangular lattice in a magnetic field are investigated using a weak-interchain-coupling approach combined with exact solutions of a chain. Dominant modes induced by ... More

A local expression of the Diederich--Fornaess exponent and the exponent of conformal harmonic measuresMar 13 2014Mar 22 2015A local expression of the Diederich--Fornaess exponent of complements of Levi-flat real hypersurfaces is exhibited. This expression describes the correspondence between pseudoconvexity of their complements and positivity of their normal bundles, which ... More

Cosmology of multigravityFeb 01 2009Feb 06 2009We have constructed a nonlinear multi-graviton theory. An application of this theory to cosmology is discussed. We found that scale factors in a solution for this theory repeat acceleration and deceleration.

New Developments in Lattice QCD: Calculation of Flavor Singlet Nucleon Matrix Elements and Hadron Scattering LengthsOct 26 1995Recent developments in lattice QCD calculation of flavor singlet nucleon matrix elements are reviewed. Substantial sea quark contributions are found in the $\pi$-$N\ \sigma$ term and the quark spin content of the nucleon such that the total magnitude ... More

Complexity in Quantum System and Its Application to Brain FunctionJun 30 2004The complexity and the chaos degree can be used to examine the chaotic aspects of not only several nonlinear classical and quantum physical physics but also life sciences. We will construct a model describing the function of brain in the context of Quantum ... More

Interpretation of relativistic, transverse, and longitudinal mass using the Lorentz transformation of reference time: Explanation of time dilation via spherical light clockJul 17 2007Mar 12 2008An interpretation of the inertial mass increase due to an object's velocity which is derived from the theory of special relativity is discussed. A Lorentz transformation of the reference time causes the inertial mass increase. It is assumed that the real ... More

A revisit of the papers on the theory of relativity: Reconsideration of the hypothesis of ether-draggingApr 16 2007Nov 13 2009This paper revisits previous papers related to the theory of relativity. Afterwards, a reconsideration of the hypothesis of ether-dragging is discussed. The ether is compatible with the theory of relativity and historical experiments; this paper explains ... More

Sets of finite perimeter and the Hausdorff-Gauss measure on the Wiener spaceJul 01 2009Jul 14 2009In Euclidean space, the integration by parts formula for a set of finite perimeter is expressed by the integration with respect to a type of surface measure. According to geometric measure theory, this surface measure is realized by the one-codimensional ... More

Quasiparticles of string solutions in the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic fieldJan 04 2012Spectral properties of the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field are investigated by using exact Bethe-ansatz solutions. We argue that not only quasiparticles called psinon and antipsinon but also a quasiparticle representing ... More

Dynamically dominant excitations of string solutions in the spin-1/2 antiferromagnetic Heisenberg chain in magnetic fieldsDec 15 2008Using Bethe-ansatz solutions, we uncover a well-defined continuum in dynamical structure factor $S^{+-}(k,\omega)$ of the spin-1/2 antiferromagnetic Heisenberg chain in magnetic fields. It comes from string solutions which continuously connect the mode ... More

Aspects of the ground state of the $U=\infty$ Hubbard ladderSep 16 1997Sep 17 1997We consider two aspects of the ground state of the $U=\infty$ Hubbard ladder: ferromagnetism and the metal-insulator transition at quarter-filling. First, we present rigorous results for the $U=\infty$ Hubbard ladder in the limit of the large inter-chain ... More

Some properties of energy measures on Sierpinski gasket type fractalsOct 02 2015We confirm, in a more general framework, a part of the conjecture posed by R. Bell, C.-W. Ho, and R. S. Strichartz [Energy measures of harmonic functions on the Sierpi\'nski gasket, Indiana Univ. Math. J. 63 (2014), 831--868] on the distribution of energy ... More

A question on image of syntomic regulator on CH^2(X,1)Sep 08 2011Nov 22 2011This paper has been withdrawn.

Weighted Bergman spaces of domains with Levi-flat boundary: geodesic segments on compact Riemann surfacesMar 23 2017The aim of this study is to understand to what extent a 1-convex domain with Levi-flat boundary is capable of holomorphic functions with slow growth. This paper discusses the case of the space of all the geodesic segments on a hyperbolic compact Riemann ... More

On behavior of pairs of Teichmüller geodesic raysApr 18 2013In this paper, we obtain the explicit limit value of the Teichm\"{u}ller distance between two Teichm\"{u}ller geodesic rays which are determined by Jenkins-Strebel differentials having a common end point on the augmented Teichm\"{u}ller space. Furthermore, ... More

The asymptotic behavior of Teichmüller raysFeb 14 2014In this paper, we consider the asymptotic behavior of two Teichm\"uller geodesic rays determined by Jenkins-Strebel differentials, and we obtain a generalization of a theorem in \cite{Amano14}. We also consider the infimum of the asymptotic distance in ... More

Fundamentals of quantum mutual entropy and capacityJun 12 1998Jun 14 1998The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy for classical ... More

Quantum Algorithm for SAT Problem and Quantum Mutual EntropyJun 29 2004It is von Neumann who opened the window for today's Information epoch. He defined quantum entropy including Shannon's information more than 20 years ahead of Shannon, and he introduced a concept what computation means mathematically. In this paper I will ... More

Single photon Michelson-Morley experiment via de Broglie-Bohm picture: An interpretation based on the hypothesis of frame draggingJan 21 2008Feb 28 2008The Michelson-Morley experiment is considered via a single photon interferometer and a hypothesis of the dragging of the permittivity of free space and permeability of free space. The Michelson-Morley experimental results can be interpreted using de Broglie-Bohm ... More

Proposed experiment on the continuity of quantum entanglementMay 26 2004Sep 22 2004We propose experiments on quantum entanglement for investigating the Einstein Podolsky Rosen (EPR) problem with the polarization directions of photons. These experiments are performed to investigate whether the defined polarization directions in an entangled ... More

Compatibility of the theory of special relativity with an absolute reference frame with a longitudinal Doppler shiftOct 19 2006We show the compatibility of the theory of special relativity with the absolute reference frame with a longitudinal Doppler shift. Using two absolute velocities vA and vS, the relative velocity u is derived. Thereafter the Doppler frequency is derived ... More

Analogies between Knots and Primes, 3-Manifolds and Number RingsApr 22 2009This is an expository article of our work on analogies between knot theory and algebraic number theory. We shall discuss foundational analogies between knots and primes, 3-manifolds and number rings mainly from the group-theoretic point of view.

On a global estimate of the Diederich--Fornaess index of Levi-flat real hypersurfacesOct 10 2014In this expository paper, we review a recent progress of the study of the Diederich--Fornaess index of complex domains with emphasis on the case of domains with Levi-flat boundary. It is exhibited that for any compact Levi-flat real hypersurface, the ... More

Relation between high-energy quasiparticles of quasi-one-dimensional antiferromagnets in a magnetic field and a doublon of a Hubbard chainJan 04 2012In spin-1/2 one-dimensional Heisenberg antiferromagnets and anisotropic triangular Heisenberg antiferromagnets, high-energy states carrying considerable spectral weights have been observed in a magnetic field using inelastic neutron scattering. Such high-energy ... More

Spectral properties near the Mott transition in the two-dimensional t-J modelJul 17 2015Aug 19 2015The single-particle spectral properties of the two-dimensional t-J model in the parameter regime relevant to cuprate high-temperature superconductors are investigated using cluster perturbation theory. Various anomalous features observed in cuprate high-temperature ... More

Spectral Properties near the Mott Transition in the One-Dimensional Hubbard ModelJul 21 2010Sep 01 2010Single-particle spectral properties near the Mott transition in the one-dimensional Hubbard model are investigated by using the dynamical density-matrix renormalization group method and the Bethe ansatz. The pseudogap, hole-pocket behavior, spectral-weight ... More

On dlog image of K_2 of elliptic surface minus singular fibersNov 08 2005Apr 06 2006Modular section added

Geodesic distances and intrinsic distances on some fractal setsNov 20 2013Given strong local Dirichlet forms and $\mathbb{R}^N$-valued functions on a metrizable space, we introduce the concepts of geodesic distance and intrinsic distance on the basis of these objects. They are defined in a geometric and an analytic way, respectively, ... More

Martingale dimensions for fractalsNov 14 2007We prove that the martingale dimensions for canonical diffusion processes on a class of self-similar sets including nested fractals are always one. This provides an affirmative answer to the conjecture of S. Kusuoka [Publ. Res. Inst. Math. Sci. 25 (1989) ... More

Energy measures and indices of Dirichlet forms, with applications to derivatives on some fractalsJun 23 2009We introduce the concept of index for regular Dirichlet forms by means of energy measures, and discuss its properties. In particular, it is proved that the index of strong local regular Dirichlet forms is identical with the martingale dimension of the ... More

Subaru Studies of the Cosmic DawnOct 02 2011An overview on the current status of the census of the early universe population is given. Observational surveys of high redshift objects provide direct opportunities to study the early epoch of the Universe. The target population included are Lyman Alpha ... More

High redshift galaxy surveysAug 30 2008A brief overview on the current status of the census of the early universe population is given. Observational surveys of high redshift galaxies provide direct opportunities to witness the cosmic dawn and to have better understanding of how and when infant ... More

A mathematical foundation of quantum information and quantum computer -on quantum mutual entropy and entanglement-Aug 26 1998The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy for classical ... More

Proposed experiment of which-way detection by longitudinal momentum transfer in Young's double slit experimentJun 01 2004May 14 2009The momentum of a photon may reveal the answer to the "which way" problem of Young's double slit experiments. A photon passing through the boundary between two media, in which a photon travels at different velocities, undergoes a momentum change according ... More

Incompatibility between the principle of the constancy of the speed of light and the Lorentz contraction in the GPS ExperimentMar 12 2007Incompatibility between the principle of the constancy of the speed of light and the Lorentz contraction in the global positioning system (GPS) is discussed. The GPS works precisely in the earth-centered locally inertial (ECI) coordinate system on the ... More

Proposal of Signaling by Interference Control of Delayed-Choice Experimental SetupSep 10 2004Mar 29 2006We propose a new signaling system using the experimental setup of Wheeler's delayed-choice experiment previously carried out. In the delayed-choice experiment, the experimental setup shows a wave property or a particle property at the time when the experimental ... More

Functions of locally bounded variation on Wiener spacesMar 13 2014We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.

Measurable Riemannian structures associated with strong local Dirichlet formsDec 26 2012We introduce Riemannian-like structures associated with strong local Dirichlet forms on general state spaces. Such structures justify the principle that the pointwise index of the Dirichlet form represents the effective dimension of the virtual tangent ... More