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CPT theorem and classification of topological insulators and superconductorsJun 02 2014We present a systematic topological classification of fermionic and bosonic topological phases protected by time-reversal, particle-hole, parity, and combination of these symmetries. We use two complementary approaches: one in terms of K-theory classification ... More

Scaling laws for nonlinear electromagnetic responses of Dirac fermionsOct 08 2015Mar 22 2016We theoretically propose that the Dirac fermion in two-dimensions shows the giant nonlinear responses to electromagnetic fields in terahertz region. A scaling form is obtained for the current and magnetization as functions of the normalized electromagnetic ... More

Weyl and Dirac semimetals with Z_2 topological chargeMar 31 2014Jun 25 2014We study the stability of gap-closing (Weyl or Dirac) points in the three-dimensional Brillouin zone of semimetals using Clifford algebras and their representation theory. We show that a pair of Weyl points with $\mathbb{Z}_2$ topological charge are stable ... More

Chiral anomaly and giant magnetochiral anisotropy in noncentrosymmetric Weyl semimetalsMay 18 2016Sep 30 2016We theoretically propose that giant magnetochiral anisotropy is achieved in Weyl semimetals in noncentrosymmetric crystals as a consequence of the chiral anomaly. The magnetochiral anisotropy is the nonlinearity of the resistivity $\rho$ that depends ... More

Giant bulk photovoltaic effect and spontaneous polarization of single-layer monochalcogenidesOct 20 2016We use a first-principles density functional theory approach to calculate the shift current of uniformly illuminated single-layer Ge and Sn monochalcogenides. We find a larger effective three-dimensional shift current ($\sim 200$ $\mu$A/V$^2$) than has ... More

Chiral Floquet Phases of Many-body Localized BosonsAug 31 2016Oct 17 2016We construct and classify chiral topological phases in driven (Floquet) systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. The construction proceeds by introducing exactly soluble models with ... More

Stability of surface states of weak $\mathbb{Z}_2$ topological insulators and superconductorsOct 22 2013Jan 20 2014We study the stability against disorder of surface states of weak $\mathbb{Z}_2$ topological insulators (superconductors) which are stacks of strong $\mathbb{Z}_2$ topological insulators (superconductors), considering representative Dirac Hamiltonians ... More

Gate-induced Dirac cones in multilayer graphenesNov 30 2012Feb 21 2013We study the electronic structures of ABA (Bernal) stacked multilayer graphenes in uniform perpendicular electric field, and show that the interplay of the trigonal warping and the potential asymmetry gives rise to a number of emergent Dirac cones nearly ... More

Two parameter flow of σ_{xx}(ω) - σ_{xy}(ω) for the graphene quantum Hall system in ac regimeAug 09 2011Apr 27 2012Flow diagram of $(\sigma_{xx}, \sigma_{xy})$ in finite-frequency ($\omega$) regime is numerically studied for graphene quantum Hall effect (QHE) system. The ac flow diagrams turn out to show qualitatively similar behavior as the dc flow diagrams, which ... More

Topological aspects of nonlinear excitonic processes in noncentrosymmetric crystalsDec 02 2015Jul 08 2016We study excitonic processes second order in the electric fields in noncentrosymmetric crystals. We derive formulas for shift current and second harmonic generation produced by exciton creation, by using the Floquet formalism combined with the Keldysh ... More

Topological nature of nonlinear optical effects in solidsOct 27 2015May 24 2016There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by the strong light irradiation to materials that results in nonlinear polarizations in the electric ... More

Topological classification with additional symmetries from Clifford algebrasJun 11 2013Oct 04 2013We classify topological insulators and superconductors in the presence of additional symmetries such as reflection or mirror symmetries. For each member of the 10 Altland-Zirnbauer symmetry classes, we have a Clifford algebra defined by operators of the ... More

Weyl Mott InsulatorAug 13 2015Jan 29 2016Relativistic Weyl fermion (WF) often appears in the band structure of three dimensional magnetic materials and acts as a source or sink of the Berry curvature, i.e., the (anti-)monopole. It has been believed that the WFs are stable due to their topological ... More

Dynamically enriched topological orders in driven two-dimensional systemsOct 11 2016Coherent periodic time-dependent driving can enable new non-equilibrium topological phases of matter that are intrinsically dynamical, i.e. that cannot exist in static systems. We investigate examples of this phenomena in 2D Floquet systems focusing first ... More

Quantized Photocurrents in the Chiral Multifold Fermion System RhSiFeb 08 2019The rapid pace of discovery of new classes of Weyl semimetals is driving a search for properties that derive from their unique bandstructure topology. One of the most striking of the predicted properties is the quantized circular photogalvanic effect ... More

Dynamically enriched topological orders in driven two-dimensional systemsOct 11 2016Dec 01 2016Time-periodic driving of a quantum system can enable new dynamical topological phases of matter that could not exist in thermal equilibrium. We investigate two related classes of dynamical topological phenomena in 2D systems: Floquet symmetry protected ... More

On composite types of tunnel number two knotsSep 03 2014Let $K$ be a tunnel number two knot. Then, by considering the $(g, b)$-decompositions, $K$ is one of (3, 0)-, (2, 1)-, (1, 2)- or (0, 3)-knots. In the present paper, we analyze the connected sum summands of composite tunnel number two knots and give a ... More

On tangle decompositions of twisted torus knotsOct 25 2011Jun 20 2012In the present paper, we will show that for any integer n>0 there are infinitely many twisted torus knots with n-string essential tangle decompositions.

On Heegaard splittings of knot exteriors with tunnel number degenerationsOct 28 2013Let $K_1, K_2$ be two knots with $t(K_1)+t(K_2)>2$ and $t(K_1 # K_2)=2$. Then, in the present paper, we will show that any genus three Heegaard splittings of $E(K_1 # K_2)$ is strongly irreducible and that $E(K_1 # K_2)$ has at most four genus three Heegaard ... More

Topological magneto-electric effects in thin films of topological insulatorsMay 23 2015Aug 11 2015We propose that the topological magneto-electric (ME) effect, a hallmark of topological insulators (TIs), can be realized in thin films of TIs in the $\nu=0$ quantum Hall state under magnetic field or by doping two magnetic ions with opposite signs of ... More

Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetryJun 12 2014We explore a new class of topologically stable zero energy modes which are protected by coexisting chiral and spatial symmetries. If a chiral symmetric Hamiltonian has an additional spatial symmetry such as reflection, inversion and rotation, the Hamiltonian ... More

Bosonic symmetry protected topological phases with reflection symmetrySep 15 2015Dec 16 2015We study two-dimensional bosonic symmetry protected topological (SPT) phases which are protected by reflection symmetry and local symmetry [$Z_N\rtimes R$, $Z_N\times R$, U(1)$\rtimes R$, or U(1)$\times R$], in the search for two-dimensional bosonic analogs ... More

Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactionsMay 23 2015Sep 04 2015The conditions for both the stability and the breakdown of the topological classification of gapped ground states of noninteracting fermions, the tenfold way, in the presence of quartic fermion-fermion interactions are given for any dimension of space. ... More

Cyclotron radiation and emission in grapheneDec 27 2007Dec 28 2007Peculiarity in the cyclotron radiation and emission in graphene is theoretically examined in terms of the optical conductivity and relaxation rates to propose that graphene in magnetic fields can be a candidate to realize the Landau level laser, proposed ... More

Faraday rotation in bilayer and trilayer graphene in the quantum Hall regimeMay 14 2012Oct 16 2012Optical Hall conductivity, as directly related to Faraday rotation, is theoretically studied for bilayer and trilayer graphene. In bilayer graphene, the trigonal warping of the band dispersion greatly affects the resonance structures in Faraday rotation ... More

Optical Hall conductivity in ordinary and graphene QHE systemsApr 16 2009Sep 16 2009We have revealed from a numerical study that the optical Hall conductivity $\sigma_{xy}(\omega)$ has a characteristic feature even in the ac ($\sim$ THz) regime in that the Hall plateaus are retained both in the ordinary two-dimensional electron gas and ... More

Dynamical scaling analysis of the optical Hall conductivity in the quantum Hall regimeApr 27 2010Dynamical scaling analysis is theoretically performed for the ac (optical) Hall conductivity $\sigma_{xy}(\varepsilon_F,\omega)$ as a function of Fermi energy $\varepsilon_F$ and frequency $\omega$ for the two-dimensional electron gas and for graphene. ... More

Optical Hall conductivity in 2DEG and graphene QHE systemsNov 02 2009We have revealed from a numerical study that the Hall plateaus are retained in the optical Hall conductivity $\sigma_{xy}(\omega)$ in the ac ($\sim$ THz) regime in both of the ordinary two-dimensional electron gas and graphene in the quantum Hall regime, ... More

Topological charges of three-dimensional Dirac semimetals with rotation symmetryJun 04 2015Oct 24 2015In general, the stability of a band crossing point indicates the presence of a quantized topological number associated with it. In particular, the recent discovery of three-dimensional Dirac semimetals in Na$_{3}$Bi and Cd$_{3}$As$_{2}$ demonstrates that ... More

Charge and spin transport in edge channels of a $ν=0$ quantum Hall system on the surface of topological insulatorsDec 29 2014Apr 13 2015Three-dimensional topological insulators of finite thickness can show the quantum Hall effect (QHE) at the filling factor $\nu=0$ under an external magnetic field if there is a finite potential difference between the top and bottom surfaces. We calculate ... More

Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetalsSep 16 2016Although Weyl fermions have proven elusive in high-energy physics, their existence as emergent quasiparticles was recently predicted in certain crystalline solids in which either inversion or time-reversal symmetry is broken\cite{WanPRB2011,BurkovPRL2011, ... More

On the degeneration ratio of tunnel numbers and free tangle decompositions of knotsMar 31 2009In this paper, we introduce a notion called n/k-free tangle and study the degeneration ratio of tunnel numbers of knots.

On a certain local identity for Lapid-Mao's conjecture and formal degree conjecture : even unitary group caseFeb 13 2019Lapid and Mao formulated a conjecture on an explicit formula of Whittaker Fourier coefficients of automorphic forms on quasi-split classical groups and metaplectic groups as an analogue of Ichino-Ikeda conjecture. They also showed that this conjecture ... More

Topological classification of interacting 1D Floquet phasesFeb 16 2016Mar 28 2016Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper we systematically classify one-dimensional topological and symmetry-protected topological (SPT) phases in interacting fermionic and ... More

Shift charge and spin photocurrents in Dirac surface states of topological insulatorJul 13 2016The generation of photocurrent in condensed matter is of main interest for photovoltaic and optoelectronic applications. Shift current, a nonlinear photoresponse, has attracted recent intensive attention as a dominant player of bulk photovoltaic effect ... More

Anderson localization and the topology of classifying spacesFeb 28 2015Jun 11 2015We construct the generic phase diagrams encoding the topologically distinct localized and delocalized phases of noninteracting fermionic quasiparticles for any symmetry class from the tenfold way in one, two, and three dimensions. To this end, we start ... More

Algebraic Structure of Vector Fields in Financial Diffusion Models and its ApplicationsOct 07 2015Dec 15 2015High order discretization schemes of SDEs by using free Lie algebra valued random variables are introduced by Kusuoka, Lyons-Victoir, Ninomiya-Victoir and Ninomiya-Ninomiya. These schemes are called KLNV methods. They involve solving the flows of vector ... More

Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetalsSep 19 2016We study nonlinear magneto-optical responses of metals by a semiclassical Boltzmann equation approach. We derive general formulas for linear and second order nonlinear optical effects in the presence of magnetic fields that include both Berry curvature ... More

Anomalous criticality in the quantum Hall transition at $n=0$ Landau level of graphene with chiral-symmetric disordersAug 16 2010We investigate numerically whether the chiral symmetry is the sole factor dominating the criticality of the quantum Hall transitions in disordered graphene. When the disorder respects the chiral symmetry, the plateau-to-plateau transition at the $n=0$ ... More

Efficient Prediction of Time- and Angle-Resolved Photoemission Spectroscopy Measurements on a Non-Equilibrium BCS SuperconductorSep 24 2018Jan 09 2019We study how time- and angle-resolved photoemission (tr-ARPES) reveals the dynamics of BCS-type, s-wave superconducting systems with time-varying order parameters. Approximate methods are discussed, based on previous approaches to either optical conductivity ... More

Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetalsSep 19 2016Nov 22 2016We study nonlinear magneto-optical responses of metals by a semiclassical Boltzmann equation approach. We derive general formulas for linear and second order nonlinear optical effects in the presence of magnetic fields that include both Berry curvature ... More

Topological Phases Protected By Reflection Symmetry and Cross-cap StatesJan 28 2015May 26 2015Twisting symmetries provides an efficient method to diagnose symmetry-protected topological (SPT) phases. In this paper, edge theories of (2+1)-dimensional topological phases protected by reflection as well as other symmetries are studied by twisting ... More

Generalization of Chiral Symmetry for Tilted Dirac ConesJan 25 2012The notion of chiral symmetry for the conventional Dirac cone is generalized to include the tilted Dirac cones, where the generalized chiral operator turns out to be non-hermitian. It is shown that the generalized chiral symmetry generically protects ... More

Generalized Chiral Symmetry and Stability of Zero Modes for Tilted Dirac ConesJan 22 2011While it has been well-known that the chirality is an important symmetry for Dirac-fermion systems that gives rise to the zero-mode Landau level in graphene, here we explore whether this notion can be extended to tilted Dirac cones as encountered in organic ... More

Refined global Gross-Prasad conjecture on special Bessel periods and Boecherer's conjectureNov 17 2016Jan 27 2019In this paper we pursue the refined global Gross-Prasad conjecture for Bessel periods formulated by Yifeng Liu in the case of special Bessel periods for $\mathrm{SO}\left(2n+1\right)\times\mathrm{SO}\left(2\right)$. Recall that a Bessel period for $\mathrm{SO}\left(2n+1\right)\times\mathrm{SO}\left(2\right)$ ... More

Topological semimetals protected by type-II nonsymmorphic symmetriesApr 04 2016Jul 16 2016Topological semimetals have energy bands near the Fermi energy sticking together at isolated points/lines/planes in the momentum space, which are often accompanied by stable surface states and intriguing bulk topological responses. Although it has been ... More

Z_3 symmetry-protected topological phases in the SU(3) AKLT modelSep 05 2014Dec 19 2014We study $\mathbb{Z}_3$ symmetry-protected topological (SPT) phases in one-dimensional spin systems with $Z_3 \times Z_3$ symmetry. We construct ground-state wave functions of the matrix product form for nontrivial $\mathbb{Z}_3$ phases and their parent ... More

Topological semimetals protected by off-centered symmetries in nonsymmorphic crystalsApr 04 2016Oct 28 2016Topological semimetals have energy bands near the Fermi energy sticking together at isolated points/lines/planes in the momentum space, which are often accompanied by stable surface states and intriguing bulk topological responses. Although it has been ... More

Chiral Floquet Phases of Many-body Localized BosonsAug 31 2016Sep 20 2016We construct and classify chiral topological phases in driven (Floquet) systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. The construction proceeds by introducing exactly soluble models with ... More

Optical Hall Effect in the Integer Quantum Hall RegimeApr 02 2010Jun 25 2010Optical Hall conductivity $\sigma_{xy}(\omega)$ is measured from the Faraday rotation for a GaAs/AlGaAs heterojunction quantum Hall system in the terahertz frequency regime. The Faraday rotation angle ($\sim$ fine structure constant $\sim$ mrad) is found ... More

Quantized circular photogalvanic effect in Weyl semimetalsNov 17 2016The circular photogalvanic effect (CPGE) is the part of a photocurrent that switches depending on the sense of circular polarization of the incident light. It has been consistently observed in systems without inversion symmetry and depends on non-universal ... More

Large bulk photovoltaic effect and spontaneous polarization of single-layer monochalcogenidesOct 20 2016Aug 27 2017We use a first-principles density functional theory approach to calculate the shift current and linear absorption of uniformly illuminated single-layer Ge and Sn monochalcogenides. We predict strong absorption in the visible spectrum and a large effective ... More

Heat conduction in the diatomic Toda lattice revisitedNov 28 1998The problem of the diverging thermal conductivity in one-dimensional (1-D) lattices is considered. By numerical simulations, it is confirmed that the thermal conductivity of the diatomic Toda lattice diverges, which is opposite to what one has believed ... More

Rheology and dynamical heterogeneity in frictionless beads at jamming densityApr 03 2008Dec 20 2015We investigate the rheological properties of an assembly of inelastic (but frictionless) particles close to the jamming density using numerical simulation, in which uniform steady states with a constant shear rate $\dot\gamma$ is realized. The system ... More

Power-law friction in closely-packed granular materialsDec 14 2006May 08 2007In order to understand the nature of friction in closely-packed granular materials, a discrete element simulation on granular layers subjected to isobaric plain shear is performed. It is found that the friction coefficient increases as the power of the ... More

Dynamics of a dislocation bypassing an impenetrable precipitate: the Hirsch mechanism revisitedNov 15 2005May 08 2006Dynamical process where an edge dislocation in fcc copper bypasses an impenetrable precipitate is investigated by means of molecular dynamics simulation. A mechanism which is quite different from the Orowan mechanism is observed, where a dislocation leaves ... More

Homotopy types of Hom complexes of graphsSep 13 2015Apr 19 2016The Hom complex ${\rm Hom}(T,G)$ of graphs is a CW-complex associated to a pair of graphs $T$ and $G$. It is known that certain homotopy invariants of ${\rm Hom}(T,G)$ sometimes give lower bounds for the chromatic number of $G$. On the other hand, we ... More

Morphism complexes of sets with relationsFeb 03 2014Apr 19 2016Let $r$ be a positive integer. An $r$-set is a pair $X= (V(X),R(X))$ consisting of a set $V(X)$ with a subset $R(X)$ of the direct product $V(X)^r$. The object of this paper is to investigate the Hom complexes of $r$-sets, which were introduced for graphs ... More

Answers of some problems about graph coloring test graphsMar 06 2013We give answers of two problems about graph coloring test graphs suggested by Kozlov. We prove that a graph whose chromatic number is 2 is a homotopy test graph. We prove there is a graph $T$ with two involutions $\gamma_1$ and $\gamma_2$ where $(T,\gamma_1)$ ... More

Extinction Map of the Galactic center: OGLE-II Galactic bulge fieldsSep 06 2003Dec 01 2003We present the reddening (E(V-I)) and Extinction maps in V-band (A_V) and I-band (A_I) for 48 Optical Gravitational Lensing Experiment II (OGLE-II) Galactic bulge (GB) fields, covering a range of $-11^\circ <l< 11^\circ$, with the total area close to ... More

Higher-dimensional contact manifolds with infinitely many Stein fillingsAug 04 2016Nov 17 2016For any integer $n\geq 2$, we construct an infinite family of Stein fillable contact $(4n-1)$-manifolds each of which admits infinitely many pairwise homotopy inequivalent Stein fillings.

Trace and extension operators for Besov spaces and Triebel-Lizorkin spaces with variable exponentsOct 05 2014This paper is concerned with a boundedness of trace and extension operators for Besov spaces and Triebel-Lizorkin spaces on upper half space with variable exponents. To define trace and extension operators, we introduce a quarkonial decomposition for ... More

Recent Results on High-Q2 Neutral and Charged Current Cross Sections at HERAJun 07 2001High-Q^2 NC and CC DIS cross sections have been measured by H1 and ZEUS at HERA. Both NC and CC results based on data taken during the year 1994-2000 are in good agreement with Standard Model expectations. The structure function xF_3 is extracted from ... More

Wall-crossing, Toric divisor and Seiberg dualityApr 30 2013We study the wall-crossing phenomena of BPS D4-D2-D0 states on the conifold and orbifold C^2/Z_2, from the viewpoint of the quiver quantum mechanics on the D-branes. The Kahler moduli dependence of the BPS index is translated into the FI parameter dependence ... More

On non-abelian Lubin-Tate theory for GL(2) in the odd equal characteristic caseApr 29 2016In this paper, we define a family of affinoids in the tubular neighborhoods of CM points in the Lubin-Tate curve with suitable level structures, and compute the reductions of them in the equal characteristic case. By using etale cohomology theory of adic ... More

Fourier and Cauchy-Stieltjes transforms of power laws including stable distributionsJul 20 2011Oct 16 2011We introduce a class of probability measures whose densities near infinity are mixtures of Pareto distributions. This class can be characterized by the Fourier transform which has a power series expansion including real powers, not only integer powers. ... More

A comment on trans-Planckian physics in inflationary universeDec 20 2000Feb 21 2001There are several works searching for a clue of trans-Planckian physics on the primordial density perturbation spectrum. Here we would like to point out an important aspect which has been overlooked so far. When we consider a model in which the primordial ... More

Rate and state friction law as derived from atomistic processes at asperitiesDec 16 2015A theoretical account is given of the microscopic basis of the rate- and state-dependent friction (RSF) law. The RSF law describes rock friction quantitatively and therefore it is commonly used to model earthquakes and the related phenomena. But the RSF ... More

Scaling of the critical slip distance in granular layersJun 20 2009We investigate the nature of friction in granular layers by means of numerical simulation focusing on the critical slip distance, over which the system relaxes to a new stationary state. Analyzing a transient process in which the sliding velocity is instantaneously ... More

On localizations of the characteristic classes of l-adic sheaves and conductor formula in characteristic p>0May 12 2009The Grothendieck-Ogg-Shafarevich formula calculates the l-adic Euler-Poincare number of an l-adic sheaf on a curve by an invariant produced by the wild ramification of the l-adic sheaf named Swan class. A. Abbes, K. Kato and T. Saito generalize this formula ... More

Box complexes and homotopy theory of graphsMay 20 2016We introduce a model structure on the category of graphs, and showed that it is Quillen equivalent to the category of $\mathbb{Z}_2$-spaces. A weak equivalence of the model structure is a graph homomorphism which induces a $\mathbb{Z}_2$-homotopy equivalence ... More

Some examples of non-tidy spacesApr 23 2014Apr 26 2014We construct a free $\mathbb{Z}_2$-manifold $X_n$ for a positive integer $n$ such that $w_1(X_n)^n \neq 0$, but there is no $\mathbb{Z}_2$-equivariant map from $S^2$ to $X_n$.

Box complex and Kronecker double coveringApr 06 2014Sep 13 2015The box complex $B(G)$ is a $\mathbb{Z}_2$-poset associated with a graph $G$, which was introduced in the context of the graph coloring problem. We study the poset structure of box complex. Our main theorem states that, up to isolated vertices, the $\Z_2$-poset ... More

Fundamental groups of neighborhood complexesOct 10 2012Sep 13 2015We introduce the notions of $r$-neighborhood complexes, $r$-fundamental groups and $r$-covering maps of graphs, for a positive integer $r$. The $r$-neighborhood complex $N_r(G)$ is a natural generalization of the neighborhood complex introduced by Lov\'asz. ... More

Compact Stein surfaces as branched covers with same branch setsAug 05 2015Jan 21 2016Loi and Piergallini showed that a smooth compact, connected $4$-manifold $X$ with boundary admits a Stein structure if and only if $X$ is a simple branched cover of a $4$-disk $D^4$ branched along a positive braided surface $S$ in a bidisk $D_{1}^{2} ... More

Supremum of the function $S_1(t)$ on short intervalsJan 01 2013Nov 18 2013We prove a lower bound on the supremum of the function $S_1(T)$ on short intervals, defined by the integration of the argument of the Riemann zeta-function. The same type of result on the supremum of $S(T)$ have already been obtained by Karatsuba and ... More

Multiple D4-D2-D0 on the Conifold and Wall-crossing with the FlopOct 28 2010Dec 22 2010We study the wall-crossing phenomena of D4-D2-D0 bound states with two units of D4-brane charge on the resolved conifold. We identify the walls of marginal stability and evaluate the discrete changes of the BPS indices by using the Kontsevich-Soibelman ... More

Macroscopic Expression Connecting the Rate of Energy Dissipation and Violation of the Fluctuation-Response RelationNov 03 2008Feb 14 2009A direct connection between the magnitude of the violation of the fluctuation-response relation (FRR) and the rate of energy dissipation is presented in terms of field variables of nonequilibrium systems. Here, we consider the density field of a colloidal ... More

Free infinite divisibility for beta distributions and related onesMay 04 2013Sep 18 2014We prove that many of beta, beta prime, gamma, inverse gamma, Student t- and ultraspherical distributions are freely infinitely divisible, but some of them are not. The latter negative result follows from a local property of probability density functions. ... More

White noise analysis on manifolds and the energy representation of a gauge groupMay 09 2008Jan 15 2011The energy representation of a gauge group on a Riemannian manifold has been discussed by several authors. Y. Shimada has shown the irreducibility for compact Riemannian manifold, using white noise analysis. In this paper we extend its technique to noncompact ... More

Twisted Alexander polynomials and incompressible surfaces given by ideal pointsDec 15 2014We study incompressible surfaces constructed by Culler-Shalen theory in the context of twisted Alexander polynomials. For a $1$st cohomology class of a $3$-manifold the coefficients of twisted Alexander polynomials induce regular functions on the $SL_2(\mathbb{C})$-character ... More

On localizations of characteristic classes of l-adic sheaves of rank 1May 13 2009The Grothendieck-Ogg-Shafarevich formula is generalized to any dimensional scheme by Abbes-Kato-Saito. In this paper, we introduce two methods of localization of the characteristic classes for sheaves of rank 1 and compare them. As a corollary of this ... More

Deformations of box complexesDec 11 2013Jun 28 2015Box complex is a $\mathbb{Z}_2$-space associated to a graph, and it is known that a certain $\mathbb{Z}_2$-homotopy invariant of it, called the $\mathbb{Z}_2$-index, gives an effective lower bound for the chromatic number. On the other hand, we show that ... More

$r$-fundamental groups of graphsJan 30 2013Sep 13 2015In this paper, we introduce the notions of $r$-fundamental groups of graphs, $r$-covering maps, and $r$-neighborhood complexes of graphs for a positive integer $r$. There is a natural correspondence between $r$-covering maps and $r$-fundamental groups ... More

Hilbertian matrix cross normed spaces arising from normed idealsJul 31 2006Jan 14 2007Generalizing Pisier's idea, we introduce a Hilbertian matrix cross normed space associated with a pair of symmetric normed ideals. When the two ideals coincide, we show that our construction gives an operator space if and only if the ideal is the Schatten ... More

New associative product of three states generalizing free, monotone, anti-monotone, Boolean, conditionally free and conditionally monotone productsSep 08 2010We define a new independence in three states called indented independence which unifies many independences: free, monotone, anti-monotone, Boolean, conditionally free, conditionally monotone and conditionally anti-monotone independences. This unification ... More

Conditionally monotone independence II: Multiplicative convolutions and infinite divisibilityOct 07 2009Mar 26 2011We study the multiplicative convolution for c-monotone independence. This convolution unifies the monotone, Boolean and orthogonal multiplicative convolutions. We characterize convolution semigroups for the c-monotone multiplicative convolution on the ... More

Conditionally monotone independence I: Independence, additive convolutions and related convolutionsJul 31 2009Mar 26 2011We define a product of algebraic probability spaces equipped with two states. This product is called a conditionally monotone product. This product is a new example of independence in non-commutative probability theory and unifies the monotone and Boolean ... More

The gravity duals of SO/USp superconformal quiversFeb 29 2012Apr 19 2012We study the gravity duals of SO/USp superconformal quiver gauge theories realized by M5-branes wrapping on a Riemann surface ("G-curve") together with a Z_2-quotient. When the G-curve has no punctures, the gravity solutions are classified by the genus ... More

Calogero-Moser hierarchy and KP hierarchyFeb 03 1994The space of solutions of the rational Calogero-Moser hierarchy, and the space of solutions of the KP hierarchy whose tau functions are monic polynomials in $t_1$ with coefficients depending on $t_n$, $n > 1$, are identified, generalizing earlier results ... More

Normalization of twisted Alexander invariantsMay 16 2007Jul 05 2015Twisted Alexander invariants of knots are well-defined up to multiplication of units. We get rid of this multiplicative ambiguity via a combinatorial method and define normalized twisted Alexander invariants. We then show that the invariants coincide ... More

Loop space construction of bigraphs and box complexesOct 19 2016Dochtermann introduced the loop space construction of a based graph $(G,v)$ whose basepoint is a looped vertex. He showed that the complex $C(\Omega(G,v))$ is homotopy equivalent to the loop space $\Omega(C(G),v)$ of $C(G)$. Here we write $C(G)$ to mean ... More

Equivalence Problem for Second Order Partially Differential Equations and Double Fibration as a Flat Model SpaceMar 26 2007In this paper, we consider an equivalence problem of second order partially differential equations (PDE) and a duality of the flat differential equation. For the equivalence problem, explicit form of invariants (curvatures) are given. We also investigate ... More

On prolongations of second-order regular overdetermined systems with two independent and one dependent variablesOct 18 2012The purpose of this present paper is to investigate the geometric structure of regular overdetermined systems of second order with two independent and one dependent variables from the point of view of rank 2 prolongations. Utilizing this notion of prolongations, ... More

Specific heat of the ideal gas obeying the generalized exclusion statisticsMay 20 2000Feb 02 2001We calculate the specific heat of the ideal gas obeying the generalized exclusion statistics (GES) in the continuum model and the tight binding model numerically. In the continuum model of 3-d space, the specific heat increases with statistical parameter ... More

Free infinite divisibility for powers of random variablesSep 29 2015Mar 10 2016We prove that $X^r$ follows a free regular distribution, i.e. the law of a nonnegative free L\'evy process if: (1) $X$ follows a free Poisson distribution without an atom at 0 and $r\in(-\infty,0]\cup[1,\infty)$; (2) $X$ follows a free Poisson distribution ... More

Classical black hole evaporation in Randall-Sundrum infinite braneworldMar 24 2002Apr 03 2002After the gravity induced on the brane in the Randall-Sundrum (RS) infinite braneworld is briefly reviewed, we discuss the possibility that black holes evaporate as a result of classical evolution in this model based on the AdS/CFT correspondence. If ... More

The No-Negative Mode Theorem in False Vacuum Decay with GravityJan 28 1999Feb 23 1999The so-called negative mode problem in the path integral approach to the false vacuum decay with the effect of gravity has been an unsolved problem. Several years ago, we proposed a conjecture which is to be proved in order to give a consistent solution ... More

Weak gravity in DGP braneworld modelMay 08 2003May 12 2003We analyze the weak gravity in the braneworld model proposed by Dvali-Gabadadze-Porrati, in which the unperturbed background spacetime is given by five dimensional Minkowski bulk with a brane which has the induced Einstein Hilbert term. This model has ... More

Analytic continuations of Fourier and Stieltjes transforms and generalized moments of probability measuresSep 08 2010Jan 15 2011We consider analytic continuations of Fourier transforms and Stieltjes transforms. This enables us to define what we call complex moments for some class of probability measures which do not have moments in the usual sense. There are two ways to generalize ... More