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Nonreciprocal current from electron interactions in noncentrosymmetric crystals: roles of time reversal symmetry and dissipationJun 27 2017Feb 14 2018In noncentrosymmetric crystals with broken inversion symmetry $\mathcal{I}$, the $I-V$ ($I$: current, $V$: voltage) characteristic is generally expected to depend on the direction of $I$, which is known as nonreciprocal response and, for example, found ... 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

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

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

Symmetry protected topological phases in two-orbital SU(4) fermionic atomsMay 22 2018Jul 23 2018We study one-dimensional systems of two-orbital SU(4) fermionic cold atoms. In particular, we focus on an SU(4) spin model [named SU(4) $e$-$g$ spin model] that is realized in a low-energy state in the Mott insulator phase at the filling $n_g=3, n_e=1$ ... More

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

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

$Z_N$ Berry Phases in Symmetry Protected Topological PhasesSep 05 2017We show that the $Z_N$ Berry phase (Berry phase quantized into $2\pi/N$) provides a useful tool to characterize symmetry protected topological phases with correlation that can be directly computed through numerics of a relatively small system size. The ... 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

Floquet topological phases protected by time glide symmetryMar 07 2017May 26 2017We study Floquet topological phases in periodically driven systems that are protected by "time glide symmetry", a combination of reflection and half time period translation. Time glide symmetry is an analog of glide symmetry with partial time translation ... More

Current-voltage characteristic and shot noise of shift current photovoltaicsMay 24 2018Nov 30 2018We theoretically study the current-voltage relation, $I-V$ characteristic, of the photovoltaics due to the shift current, i.e., the photocurrent generated ${\it without}$ the external dc electric field in noncentrosymmetric crystals through the Berry ... More

Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisitedMar 13 2019Apr 02 2019The phase diagram of the quantum spin-1/2 antiferromagnetic $J^{\,}_{1}$-$J^{\,}_{2}$ XXZ chain was obtained by Haldane using bosonization techniques. It supports three distinct phases for $0\leq J^{\,}_{2}/J^{\,}_{1}<1/2$, i.e., a gapless algebraic spin ... 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

Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetalsSep 19 2016Dec 17 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

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

Nondestructive real-space imaging of current density distributions in randomly networked conductive nanomaterialsNov 27 2018For realization the new functional materials and devices by conductive nanomaterials, how to control and realize the optimum networks structures are import point for fundamental, applied and industrial science. In this manuscript, the nondestructive real-space ... 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

Chiral Optical Response of Multifold FermionsJun 25 2018Jul 20 2018Multifold fermions are generalizations of two-fold degenerate Weyl fermions with three-, four-, six- or eight-fold degeneracies protected by crystal symmetries, of which only the last type is necessarily non-chiral. Their low energy degrees of freedom ... 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

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

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

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

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

Topological Floquet-Thouless energy pumpOct 31 2017Nov 23 2017We explore adiabatic pumping in the presence of periodic drive, finding a new phase in which the topologically quantized pumped quantity is energy rather than charge. The topological invariant is given by the winding number of the micromotion with respect ... 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 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

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 composite twisted torus knotsSep 15 2011In the present note, we will show that there are infinitely many composite twisted torus knots.

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 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

Classification of Interacting Topological Floquet Phases in One DimensionFeb 16 2016May 25 2017Periodic 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

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.

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

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

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

Diagrammatic approach to nonlinear optical response with application to Weyl semimetalsJul 24 2018Jan 10 2019Nonlinear optical responses are a crucial probe of physical systems including periodic solids. In the absence of electron-electron interactions, they are calculable with standard perturbation theory starting from the band structure of Bloch electrons, ... 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

Quantitative relationship between polarization differences and the zone-averaged shift photocurrentDec 31 2016Aug 18 2017A relationship is derived between differences in electric polarization between bands and the "shift vector" that controls part of a material's bulk photocurrent, then demonstrated in several models. Electric polarization has a quantized gauge ambiguity ... 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

Balancer effects in opinion dynamicsJul 27 2015Oct 30 2015We introduce a novel type of contrarian agent, the balancer, to Galam model of opinion dynamics, in order to account for the existence of social skepticism over one-sidedness. We find that the inclusion of balancers, along with majoritarian floaters and ... 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

Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisitedMar 13 2019The phase diagram of the quantum spin-1/2 antiferromagnetic $J^{\,}_{1}$-$J^{\,}_{2}$ XXZ chain was obtained by Haldane using bosonization techniques. It supports three distinct phases for $0\leq J^{\,}_{2}/J^{\,}_{1}<1/2$, i.e., a gapless algebraic spin ... 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

Ultra-analytic effect of Cauchy problem for a class of kinetic equationsMar 22 2009The smoothing effect of the Cauchy problem for a class of kinetic equations is studied. We firstly consider the spatially homogeneous non linear Landau equation with Maxwellian molecules and inhomogeneous linear Fokker-Planck equation to show the ultra-analytic ... 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.

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

$L^2$ estimates and vanishing theorems for holomorphic vector bundles equipped with singular Hermitian metricsFeb 28 2018We investigate singular Hermitian metrics on vector bundles, especially strictly Griffiths positive ones. $L^2$ esitimates and vanishing theorems usually require an assumption that vector bundles are Nakano positive. However there is no general definition ... 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

Coribbon Hopf (face) algebras generated by lattice modelsApr 16 1999By studying ``points of the underlying quantum groups''of coquasitriangular Hopf (face) algebras, we construct ribbon categories for each lattice models without spectral parameter of both vertex and face type. Also, we give a classification of the braiding ... More

Double graph complex and characteristic classes of fibrationsMay 15 2018Jan 04 2019In this paper, we construct a double chain complex generated by certain graphs and a chain map from that to the Chevalley-Eilenberg double complex of the dgl of symplectic derivations on a free dgl. It is known that the target of the map is related to ... More

Symmetry of Reidemeister torsion on $SU_2$-representation spaces of knotsJan 24 2008Sep 17 2009We study two sorts of actions on the space of conjugacy classes of irreducible $SU_2$-representations of a knot group. One of them is an involution which comes from the algebraic structure of $SU_2$ and the other is the action by the outer automorphism ... More

Zon-Cohen singularity and negative inverse temperature in a trapped particle limitMay 09 2012Jun 22 2012We study a Brownian particle on a moving periodic potential. We focus on the statistical properties of the work done by the potential and the heat dissipated by the particle. When the period and the depth of the potential are both large, by using a boundary ... More

Ample canonical heights for endomorphisms on projective varietiesOct 15 2017Feb 02 2018We define an "ample canonical height" for an endomorphism on a projective variety, which is essentially a generalization of the canonical heights for polarized endomorphisms introduced by Call--Silverman. We formulate a dynamical analogue of the Northcott ... More

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

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

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

Quantized circular photogalvanic effect in Weyl semimetalsNov 17 2016Jul 25 2017The 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

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

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

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

AdS/CFT correspondence in a Friedmann-Lemaitre-Robertson-Walker braneFeb 15 2004Aug 30 2004According to the AdS/CFT correspondence conjecture, the Randall-Sundrum infinite braneworld is equivalent to four dimensional Einstein gravity with ${\cal N}=4$ super Yang-Mills fields at low energies. Here we derive a four dimensional effective equation ... 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

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

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

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