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A Serre weight conjecture for geometric Hilbert modular forms in characteristic pDec 11 2017Let p be a prime and F a totally real field in which p is unramified. We consider mod p Hilbert modular forms for F, defined as sections of automorphic line bundles on Hilbert modular varieties of level prime to p in characteristic p. For a mod p Hilbert ... More

Neutrino Telescope Array Letter of Intent: A Large Array of High Resolution Imaging Atmospheric Cherenkov and Fluorescence Detectors for Survey of Air-showers from Cosmic Tau Neutrinos in the PeV-EeV Energy RangeAug 26 2014Jul 22 2015This Letter of Intent (LoI) describes the outline and plan for the Neutrino Telescope Array (NTA) project. High-energy neutrinos provide unique and indisputable evidence for hadronic acceleration. Recently, IceCube has reported astronomical neutrino candidates ... More

$p$-adic Gross-Zagier formula at critical slope and a conjecture of Perrin-Riou - INov 20 2018Let $p$ be an odd prime. Given an imaginary quadratic field $K=\mathbb{Q}(\sqrt{-D_K})$ where $p$ splits with $D_K>3$, and a $p$-ordinary newform $f \in S_k(\Gamma_0(N))$ such that $N$ verifies the Heegner hypothesis relative to $K$, we prove a $p$-adic ... More

Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified caseApr 03 2012May 21 2013We extend the modularity lifting result of the arXiv:1111.2804 to allow Galois representations with some ramification at p. We also prove modularity mod 2 and 5 of certain Galois representations. We use these results to prove many new cases of the strong ... More

Exactly and quasi-exactly solvable `discrete' quantum mechanicsApr 27 2010Brief introduction to the discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators, dynamical ... More

Quasi Exactly Solvable Difference EquationsAug 06 2007Oct 11 2007Several explicit examples of quasi exactly solvable `discrete' quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogues of the well-known quasi exactly ... More

Reformulation of the Stochastic Potential Switching Algorithm and a Generalized Fourtuin-Kasteleyn RepresentationJan 07 2010Aug 30 2010A new formulation of the stochastic potential switching algorithm is presented. This reformulation naturally leads us to a generalized Fourtuin-Kasteleyn representation of the partition function Z. A formula for internal energy E and that of heat capacity ... More

Latent Semantic Word Sense Disambiguation Using Global Co-occurrence InformationMar 05 2014In this paper, I propose a novel word sense disambiguation method based on the global co-occurrence information using NMF. When I calculate the dependency relation matrix, the existing method tends to produce very sparse co-occurrence matrix from a small ... More

Chiral Symmetry Breaking, Trace Anomaly and Baryons in Hot and Dense MatterNov 02 2011We propose an effective chiral Lagrangian with a chiral scalar introduced as a dilaton associated with broken conformal symmetry and responsible for the trace anomaly in QCD and discuss the properties of hadronic matter at high density and temperature. ... More

Pion Velocity near the Chiral Phase TransitionFeb 02 2004We study the pion velocity near the critical temperature $T_c$ of chiral symmetry restoration in QCD. Using the hidden local symmetry (HLS) model as the effective field theory, where the chiral symmetry restoration is realized as the vector manifestation ... More

Chiral Thermodynamics of Dense QCDJul 01 2010We show a phase diagram of a two-flavored parity doublet model on top of the nuclear matter ground state within the mean field approximation. An exotic phase with unbroken center symmetry of chiral group is also discussed. When crossing this phase boundary ... More

An intersection functional on the space of subset currents on a free groupMar 26 2014Feb 05 2015Kapovich and Nagnibeda introduced the space $\mathcal{S} {\rm Curr}(F_N)$ of subset currents on a free group $F_N$ of rank $N\geq 2$, which can be thought of as a measure-theoretic completion of the set of all conjugacy classes of finitely generated subgroups ... More

A Cartan decomposition for non-symmetric reductive spherical pairs of rank-one type and its application to visible actionsJul 31 2018Oct 15 2018A Cartan decomposition for symmetric pairs plays an important role to study not only orbit geometry of the symmetric spaces but also harmonic analysis on them. For non-symmetric reductive pairs, there are examples of generalizations of Cartan decompositions ... More

Inverse scattering problems for the Hartree equation whose interaction potential decays rapidlyAug 06 2011We consider inverse scattering problems for the three-dimensional Hartree equation. We prove that if the unknown interaction potential $V(x)$ of the equation satisfies some rapid decay condition, then we can uniquely determine the exact value of $\partial_\xi^\alpha ... More

Nonlinear curvature perturbations in an exactly soluble model of multi-component slow-roll inflationFeb 07 2007Mar 27 2007Using the nonlinear $\delta N$ formalism, we consider a simple exactly soluble model of multi-component slow-roll inflation in which the nonlinear curvature perturbation can be evaluated analytically.

Post-Newtonian Expansion of the Ingoing-Wave Regge-Wheeler FunctionFeb 24 1994We present a method of post-Newtonian expansion to solve the homogeneous Regge-Wheeler equation which describes gravitational waves on the Schwarzschild spacetime. The advantage of our method is that it allows a systematic iterative analysis of the solution. ... More

Symmetric Morse potential is exactly solvableNov 18 2016Nov 28 2016Morse potential $V_M(x)= g^2\exp (2x)-g(2h+1)\exp(x)$ is defined on the full line, $-\infty<x<\infty$ and it defines an exactly solvable 1-d quantum mechanical system with finitely many discrete eigenstates. By taking its right half $0\le x<\infty$ and ... More

One Particle Binding of Many-Particle Semi-Relativistic Pauli-Fierz ModelMar 20 2013Mar 25 2013It is shown that at least one particle is bound in the $N$-particle semi-relativistic Pauli-Fierz model with negative potential $V(\bx)$. It is assumed that the particles have no spin and obey the Bose or Boltzmann statistics, and the one particle Hamiltonian ... More

Yang-Mills Thermodynamics: an Effective Theory ApproachDec 13 2013We derive the Polyakov-loop thermodynamic potential in the perturbative approach to pure SU(3) Yang-Mills theory. The potential expressed in terms of the Polyakov loop in the fundamental representation corresponds to that of the strong-coupling expansion, ... More

Selected Issues in Thermal Field TheoryAug 04 2014New developments on hot and dense QCD in effective field theories are reviewed. Recent investigations in lattice gauge theories for the low-lying Dirac eigenmodes suggest survival hadrons in restored phase of chiral symmetry. We discuss expected properties ... More

The Phase Structure of Dense QCD from Chiral ModelsOct 22 2009A new phase of dense QCD proposed in the limit of large number of colors, Quarkyonic Phase, is discussed in chiral approaches. The interplay between chiral symmetry breaking and confinement together with the $N_c$ dependence of the phase diagram are dealt ... More

Symmetric Morse potential is exactly solvableNov 18 2016Morse potential $V_M(x)= g^2\exp (2x)-g(2h+1)\exp(x)$ is defined on the full line, $-\infty<x<\infty$ and it defines an exactly solvable 1-d quantum mechanical system with finitely many discrete eigenstates. By taking its right half $0\le x<\infty$ and ... More

Confining non-analytic exponential potential $V(x)= g^2\exp\,(2|x|)$ and its exact Bessel-function solvabilityNov 08 2016In a previous paper we have shown that Schr\"{o}dinger equation with the non-analytic attractive exponential potential $V(x)= -g^2\exp (-|x|)$ is exactly solvable. It has finitely many discrete eigenstates described by the Bessel function of the first ... More

Interplay between chromoelectric and chromomagnetic gluons in Yang-Mills thermodynamicsDec 18 2013We propose an effective theory of SU(3) gluonic matter where interactions between color-electric and color-magnetic gluons are constrained by the center and scale symmetries. Through matching to the dimensionally-reduced magnetic theories, the magnetic ... More

Thermodynamics of dense matter in chiral approachesApr 29 2010We discuss phases in dense hadronic and quark matter from chiral model approaches. Within PNJL models the phase diagram for various number of colors $N_c$ is studied. How phases are constrained in quantum field theories are also discussed along with the ... More

Chiral Thermodynamics with CharmFeb 27 2015Chiral thermodynamics of charmed mesons is formulated at finite temperature within a $2+1+1$-flavored effective Lagrangian incorporating heavy quark symmetry. The chiral mass splittings are shown to be less sensitive to the light-quark flavors, attributed ... More

A Class of FRT Quantum Groups and Fun$_q$(G$_2$) as a Special CaseNov 25 1993Dec 22 1993Citations are updated; referred papers are increased. An error right after the eq.~(27) is corrected, and several chages (not serious) are made.

Exactly Solvable Birth and Death ProcessesMar 18 2009Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable `matrix' ... More

Fate of charmed mesons near chiral symmetry restoration in hot matterSep 11 2014Nov 07 2014Chiral thermodynamics of charmed mesons is formulated at finite temperature within a $2+1+1$-flavored effective Lagrangian incorporating heavy quark symmetry. The charmed-meson mean fields act as an extra source which breaks the chiral symmetry explicitly. ... More

Chiral thermodynamics of dense hadronic matterDec 23 2010We discuss phases of hot and dense hadronic matter using chiral Lagrangians. A two-flavored parity doublet model constrained by the nuclear matter ground state predicts chiral symmetry restoration. The model thermodynamics is shown within the mean field ... More

Non-renormalization Theorem Originating in a New Fixed Point of the Vector ManifestationMay 31 2003Apr 02 2004We study the pion velocity at the critical temperature of chiral symmetry restoration in QCD. Starting from the premise that the bare effective field theory is to be defined from the underlying QCD, we incorporate the effects of Lorentz non-invariance ... More

Suppression of the repulsive force in nuclear interactions near the chiral phase transitionJan 26 2012We introduce an effective chiral Lagrangian with a dilaton responsible for the trace anomaly in QCD. As the "dilaton limit" is taken, which drives a system to near chiral restoration density, a linear sigma model emerges from the highly non-linear structure. ... More

Chiral Phase Transition in QCD and Vector ManifestationApr 09 2005Spontaneous chiral symmetry breaking is one of the most important features in low-energy QCD. The chiral symmetry is expected to be restored at very high temperature and/or density. Accompanied by the chiral phase transition, properties of hadrons will ... More

Violation of Vector Dominance in the Vector ManifestationApr 30 2003The vector manifestation (VM) is a new pattern for realizing the chiral symmetry in QCD. In the VM, the massless vector meson becomes the chiral partner of pion at the critical point, in contrast with the restoration based on the linear sigma model. Including ... More

On zeros of exponential polynomials and quantum algorithmsAug 12 2009We calculate the zeros of an exponential polynomial of some variables by a classical algorithm and quantum algorithms which are based on the method of van Dam and Shparlinski, they treated the case of two variables, and compare with the complexity of ... More

Neural-network Kohn-Sham exchange-correlation potential and its out-of-training transferabilityFeb 08 2018We incorporate in the Kohn-Sham self consistent equation a trained neural-network projection from the charge density distribution to the Hartree-exchange-correlation potential $n \rightarrow V_{\rm Hxc}$ for possible numerical approach to the exact Kohn-Sham ... More

One loop quantum fluctuations to the energy of the non-topological soliton in Friedberg-Lee modelJul 06 2016I have used a practical method to calculate the one-loop quantum correction to the energy of the non-topological soliton in Friedberg-Lee model. The quantum effects which come from the quarks of the Dirac sea scattering with the soliton bag are calculated ... More

Spontaneous Lorentz Violation and BaryogenesisNov 15 2007Dec 18 2007In the presence of background fields that spontaneously violate Lorentz invariance, a matter-antimatter asymmetry can be generated even in thermal equilibrium. In this paper we systematically investigate models of this type, showing that either high-energy ... More

Remarks on scattering matrices for Schrödinger operators with critically long-range perturbationsApr 16 2018Nov 18 2018We consider scattering matrix for Schr\"odinger-type operators on $R^d$ with perturbation $V(x)=O(\langle x\rangle^{-1})$ as $|x|\to\infty$. We show that the scattering matrix (with time-independent modifiers) is a pseudodifferential operator. We present ... More

Microlocal resolvent estimates, revisitedFeb 10 2016Apr 25 2016Let $H$ be a Schr\"odinger type operator with long-range perturbation. We study the wave front set of the distribution kernel of $(H-\lambda\mp i0)^{-1}$, where $\lambda$ is in the absolutely continous spectrumof $H$.The result is a refinement of the ... More

Convergence Rates of Neumann problems for Stokes SystemsDec 27 2015This paper studies the convergence rates in $L^2$ and $H^1$ of Neumann problems for Stokes systems with rapidly oscillating periodic coefficients, without any smoothness assumptions on the coefficients.

Hamilton-Jacobi equations on graph and applicationsDec 08 2015This paper introduces a notion of gradient and an infimal-convolution operator that extend properties of solutions of Hamilton Jacobi equations to more general spaces, in particular to graphs. As a main application, the hypercontractivity of this class ... More

Monte Carlo modeling of Standard Model multi-boson production processes for $\sqrt{s} = 13$ TeV ATLAS analysesSep 01 2017Proceeding for LHCP2017 conference. Referencing the ATLAS publication note: http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PUBNOTES/ATL-PHYS-PUB-2017-005/

Spectral analysis of non-commutative harmonic oscillators: the lowest eigenvalue and no crossingApr 20 2013Jun 12 2013The lowest eigenvalue of non-commutative harmonic oscillators $Q$ is studied. It is shown that $Q$ can be decomposed into four self-adjoint operators, and all the eigenvalues of each operator are simple. We show that the lowest eigenvalue $E$ of $Q$ is ... More

Casoratian Identities for the Wilson and Askey-Wilson PolynomialsAug 20 2013Apr 17 2014Infinitely many Casoratian identities are derived for the Wilson and Askey-Wilson polynomials in parallel to the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials, which were reported recently by the present authors. These identities ... More

Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal PolynomialsMay 03 2011Jun 28 2011Infinite families of multi-indexed orthogonal polynomials are discovered as the solutions of exactly solvable one-dimensional quantum mechanical systems. The simplest examples, the one-indexed orthogonal polynomials, are the infinite families of the exceptional ... More

Dual Christoffel transformationsJan 28 2011May 08 2011Crum's theorem and its modification a la Krein-Adler are formulated for the discrete quantum mechanics with real shifts, whose eigenfunctions consist of orthogonal polynomials of a discrete variable. The modification produces the associated polynomials ... More

Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomialsNov 09 2009We provide analytic proofs for the shape invariance of the recently discovered (Odake and Sasaki, Phys. Lett. B679 (2009) 414-417) two families of infinitely many exactly solvable one-dimensional quantum mechanical potentials. These potentials are obtained ... More

q-oscillator from the q-Hermite PolynomialOct 11 2007Apr 04 2008By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the q-oscillator are obtained. They satisfy a q-oscillator algebra as a consequence of the shape-invariance ... More

Exact Heisenberg operator solutions for multi-particle quantum mechanicsJun 06 2007Exact Heisenberg operator solutions for independent `sinusoidal coordinates' as many as the degree of freedom are derived for typical exactly solvable multi-particle quantum mechanical systems, the Calogero systems based on any root system. These Heisenberg ... More

Another set of infinitely many exceptional (X_{\ell}) Laguerre polynomialsNov 18 2009We present a new set of infinitely many shape invariant potentials and the corresponding exceptional (X_{\ell}) Laguerre polynomials. They are to supplement the recently derived two sets of infinitely many shape invariant thus exactly solvable potentials ... More

Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent statesFeb 07 2008Various examples of exactly solvable `discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent states. The eigenfunctions ... More

Shape Invariant Potentials in "Discrete Quantum Mechanics"Oct 10 2004Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant ``discrete quantum mechanical systems" are introduced and discussed in some detail. They arise in the problem of describing the ... More

Classical vs Quantum Mechanics: role of elementary excitationsAug 07 2003Oct 16 2003Simple theorems relating a quantum mechanical system to the corresponding classical one at equilibrium and connecting the quantum eigenvalues to the frequencies of normal modes oscillations are presented. Corresponding to each quantum eigenfunction, a ... More

Numerical Detection of the Ergodicity Breaking in a Lattice Glass ModelJan 20 2014We directly detect the ergodicity breaking in a lattice glass model by a numerical simulation. The obtained results nicely agree with those by the cavity method that the model on a regular random graph exhibits a dynamical transition with the ergodicity ... More

Braneworld inflation driven by dynamics of a bulk scalar fieldFeb 13 2003Feb 21 2003We review a viable alternative scenario of the inflationary universe in the context of the Randall-Sundrum (RS) braneworld. In this scenario, the dynamics of a 5-dimensional scalar field, which we call a bulk scalar field, plays the central role. Focusing ... More

Radion on the de Sitter braneNov 22 2000Dec 04 2000The radion on the de Sitter brane is investigated at the linear perturbation level, using the covariant curvature tensor formalism developed by Shiromizu, Maeda and Sasaki. It is found that if there is only one de Sitter brane with positive tension, there ... More

Grad-Shafranov equation in noncircular stationary axisymmetric spacetimesFeb 26 2003Sep 08 2003A formulation is developed for general relativistic ideal magnetohydrodynamics in stationary axisymmetric spacetimes. We reduce basic equations to a single second-order partial differential equation, the so-called Grad-Shafranov (GS) equation. Our formulation ... More

Cherenkov Tau Shower Earth-Skimming Method for PeV-EeV Tau Neutrino Observation with AshraFeb 25 2012Oct 01 2012We describe a method of observation for PeV--EeV tau neutrinos using Cherenkov light from the air showers of decayed taus produced by tau neutrino interactions in the Earth. Aiming for the realization of neutrino astronomy utilizing the Earth-skimming ... More

Large-scale magnetic fields in the inflationary universeNov 22 2006The generation of large-scale magnetic fields is studied in inflationary cosmology. We consider the violation of the conformal invariance of the Maxwell field by dilatonic as well as non-minimal gravitational couplings. We derive a general formula for ... More

Stability of Q-balls and CatastropheDec 10 2007Jun 05 2008We propose a practical method for analyzing stability of Q-balls for the whole parameter space, which includes the intermediate region between the thin-wall limit and thick-wall limit as well as Q-bubbles (Q-balls in false vacuum), using the catastrophe ... More

Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receiversJun 07 2007Aug 14 2008We address the limit of the Gaussian operations and classical communication in the problem of quantum state discrimination. We show that the optimal Gaussian strategy for the discrimination of the binary phase shift keyed (BPSK) coherent signal is a simple ... More

Novel spectral broadening from vector--axial-vector mixing in dense matterOct 18 2009In this write-up we summarize main result of our recent analysis on the mixing between transverse $\rho$ and $a_1$ mesons through a set of $\omega\rho a_1$-type interactions in dense baryonic matter. In the analysis, we showed that a clear enhancement ... More

Dilepton Production from Dropping rho in the Vector ManifestationFeb 25 2008In this write-up we summarize the main result of our analysis on the thermal dilepton production rate from the dropping rho based on the vector manifestation (VM). In the analysis, we showed that the effect of the strong violation of the vector dominance ... More

Transport coefficients near chiral phase transitionNov 28 2008We analyze the transport properties of relativistic fluid composed of constituent quarks at finite temperature and density. We focus on the shear and bulk viscosities and study their behavior near chiral phase transition. We model the constituent quark ... More

Memory Effect, Rejuvenation and Chaos Effect in the Multi-layer Random Energy ModelFeb 02 2000We introduce magnetization to the Multi-layer Random Energy Model which has a hierarchical structure, and perform Monte Carlo simulation to observe the behavior of ac-susceptibility. We find that this model is able to reproduce three prominent features ... More

Correlations between light and heavy flavors near the chiral crossoverDec 23 2014Mar 07 2015Thermal fluctuations and correlations between the light and heavy-light mesons are explored within a chiral effective theory implementing heavy quark symmetry. We show, that various heavy-light flavor correlations indicate a remnant of the chiral criticality ... More

Non-equilibrium Ionization State of Warm-Hot Intergalactic MediumMar 03 2006Jun 13 2006Time evolution of the ionization state of metals in the cosmic baryons is investigated in a cosmological context without the assumption of ionization equilibrium. We find that a significant fraction of ionized oxygen ions (OVII and OVIII) in the warm-hot ... More

Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theorySep 22 2016We study several types of tree-level improvement in the Yang-Mills gradient flow method in order to reduce the lattice discretization errors in line with a reference [Fodor et al., arXiv:1406.0827]. The tree-level $\mathcal{O}(a^2)$ improvement can be ... More

Quantum Fluctuations for de Sitter Branes in Bulk AdS(5)Nov 17 2004Jan 30 2005The vacuum expectation value of the square of the field fluctuations of a scalar field on a background consisting of {\it two} de Sitter branes embedded in an anti-de Sitter bulk are considered. We apply a dimensional reduction to obtain an effective ... More

Linearized gravity on the de Sitter brane in the Einstein Gauss-Bonnet theoryApr 22 2004May 02 2004We investigate the linearized gravity on a single de Sitter brane in the anti-de Sitter (AdS) bulk in the Einstein Gauss-Bonnet (EGB) theory. We find that the Einstein gravity is recovered for a high energy brane, i.e., in the limit of the large expansion ... More

Geometrical Conditions for CPTP Maps and their Application to a Quantum Repeater and a State-dependent Quantum Cloning MachineApr 02 2003We address the problem of finding optimal CPTP (completely positive, trace preserving) maps between a set of binary pure states and another set of binary generic mixed state in a two dimensional space. The necessary and sufficient conditions for the existence ... More

Casimir energy for de Sitter branes in bulk AdS(5)May 27 2002Aug 14 2002The vacuum energy for a massless conformally coupled scalar field in a brane world set up, corresponding to de Sitter branes in a bulk anti-de Sitter spacetime, is calculated. We use the Euclidean version of the metric which can be conformally related ... More

Quantum Radion on de Sitter branesJan 10 2002The quantum fluctuation of the relative location of two (n-1)-dimensional de Sitter branes (i.e., of n spacetime dimensions) embedded in the (n+1)-dimensional anti-de Sitter bulk, which we shall call the quantum radion, is investigated at the linear perturbation ... More

Polarization Signal of Distant Clusters and Reconstruction of Primordial Potential FluctuationsSep 14 2000We examine the polarization signal of the cosmic microwave background radiation associated with distant clusters. The polarization is induced by the Thomson scattering of microwave photons with ionized gas of clusters and contains information of quadrupole ... More

Effective gluon potential and Yang-Mills thermodynamicsJan 31 2013We derive the Polyakov-loop thermodynamic potential in the perturbative approach to pure SU(3) Yang-Mills theory. The potential expressed in terms of the Polyakov loop in the fundamental representation corresponds to that of the strong-coupling expansion, ... More

Reflectionless Potentials for Difference Schrödinger EquationsNov 10 2014Jan 31 2015As a part of the program `discrete quantum mechanics,' we present general reflectionless potentials for difference Schr\"odinger equations with pure imaginary shifts. By combining contiguous integer wave number reflectionless potentials, we construct ... More

Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum DilogarithmJun 11 2014Jun 26 2015Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the main parts of the eigenfunctions of new solvable discrete quantum mechanical systems. Their orthogonality weight functions consist of quantum dilogarithm functions, which are ... More

Multi-indexed (q-)Racah PolynomialsMar 27 2012Aug 01 2012As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of `discrete quantum mechanics' with real shifts in one dimension, the multi-indexed (q-)Racah polynomials. They are obtained from the (q-)Racah polynomials ... More

Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum MechanicsMay 09 2005Certain aspects of the integrability/solvability of the Calogero-Sutherland-Moser systems and the Ruijsenaars-Schneider-van Diejen systems with rational and trigonometric potentials are reviewed. The equilibrium positions of classical multi-particle systems ... More

Polynomials Associated with Equilibrium Positions in Calogero-Moser SystemsJun 19 2002In a previous paper (Corrigan-Sasaki), many remarkable properties of classical Calogero and Sutherland systems at equilibrium are reported. For example, the minimum energies, frequencies of small oscillations and the eigenvalues of Lax pair matrices at ... More

Non-polynomial extensions of solvable potentials a la Abraham-MosesJul 03 2013Abraham-Moses transformations, besides Darboux transformations, are well-known procedures to generate extensions of solvable potentials in one-dimensional quantum mechanics. Here we present the explicit forms of infinitely many seed solutions for adding ... More

Generalized Systematic Debugging for Attribute GrammarsOct 15 2003Attribute grammars (AGs) are known to be a useful formalism for semantic analysis and translation. However, debugging AGs is complex owing to inherent difficulties of AGs, such as recursive grammar structure and attribute dependency. In this paper, a ... More

Odd-frequency Cooper pairs in two-band superconductors and their magnetic responseOct 26 2015Dec 21 2015We discuss odd-frequency Cooper pairs appearing in two-band superconductors by solving the Gor'kov equation analytically. We introduce the equal-time $s$-wave pair potentials as realized in MgB$_2$ and iron pnictides. Although the order parameter symmetry ... More

Quantum-Gravity Phenomenology and the DSR Ether TheoriesSep 20 2010Guided primarily by versions of a theoretical framework called Doubly Special Relativity, or DSR, that are supposed to entail speeds of light that vary with energy while preserving the relativity of inertial frames, quantum-gravity phenomenologists have ... More

I=2 Two-Pion Wave Functions with Non-zero Total MomentumOct 02 2007We calculate the two-pion wave function for the I=2 $S$-wave two-pion system with a finite scattering momentum and estimate the interaction range between two pions. It allows us to examine the validity of the necessary condition for the finite-volume ... More

Characteristic Behavior of Toroidal Carbon Nanotubes: Kinematics of Persistent CurrentsJul 15 2003Aug 24 2004The electrical properties of a carbon nanotube depend strongly on its lattice structure as defined by chiral and translational vectors. A toroidal shape for a nanotube allows various twisted structures to exist along the direction of the tube axis. We ... More

Polarized and Unpolarized Structures of the Virtual PhotonOct 12 2000We discuss the structure functions and the parton distributions in the virtual photon target, both polarized and unpolarized, beyond the leading order in QCD. We study the factorization-scheme dependence of the parton distributions.

The Gluon Self-Energy in the Coulomb and Temporal Axial Gauges via the Pinch TechniqueJun 07 1996The $S$-matrix pinch technique is used to derive an effective gluon self-energy to one-loop order, when the theory is quantized in the Coulomb gauge (CG) and in the temporal axial gauge (TAG). When the pinch contributions are added, the gluon self-energies ... More

Generalized Entropy Composition with Different q Indices: A TrialApr 11 2000We analyze systematically composable composite entropy of two Tsallis subsystems with different q indices. H-theorem and thermal balance relation are commented.

Polarized Parton Distributions in the Photon and Factorization Scheme DependenceNov 20 1999Dec 09 1999Spin-dependent parton distributions in the polarized virtual photon are investigated in QCD up to the next-to-leading order (NLO). In the case $\Lambda^2 \ll P^2 \ll Q^2$, where $-Q^2$ ($-P^2$) is the mass squared of the probe (target) photon, parton ... More

Muonium-Antimuonium Conversion in Models with Dilepton Gauge BosonsApr 04 1995We examine the magnetic field dependence of the muonium($\mu^+ e^-$) - antimuonium($\mu^- e^+$) conversion in the models which accommodate the dilepton gauge bosons. The effective Hamiltonian for the conversion due to dileptons turns out to be in the ... More

Boundary Effects in Integrable Field Theory on a Half LineMar 13 1995Abstarct: Boundary effects caused by the boundary interactions in various integrable field theories on a half line are discussed at the classical as well as the quantum level. Only the so-called ``integrable" boundary interactions are discussed. They ... More

Conjugacy of Borel subalgebras of restricted Lie algeberas and the associated solvabel algebraic groups (I)Apr 04 2014Let (g,[p]) be a finite-dimensional restricted Lie algebra defined over an algebraically closed field K of characteristic p > 0, and G be the adjoint group of g. A Borel subalgebra (or Borel for short) of g is defined as a maximal solvable subalgebra ... More

Unitarity Bounds for New Physics from Axial Coupling at LHCNov 15 2007If a new massive vector boson with nonzero axial couplings to fermions will be observed at LHC, then an upper limit on the scale of new physics could be derived from unitarity of $\mathcal{S}$-matrix. The new physics will involve either new massive fermions, ... More

Canonical heights for random iterations in certain varietiesOct 28 2005We show the existence of canonical heights of subvarieties for bounded sequences of morphisms and give some applications.

Microlocal properties of scattering matricesJul 31 2014We consider scattering theory for a pair of operators $H_0$ and $H=H_0+V$ on $L^2(M,m)$, where $M$ is a Riemannian manifold, $H_0$ is a multiplication operator on $M$ and $V$ is a pseudodifferential operator of order $-\mu$, $\mu>1$. We show that a time-dependent ... More

Symmetric confidence regions and confidence intervals for normal map formulations of stochastic variational inequalitiesJun 26 2014Stochastic variational inequalities (SVI) model a large class of equilibrium problems subject to data uncertainty, and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample average approximation ... More

Non-geometric Five-branes in Heterotic SupergravityAug 04 2016Aug 10 2016We study T-duality chains of five-branes in heterotic supergravity where the first order $\alpha'$-corrections are present. By performing the $\alpha'$-corrected T-duality transformations of the heterotic NS5-brane solutions, we obtain the KK5-brane and ... More

Conditional generation of an arbitrary superposition of coherent statesFeb 13 2007We present a scheme to conditionally generate an arbitrary superposition of a pair of coherent states from a squeezed vacuum by means of the modified photon subtraction where a coherent state ancilla and two on/off type detectors are used. We show that, ... More