arXiv subjects
Publications and source records attributed to K. Itakura.
We study resonances for the Schr\"odinger operators with quadratic or sub-quadratic repulsive potential. In the present paper, we show the non-existence of resonances in some complex neighborhood of a fixed energy by employing schemes of Briet-Combes-Duclos and Hunziker and by introducing a proper distortion based on, but slightly modified, positive commutator method of Mourre.
We study the stationary scattering theory for a perturbed 1-body Stark operator. We prove existence and completeness of the stationary wave operators, construct the associated generalized Fourier transforms, and characterize asymptotics of the generalized eigenfunctions of minimal growths in terms of the stationary scattering matrix.
We investigate spectral theory for a large class of one-body Stark Hamiltonians using a commutator technique. Our results include Rellich's theorem, the limiting absorption principle, radiation condition bounds and Sommerfeld's uniqueness theorem, all stated and proved in the framework of Besov spaces.
We develop a new scheme of proofs for spectral theory of the $N$-body Schrödinger operators, reproducing and extending a series of sharp results under minimum conditions. Our main results include Rellich's theorem, limiting absorption principle bounds, microlocal resolvent bounds, Hölder continuity of the resolvent and a microlocal Sommerfeld uniqueness result. We present a new proof of Rellich's theorem which is unified with exponential decay estimates studied previously only for $L^2$-eigenfunctions. Each pair-potential is a sum of a long-range term with first order derivatives, a short-range term without derivatives and a singular term of operator- or form-bounded type, and the setup includes hard-core interaction. Our proofs consist of a systematic use of commutators with `zeroth order' operators. In particular they do not rely on Mourre's differential inequality technique.
In order to describe forward hadron productions in high-energy nuclear collisions, we propose a Monte-Carlo implementation of Dumitru-Hayashigaki-Jalilian-Marian formula with the unintegrated gluon distribution obtained numerically from the running-coupling BK equation. We discuss influence of initial conditions for the BK equation by comparing a model constrained by global fit of small-x HERA data and a newly proposed one from the running coupling MV model.
A homogeneous color magnetic field is known to be unstable for the fluctuations perpendicular to the field in the color space (the Nielsen-Olesen instability). We argue that these unstable modes, exponentially growing, generate an azimuthal magnetic field with the original field being in the z-direction, which causes the Nielsen-Olesen instability for another type of fluctuations. The growth rate of the latter unstable mode increases with the momentum p_z and can become larger than the former's growth rate which decreases with increasing p_z. These features may explain the interplay between the primary and secondary instabilities observed in the real-time simulation of a non-expanding glasma, i.e., stochastically generated anisotropic Yang-Mills fields without expansion.
Proceedings of ISMD08
Strong longitudinal color flux fields will be created in the initial stage of high-energy nuclear collisions. We investigate analytically time evolution of such boost-invariant color fields from Abelian-like initial conditions, and next examine stability of the boost-invariant configurations against rapidity dependent fluctuations. We find that the magnetic background field has an instability induced by the lowest Landau level whose amplitude grows exponentially. For the electric background field there is no apparent instability although pair creations due to the Schwinger mechanism should be involved.
We present an analytic study of the physics of the glasma which is a strong classical gluon field created at early stage of high-energy heavy-ion collisions. Our analysis is based on the picture that the glasma just after the collision is made of color electric and magnetic flux tubes extending in the longitudinal direction with their diameters of the order of 1/Q_s (Q_s is the saturation scale of the colliding nuclei). We find that both the electric and magnetic flux tubes expand outwards and the field strength inside the flux tube decays rapidly in time. Next we investigate whether there exist instabilities against small rapidity-dependent perturbations for a fixed color configuration. We find that the magnetic background field exhibits an instability induced by the fluctuations in the lowest Landau level, and it grows in the time scale of 1/Q_s. For the electric background field we find no apparent instability while the possible relation to the Schwinger mechanism for particle pair creations is suggested.
We investigate the effects of baryon chemical potential μon the shear viscosity coefficient ηand the viscosity to entropy density ratio η/s of a pion-nucleon gas mixture. We find that ηis an increasing function of T and μ, while the ratio η/s turns to a decreasing function in a wide region of T-μplane. In the kinematical region we studied, the smallest value of η/s is about 0.3.
I discuss recent results on the Color Glass Condensate which is a dense saturated gluonic state and appears as the universal picture of hadrons or nuclei at very high energies.
We propose an effective theory which governs Pomeron dynamics in QCD at high energy, in the leading logarithmic approximation, and in the limit where N_c, the number of colors, is large. In spite of its remarkably simple structure, this effective theory generates precisely the evolution equations for scattering amplitudes that have been recently deduced from a more complete microscopic analysis. It accounts for the BFKL evolution of the Pomerons together with their interactions: dissociation (one Pomeron splitting into two) and recombination (two Pomerons merging into one). It is constructed by exploiting a duality principle relating the evolutions in the target and the projectile, more precisely, splitting and merging processes, or fluctuations in the dilute regime and saturation effects in the dense regime. The simplest Pomeron loop calculated with the effective theory is free of both ultraviolet or infrared singularities.
We discuss the definition and the energy evolution of scattering amplitudes with $C$-odd ("odderon") quantum numbers within the effective theory for the Color Glass Condensate (CGC) endowed with the functional, JIMWLK, evolution equation. We explicitly construct gauge-invariant amplitudes describing multiple odderon exchanges in the scattering between the CGC and two types of projectiles: a color--singlet quark--antiquark pair (or `color dipole') and a system of three quarks in a colorless state. We deduce the energy evolution of these amplitudes from the general JIMWLK equation, which for this purpose is recast in a more synthetic form, which is manifestly infrared finite. For the dipole odderon, we confirm and extend the non--linear evolution equations recently proposed by Kovchegov, Szymanowski and Wallon, which couple the evolution of the odderon to that of the pomeron, and predict the rapid suppression of the odderon exchanges in the saturation regime at high energy. For the 3--quark system, we focus on the linear regime at relatively low energy, where our general equations are shown to reduce to the Bartels--Kwiecinski--Praszalowicz equation. Our gauge--invariant amplitudes, and the associated evolution equations, stay explicitly outside the Möbius representation, which is the Hilbert space where the BFKL Hamiltonian exhibits holomorphic separability.
We study the properties of light mesons in the scalar, pseudo-scalar, and vector channels within the light-front quantization, by using the (one flavor) Nambu--Jona-Lasinio model with vector interaction. After taking into account the effects of chiral symmetry breaking, we derive the bound-state equation in each channel in the large N limit (N is the number of colors), which means that we consider the lowest q\bar{q} Fock state with the constituent quark and antiquark. By solving the bound-state equation, we simultaneously obtain a mass and a light-cone (LC) wavefunction of the meson. While we reproduce the previous results for the scalar and pseudo-scalar mesons, we find that, for a vector meson, the bound-state equations for the transverse and longitudinal polarizations look different from each other. However, eventually after imposing a cutoff which is invariant under the parity and boost transformations, one finds these two are identical, giving the same mass and the same (spin-independent) LC wavefunction. When the vector interaction becomes larger than a critical value, the vector state forms a bound state, whose mass decreases as the interaction becomes stronger. While the LC wavefunction of the pseudo-scalar meson is broadly distributed in longitudinal momentum (x) space, that of the vector meson is squeezed around x=1/2.
We present a systematic, and fully analytic, study of the ratio R_{pA} between the gluon distribution in a nucleus and that in a proton scaled up by the atomic number A. We consider initial conditions of the McLerran-Venugopalan type, and quantum evolution in the Color Glass Condensate, with both fixed and running coupling. We perform an analytic study of the Cronin effect in the initial conditions and point out an interesting difference between saturating effects and twist effects in the nuclear gluon distribution. We show that the distribution of the gluons which make up the condensate in the initial conditions is localized at low momenta, but this particular feature does not survive after the quantum evolution. We demonstrate that the rapid suppression of the ratio R_{pA} in the early stages of the evolution is due to the DGLAP-like evolution of the proton, whose gluon distribution grows much faster than that in the nucleus because of the large separation between the respective saturation momenta. The flattening of the Cronin peak, on the other hand, is due to the evolution of the nucleus. We show that the running coupling effects slow down the evolution, but eventually lead to a stronger suppression in R_{pA} at sufficiently large energies.
We apply the light-front quantization to the Nambu--Jona-Lasinio model with the vector interaction, and compute vector meson's mass and light-cone wavefunction in the large N limit. Following the same procedure as in the previous analyses for scalar and pseudo-scalar mesons, we derive the bound-state equations of a q-qbar system in the vector channel. We include the lowest order effects of the vector interaction. The resulting transverse and longitudinal components of the bound-state equation look different from each other. But eventually after imposing an appropriate cutoff, one finds these two are identical, giving the same mass and the same (spin-independent) light-cone wavefunction. Mass of the vector meson decreases as one increases the strength of the vector interaction.
We show that the HERA data for the inclusive structure function F_2(x,Q^2) for x < 0.01 and 0.045 < Q^2 < 45 GeV^2 can be well described within the color dipole picture, with a simple analytic expression for the dipole-proton scattering amplitude, which is an approximate solution to the non-linear evolution equations in QCD. For dipole sizes less than the inverse saturation momentum 1/Q_s(x), the scattering amplitude is the solution to the BFKL equation in the vicinity of the saturation line. It exhibits geometric scaling and scaling violations by the diffusion term. For dipole sizes larger than 1/Q_s(x), the scattering amplitude saturates to one. The fit involves three parameters: the proton radius R, the value x_0 of x at which the saturation scale Q_s equals 1GeV, and the logarithmic derivative of the saturation momentum λ. The value of λextracted from the fit turns out to be consistent with a recent calculation using the next-to-leading order BFKL formalism.
We demonstrate that the dipole-hadron cross-section computed from the non-linear evolution equation for the Colour Glass Condensate saturates the Froissart bound in the case of a fixed coupling and for a small dipole (Q^2 >> Lambda_{QCD}^2). That is, the cross-section increases as the logarithm squared of the energy, with a proportionality coefficient involving the pion mass and the BFKL intercept (alpha_s N_c/pi)4 ln 2. The pion mass enters via the non-perturbative initial conditions at low energy. The BFKL equation emerges as a limit of the non-linear evolution equation valid in the tail of the hadron wavefunction. We provide a physical picture for the transverse expansion of the hadron with increasing energy, and emphasize the importance of the colour correlations among the saturated gluons in suppressing non-unitary contributions due to long-range Coulomb tails. We present the first calculation of the saturation scale including the impact parameter dependence. We show that the cross-section at high energy exhibits geometric scaling with a different scaling variable as compared to the intermediate energy regime.