Universal correlations of one-dimensional interacting electrons in the gas phase

We consider dynamical correlation functions of short range interacting electrons in one dimension at finite temperature. Below a critical value of the chemical potential there is no Fermi surface anymore, and the system can no longer be described as a Luttinger liquid. Its low temperature thermodynamics is that of an ideal gas. We identify the impenetrable electron gas model as a universal model for the gas phase and present exact and explicit expressions for the asymptotics of correlation functions at small temperatures, in the presence of a magnetic field.Comment: 4 pages, Revte

On the location of two blow up points on an annulus for the mean field equation

We consider the mean field equation on two-dimensional annular domains, and prove that if $P$ and $Q$ are two blow up points of a blowing-up solution sequence of the equation, then we must have $P=-Q$.Comment: To appear in CRA

Role of Large Gluonic Excitation Energy for Narrow Width of Penta-Quark Baryons in QCD String Theory

We study the narrow decay width of low-lying penta-quark baryons in the QCD string theoryin terms of gluonic excitations. In the QCD string theory, the penta-quark baryon decays via a gluonic-excited state of a baryon and meson system, where a pair of Y-shaped junction and anti-junction is created. Since lattice QCD shows that the lowest gluonic-excitation energy takes a large value of about 1 GeV, the decay of the penta-quark baryon near the threshold is considered as a quantum tunneling process via a highly-excited state (a gluonic-excited state) in the QCD string theory. This mechanism strongly suppresses the decay and leads to an extremely narrow decay width of the penta-quark system.Comment: Talk given at International Conference on the Structure of Baryons (Baryons 04) October 25 - 29, 2004, Ecole Polytechnique, Palaiseau, Franc

Relationship between single-particle excitation and spin excitation at the Mott Transition

An intuitive interpretation of the relationship between the dispersion relation of the single-particle excitation in a metal and that of the spin excitation in a Mott insulator is presented, based on the results for the one- and two-dimensional Hubbard models obtained by using the Bethe ansatz, dynamical density-matrix renormalization group method, and cluster perturbation theory. The dispersion relation of the spin excitation in the Mott insulator is naturally constructed from that of the single-particle excitation in the zero-doping limit in both one- and two-dimensional Hubbard models, which allows us to interpret the doping-induced states as the states that lose charge character toward the Mott transition. The characteristic feature of the Mott transition is contrasted with the feature of a Fermi liquid and that of the transition between a band insulator and a metal.Comment: 6 pages, 2 figures, to appear in JPS Conf. Pro

Low-lying Dirac eigenmodes and monopoles in 3+1D compact QED

We study the properties of low-lying Dirac modes in quenched compact QED at $\beta =1.01$, employing $12^3\times N_t$ ($N_t =4,6,8,10,12$) lattices and the overlap formalism for the fermion action. We pay attention to the spatial distributions of low-lying Dirac modes below and above the ``phase transition temperature'' $T_c$. Near-zero modes are found to have universal anti-correlations with monopole currents, and are found to lose their temporal structures above $T_c$ exhibiting stronger spatial localization properties. We also study the nearest-neighbor level spacing distribution of Dirac eigenvalues and find a Wigner-Poisson transition.Comment: 10 pages, 10 figures, 1 tabl

Flat Spectrum X-ray Emission from the Direction of a Molecular Cloud Associated with SNR RX J1713.7-3946

We report on the discovery of a hard X-ray source with ASCA from a molecular cloud in the vicinity of the SNR RX J1713.7-3946. The energy spectrum (1--10 keV) shows a flat continuum which is described by a power-law with photon index 1.0 +-0.4. We argue that this unusually flat spectrum can be best interpreted in terms of characteristic bremsstrahlung emission from the ionization-loss-flattened distribution of either sub-relativistic protons or mildly-relativistic electrons. The strong shock of the SNR RX J1713.7-3946, which presumably interacts with the molecular cloud, as evidenced by observations of CO-lines, seems to be a natural site of acceleration of such sub- or mildly-relativistic nonthermal particles. However, the observed X-ray luminosity of 1.7 10^35 erg/s (for 6 kpc distance) requires that a huge kinetic energy of about 10^50 erg be released in the form of nonthermal particles to illuminate the cloud. The shock-acceleration at RX J1713.7-3946 can barely satisfy this energetic requirement, unless (i) the source is located much closer than 6 kpc and/or (ii) the mechanical energy of the explosion essentially exceeds 10^51 erg. Another possibility would be that an essential part of the "lost" energy is somehow converted to plasma waves, which return this energy to nonthermal particles through their turbulent reacceleration on plasma waves. Irrespective of mechanisms responsible for production of high-energy particles, the flat X-ray emission seems to be a signature of a new striking energetic phenomenon in molecular clouds.Comment: 6 pages, 2 figures, Accepted for publication in PAS

Galilei covariance and (4,1) de Sitter space

A vector space G is introduced such that the Galilei transformations are considered linear mappings in this manifold. The covariant structure of the Galilei Group (Y. Takahashi, Fortschr. Phys. 36 (1988) 63; 36 (1988) 83) is derived and the tensor analysis is developed. It is shown that the Euclidean space is embedded the (4,1) de Sitter space through in G. This is an interesting and useful aspect, in particular, for the analysis carried out for the Lie algebra of the generators of linear transformations in G.Comment: Late

Three Dimensional Heisenberg Spin Glass Models with and without Random Anisotropy

We reexamine the spin glass (SG) phase transition of the $\pm J$ Heisenberg models with and without the random anisotropy $D$ in three dimensions ($d = 3$) using complementary two methods, i.e., (i) the defect energy method and (ii) the Monte Carlo method. We reveal that the conventional defect energy method is not convincing and propose a new method which considers the stiffness of the lattice itself. Using the method, we show that the stiffness exponent $\theta$ has a positive value ($\theta > 0$) even when $D = 0$. Considering the stiffness at finite temperatures, we obtain the SG phase transition temperature of $T_{\rm SG} \sim 0.19J$ for $D = 0$. On the other hand, a large scale MC simulation shows that, in contrary to the previous results, a scaling plot of the SG susceptibility $\chi_{\rm SG}$ for $D = 0$ is obtained using almost the same transiton temperature of $T_{\rm SG} \sim 0.18J$. Hence we believe that the SG phase transition occurs in the Heisenberg SG model in $d = 3$.Comment: 15 pages, 9 figures, to be published in J. Phys.

Quantum Spin Chains and Riemann Zeta Function with Odd Arguments

Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model. We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in thermodynamics limit. We prove that for short strings the probability can be expressed in terms of Riemann zeta function with odd arguments.Comment: LaTeX, 7 page