Abstract:
A possiblity of measuring the cosmic neutrino temperature $\sim 1.9 K$ and other important quantities such as the chemical potential $\mu$ and the decoupling temperature $T_d$ is discussed, using the recently proposed process of photon irradiated neutrino pair emission from metastable atoms. The Pauli blocking effect of relic neutrinos reduces the rate by a large factor $\approx (1 + m_1/T_d)/4$ at the threshold of the lightest neutrino pair (of mass $2m_1$). Correction of linear order in $\mu$ near the mass thresholds can be used to improve the constraint on the lepton asymmetry.

Abstract:
We consider prescriptions that are free from the direct charge-screening effects by quark loops and enable us to clarify the confining nature of a vacuum. We test two candidates for an order parameter, a Polyakov loop ($P$) evaluated in zero-triality backgrounds and fermionic determinants (${\mathcal D}_{1,2}$) with non-zero triality. Especially, ${\mathcal D}_{1,2}$ has very small fluctuations in comparison with a Polyakov loop in zero-triality sector, and seems to well reflect the characteristic of a vacuum. Such prescriptions could be still usable for the clarification of the confinement property of a vacuum.

Abstract:
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.

Abstract:
The magnetization process of the S=3/2 antiferromagnetic Heisenberg chain with the single-ion anisotropy D at T=0 is investigated by the exact diagonalization of finite clusters and finite-size scaling analyses. It is found that a magnetization plateau appears at m=1/2 for $D>D_c=0.93 \pm 0.01$. The phase transition with respect to D at D_c is revealed to be the Kosterlitz-Thouless-type. The magnetization curve of the infinite system is also presented for some values of D.

Abstract:
Dynamical properties of 2D antiferromagnets with hole doping are investigated to see the effects of short range local magnetic order on the temperature dependence of the dynamical magnetic susceptibility. We show the pseudo-gap like behavior of the temperature dependence of the NMR relaxation rate. We also discuss implications of the results in relations to the observed spin gap like behavior of low-doped copper oxide high-$T_c$ superconductors.

Abstract:
The pseudogap phenomena observed on cuprate high temperature superconductors are investigated based on the exact diagonalization method on the finite cluster t-J model. The results show the presence of the gap-like behavior in the temperature dependence of various magnetic properties; the NMR relaxation rate, the neutron scattering intensity and the static susceptibility. The calculated spin correlation function indicates that the pseudogap behavior arises associated with the development of the antiferromagnetic spin correlation with decreasing the temperature. The numerical results are presented to clarify the model parameter dependence, that covers the realistic experimental situation. The effect of the next-nearest neighbor hopping $t'$ is also studied.

Abstract:
The ground state magnetization curve around the critical magnetic field $H_c$ of quantum spin chains with the spin gap is investigated. We propose a size scaling method to estimate the critical exponent $\delta$ defined as $m\sim |H-H_c|^{1/\delta}$ from finite cluster calculation. The applications of the method to the S=1 antiferromagnetic chain and S=1/2 bond alternating chain lead to a common conclusion $\delta =2$. The same result is derived for both edges of the magnetization plateau of the S=3/2 antiferromagnetic chain with the single ion anisotropy.

Abstract:
A possiblity of measuring the cosmic neutrino temperature $\sim 1.9 K$ and other important quantities such as the chemical potential $\mu$ and the decoupling temperature $T_d$ is discussed, using the recently proposed process of photon irradiated neutrino pair emission from metastable atoms. The Pauli blocking effect of relic neutrinos reduces the rate by a large factor $\approx (1 + m_1/T_d)/4$ at the threshold of the lightest neutrino pair (of mass $2m_1$). Correction of linear order in $\mu$ near the mass thresholds can be used to improve the constraint on the lepton asymmetry.

Abstract:
We study the properties of low-lying Dirac modes in quenched compact QED at $\beta$=0.99, 1.01 and 1.03, employing $12^3\times 12$ lattices and the overlap formalism for the fermion action. We pay special attention to the spatial distributions of the low-lying Dirac modes. Near-zero modes are found to have universal anti-correlations with monopole currents below/above the critical $\beta$. We also study the nearest-neighbor level spacing distribution of Dirac eigenvalues and find a signal of a Wigner-Poisson transition. We make a possible speculation on the chiral phase transition in 4D compact QED.

Abstract:
The magnetization process of the one-dimensional antiferromagnetic Heisenberg model with the Ising-like anisotropic exchange interaction is studied by the exact diagonalization technique. It results in the evidence of the first-order spin flop transition with a finite magnetization jump in the N\'eel ordered phase for $S\geq 1$. It implies that the S=1/2 chain is an exceptional case where the metamagnetic transition becomes second-order due to large quantum fluctuations.