We confirm universal behaviors such as eigenvalue distribution and spacings predicted by random matrix theory (RMT) for the cross correlation matrix of the daily stock prices of Tokyo Stock Exchange from 1993 to 2001, which have been reported for New York Stock Exchange in previous studies. It is shown that the random part of the eigenvalue distribution of the cross correlation matrix is stable even when deterministic correlations are present. Some deviations in the small eigenvalue statistics outside the bounds of the universality class of RMT are not completely explained with the deterministic correlations as proposed in previous studies. We study the effect of randomness on deterministic correlations and find that randomness causes a repulsion between deterministic eigenvalues and the random eigenvalues. This is interpreted as a reminiscent of "level repulsion" in RMT and explains some deviations from the previous studies observed in the market data. We also study correlated groups of issues in these markets and propose a refined method to identify correlated groups based on RMT. Some characteristic differences between properties of Tokyo Stock Exchange and New York Stock Exchange are found.

Motivated by a recent development in the field theory of the fractional quantum Hall effect, we propose a supersymmetric field theoretical model of quantum critical d-wave and d + id-wave superconductors. New concept is a composite particle with the supercharge which is formed by electron (hole) and supersymmetric collective configurations of spin and charge. Quantum critical d-wave superconductor is characterized as the condensate of these composite particles.

We study spectral statistics of one-dimensional quasiperiodic systems at the metal-insulator transition. Several types of spectral statistics are observed at the critical points, lines, and region. On the critical lines, we find the bandwidth distribution P(B) (w) around the origin (in the tail) to have the form of P(B) (w) approximately w(alpha) [P(B) (w) approximately e(-beta w(gamma) ) ] (alpha,beta,gamma >0) , while in the critical region P(B) (w) approximately w(- alpha') (alpha' >0) . We also find the level spacing distribution to follow an inverse power law P(G) (s) approximately s(-delta) (delta>0) .

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We study pairing effects in the edge states of paired fractional quantum Hall states by using persistent edge currents as a probe. We give the grand partition functions for edge excitations of paired states (Haldane-Rezayi, Pfaffian, 331) coupling to an Aharanov-Bohm flux and derive the exact formulas of the persistent edge current. We show that the currents are flux periodic with the unit flux φ0 = hc/e. At low temperatures, they exhibit anomalous oscillations in their flux dependence. The shapes of the functions depend on the bulk topological order. They converge to the sawtooth function with period φ0/2 at zero temperature, which indicates pair condensation. This phenomenon provides an interesting bridge between superconductivity in 2+1 dimensions and superconductivity in 1+1 dimensions. We propose experiments of measuring the persistent current at even denominator plateau in single or double layer systems to test our predictions. PACS: 73.40Hm, One of the surprising aspects of the fractional quantum Hall effect is that the edge state forms a new kind of state of matter beyond Fermi liquid, called the chiral Tomonaga-Luttinger liquid [1]. Some experiments have already demonstrated the characteristic behavior of chiral Tomonaga-Luttinger liquid [2,3]. Recently the Aharanov-Bohm effect (AB effect) in such systems were studied by Geller et al [4,5] and Chamon et al [6]. Especially, the former authors predict new edge-current oscillations in the persistent current at the edge of the ν = 1 q Laughlin state, which has no amplitude reduction from disorder and thus results in a universal non-Fermi-liquid temperature dependence [5]. Also the persistent current for the annulus Laughlin state was recently investigated by Kettemann [7]. These studies show the current is periodic with a unit flux quanta φ 0 = hc/e in agreement with the theorem of Byers and Young [8].Motivated by these recent studies, we investigate the persistent currents in paired fractional Hall states in this paper. The states we will consider are the 331 state [9], the Haldane-Rezayi state [10] and the Pfaffian state [11]. They are quantum Hall analogs of the BCS superconductor. The pairing symmetry is p-wave with S z = 1, 0 for the Pfaffian and the 331 states respectively, and d-wave for the Haldane-Rezayi states. The Haldane-Rezayi state and the Pfaffian state are new kinds of quantum Hall state which recently attracted considerable attentions because they are supposed to exhibit some novel features beyond ordinary quantum Hall state in their topological ordering, such as nonabelian statistics and specific degeneracy on a surface with nontrivial topology. On the other hand, the 331 state is a part of generalized hierarchy [12], but can be interpreted as a paired state. These states are proposed as a candidate for the ν = 5 2 plateau in single layer systems [13] and the ν = 1 2 plateau in double layer systems [14]. Recent numerical study by Morf suggests that the ν = 5 2 state is Pfaffian-like [15]. As in the Laughlin state, these states are incompre...