Improved methods for calculating the thickness noise

Advanced methods to compute the rotor thickness noise which is predominant in the case of high speed rotor were developed. These methods were deduced from a previous method by transforming the integral coordinate, commuting the order of integration and differential, and/or performing chordwise integration analytically with some adequate assumption. The necessary computational times and waveforms obtained by the previous and three advanced methods were compared. It was then concluded that the advanced methods could save the computational time compared with the previous method with the same accuracy

Weak interference between the 1−^- states in the vicinity of α\alpha-particle threshold of 16^{16}O

The subthreshold 1$^-_1$ state at an excitation energy $E_x = 7.12$ MeV in $^{16}$O has been believed to enhance the $S$-factor of $^{12}$C($\alpha$,$\gamma$)$^{16}$O. The enhancement seems to originate from strong interference between 1$^-_1$ and 1$^-_2$ ($E_x\approx 9.6$ MeV) in the vicinity of the $\alpha$-particle threshold. However, weak interference between them and a resulting small $E$1 $S$-factor are exemplified with $R$-matrix theory. Including a higher-order correction of the resonance parameters, the present example appears to reproduce the experimental data consistently. It would therefore be possible that the $E$1 $S$-factor is reduced at low energies.Comment: 3 pages, 1 figure; to appear in "Springer Proceedings in Physics", Proc. of Nuclei in the Cosmos XV, LNGS Assergi, Italy, 24-29 June 201

Perturbative dynamics of fuzzy spheres at large N

We clarify some peculiar aspects of the perturbative expansion around a classical fuzzy-sphere solution in matrix models with a cubic term. While the effective action in the large-N limit is saturated at the one-loop level, we find that the ``one-loop dominance'' does not hold for generic observables due to one-particle reducible diagrams. However, we may exploit the one-loop dominance for the effective action and obtain various observables to all orders from one-loop calculation by simply shifting the center of expansion to the ``quantum solution'', which extremizes the effective action. We confirm the validity of this method by comparison with the direct two-loop calculation and with Monte Carlo results in the 3d Yang-Mills-Chern-Simons matrix model. From the all order result we find that the perturbative expansion has a finite radius of convergence.Comment: 21 pages, 9 figures, (v2) all order analyses added, (v3) some typos correcte

Dynamical aspects of the fuzzy CP2^{2} in the large NN reduced model with a cubic term

``Fuzzy CP^2'', which is a four-dimensional fuzzy manifold extension of the well-known fuzzy analogous to the fuzzy 2-sphere (S^2), appears as a classical solution in the dimensionally reduced 8d Yang-Mills model with a cubic term involving the structure constant of the SU(3) Lie algebra. Although the fuzzy S^2, which is also a classical solution of the same model, has actually smaller free energy than the fuzzy CP^2, Monte Carlo simulation shows that the fuzzy CP^2 is stable even nonperturbatively due to the suppression of tunneling effects at large N as far as the coefficient of the cubic term ($\alpha$) is sufficiently large. As \alpha is decreased, both the fuzzy CP$^2$ and the fuzzy S^2 collapse to a solid ball and the system is essentially described by the pure Yang-Mills model (\alpha = 0). The corresponding transitions are of first order and the critical points can be understood analytically. The gauge group generated dynamically above the critical point turns out to be of rank one for both CP^2 and S^2 cases. Above the critical point, we also perform perturbative calculations for various quantities to all orders, taking advantage of the one-loop saturation of the effective action in the large-N limit. By extrapolating our Monte Carlo results to N=\infty, we find excellent agreement with the all order results.Comment: 27 pages, 7 figures, (v2) References added (v3) all order analyses added, some typos correcte

Gauge Theory Description of Spin Ladders

A s=1/2 antiferromagnetic spin chain is equivalent to the two-flavor massless Schwinger model in an uniform background charge density in the strong coupling. The gapless mode of the spin chain is represented by a massless boson of the Schwinger model. In a two-leg spin ladder system the massless boson aquires a finite mass due to inter-chain interactions. The gap energy is found to be about .25 k |J'| when the inter-chain Heisenberg coupling J' is small compared with the intra-chain Heisenberg coupling. k is a constant of O(1). It is also shown that a cyclically symmetric N-leg ladder system is gapless or gapful for an odd or even N, respectively.Comment: 8 pages. CORRIGENDUM has been incorporated. (A factor 2 error has been corrected.

Exact fuzzy sphere thermodynamics in matrix quantum mechanics

We study thermodynamical properties of a fuzzy sphere in matrix quantum mechanics of the BFSS type including the Chern-Simons term. Various quantities are calculated to all orders in perturbation theory exploiting the one-loop saturation of the effective action in the large-N limit. The fuzzy sphere becomes unstable at sufficiently strong coupling, and the critical point is obtained explicitly as a function of the temperature. The whole phase diagram is investigated by Monte Carlo simulation. Above the critical point, we obtain perfect agreement with the all order results. In the region below the critical point, which is not accessible by perturbation theory, we observe the Hagedorn transition. In the high temperature limit our model is equivalent to a totally reduced model, and the relationship to previously known results is clarified.Comment: 22 pages, 14 figures, (v2) some typos correcte