Position and Momentum Uncertainties of the Normal and Inverted Harmonic Oscillators under the Minimal Length Uncertainty Relation

We analyze the position and momentum uncertainties of the energy eigenstates of the harmonic oscillator in the context of a deformed quantum mechanics, namely, that in which the commutator between the position and momentum operators is given by [x,p]=i\hbar(1+\beta p^2). This deformed commutation relation leads to the minimal length uncertainty relation \Delta x > (\hbar/2)(1/\Delta p +\beta\Delta p), which implies that \Delta x ~ 1/\Delta p at small \Delta p while \Delta x ~ \Delta p at large \Delta p. We find that the uncertainties of the energy eigenstates of the normal harmonic oscillator (m>0), derived in Ref. [1], only populate the \Delta x ~ 1/\Delta p branch. The other branch, \Delta x ~ \Delta p, is found to be populated by the energy eigenstates of the `inverted' harmonic oscillator (m<0). The Hilbert space in the 'inverted' case admits an infinite ladder of positive energy eigenstates provided that \Delta x_{min} = \hbar\sqrt{\beta} > \sqrt{2} [\hbar^2/k|m|]^{1/4}. Correspondence with the classical limit is also discussed.Comment: 16 pages, 31 eps figure

Lambda(1405) as a Resonance in the Baryon-Meson Scattering Coupled to the q^3 State in a Quark Model

In order to describe Lambda(1405) as a resonance in the baryon-meson scattering, we have investigated q^3-q qbar scattering system with the flavor-singlet q^3 (0s)^2(0p) state (the Lambda^1 pole). The scattering is treated by the quark cluster model (QCM). The Lambda^1 pole is treated as a bound state embedded in the continuum. We found that the peak appears below the N Kbar threshold in the spin one half, isospin 0 channel even if the mass of the Lambda^1 pole is above the threshold. This peak disappears when the coupling to the Lambda^1 pole is switched off. To use the observed hadron mass in the kinetic part of QCM is also found to be important to reproduce a peak just below the N Kbar threshold.Comment: 16 pages and 7 figure

Diffusive versus local spin currents in dynamic spin pumping systems

Using microscopic theory, we investigate the properties of a spin current driven by magnetization dynamics. In the limit of smooth magnetization texture, the dominant spin current induced by the spin pumping effect is shown to be the diffusive spin current, i.e., the one arising from only a diffusion associated with spin accumulation. That is to say, there is no effective field that locally drives the spin current. We also investigate the conversion mechanism of the pumped spin current into a charge current by spin-orbit interactions, specifically the inverse spin Hall effect. We show that the spin-charge conversion does not always occur and that it depends strongly on the type of spin-orbit interaction. In a Rashba spin-orbit system, the local part of the charge current is proportional to the spin relaxation torque, and the local spin current, which does not arise from the spin accumulation, does not play any role in the conversion. In contrast, the diffusive spin current contributes to the diffusive charge current. Alternatively, for spin-orbit interactions arising from random impurities, the local charge current is proportional to the local spin current that constitutes only a small fraction of the total spin current. Clearly, the dominant spin current (diffusive spin current) is not converted into a charge current. Therefore, the nature of the spin current is fundamentally different depending on its origin and thus the spin transport and the spin-charge conversion behavior need to be discussed together along with spin current generation

Prospects for measuring coherent neutrino-nucleus elastic scattering at a stopped-pion neutrino source

Rates of coherent neutrino-nucleus elastic scattering at a high-intensity stopped-pion neutrino source in various detector materials (relevant for novel low-threshold detectors) are calculated. Sensitivity of a coherent neutrino-nucleus elastic scattering experiment to new physics is also explored.Comment: 9 pages, 14 figures; minor modifications for publicatio

P-wave Pentaquark and its Decay in the Quark Model with Instanton Induced Interaction

P-wave pentaquarks with strangeness +1, I=0 and J^P=1/2^+ are studied in the non-relativistic quark model with instanton induced interaction (III). We present their mass splittings and orbital-spin-isospin-color structures. It is found that decompositions of the wave functions are sensitive to III, while the mass splittings are insensitive. The decay of the lowest energy pentaquark, \Theta^+, is found to be suppressed when the contribution of III is increased. Its wave function is dominated by Jaffe-Wilczek-type configuration at large III.Comment: 9 pages, 5 figure

Effects of Instanton Induced Interaction on the Pentaquarks

Roles of instanton induced interactions (III) in the masses of pentaquark baryons, Theta^+ (J=1/2 and 3/2) and Xi^{--}, and a dibaryon, H, are discussed using the MIT bag model in the negative parity case. It is shown that the two-body terms in III give a strong attraction mainly due to the increase of the number of pairs in multi-quark systems. In contrast, the three-body u-d-s interaction is repulsive. It is found that III lowers the mass of Theta^+ as much as 100 MeV from the mass predicted by the bag model without III.Comment: 11 pages, 3 figure

X-Ray Fluctuations from Locally Unstable Advection-Dominated Disks

The response of advection-dominated accretion disks to local disturbances is examined by one-dimensional numerical simulations. It is generally believed that advection-dominated disks are thermally stable. We, however, find that any disurbance added onto accretion flow at large radii does not decay so rapidly that it can move inward with roughly the free-fall velocity. Although disturbances continue to be present, the global disk structure will not be modified largely. This can account for persistent hard X-ray emission with substantial variations observed in active galactic nuclei and stellar black hole candidates during the hard state. Moreover, when the disturbance reaches the innermost parts, an acoustic wave emerges, propagating outward as a shock wave. The resultant light variation is roughly (time) symmetric and is quite reminiscent of the observed X-ray shots of Cygnus X-1.Comment: plain TeX, 11 pages, without figures; to be published in ApJ Lette