Inverse Landau-Zener-Stuckelberg problem for qubit-resonator systems

We consider theoretically a superconducting qubit - nanomechanical resonator (NR) system, which was realized by LaHaye et al. [Nature 459, 960 (2009)]. First, we study the problem where the state of the strongly driven qubit is probed through the frequency shift of the low-frequency NR. In the case where the coupling is capacitive, the measured quantity can be related to the so-called quantum capacitance. Our theoretical results agree with the experimentally observed result that, under resonant driving, the frequency shift repeatedly changes sign. We then formulate and solve the inverse Landau-Zener-Stuckelberg problem, where we assume the driven qubit's state to be known (i.e. measured by some other device) and aim to find the parameters of the qubit's Hamiltonian. In particular, for our system the qubit's bias is defined by the NR's displacement. This may provide a tool for monitoring of the NR's position.Comment: 10 pages, 7 figure

Quantum Larmor radiation in conformally flat universe

We investigate the quantum effect on the Larmor radiation from a moving charge in an expanding universe based on the framework of the scalar quantum electrodynamics (SQED). A theoretical formula for the radiation energy is derived at the lowest order of the perturbation theory with respect to the coupling constant of the SQED. We evaluate the radiation energy on the background universe so that the Minkowski spacetime transits to the Milne universe, in which the equation of motion for the mode function of the free complex scalar field can be exactly solved in an analytic way. Then, the result is compared with the WKB approach, in which the equation of motion of the mode function is constructed with the WKB approximation which is valid as long as the Compton wavelength is shorter than the Hubble horizon length. This demonstrates that the quantum effect on the Larmor radiation of the order e^2\hbar is determined by a non-local integration in time depending on the background expansion. We also compare our result with a recent work by Higuchi and Walker [Phys. Rev. D80 105019 (2009)], which investigated the quantum correction to the Larmor radiation from a charged particle in a non-relativistic motion in a homogeneous electric field.Comment: 12 pages, 4 figure, accepted for publication in Physical Review

Leaf area index and topographical effects on turburlent diffusion in a deciduous forest

In order to investigate turbulent diffusion in a deciduous forest canopy, wind velocity measurements were conducted from late autumn of 2009 to early spring of 2010, using an observation tower 20 m in height located in the campus of Kanazawa University. Four sonic anemometers mounted on the tower recorded the average wind velocities and temperatures, as well as their fluctuations, at four different heights simultaneously. Two different types of data sets were selected, in which the wind velocities, wind bearings and atmospheric stabilities were all similar, but the Leaf Area Indexes (LAI's) were different. Vertical profiles of average wind velocities were found to have an approximately exponential profile in each case. The characteristic length scales of turbulence were evaluated by both von Karman's method and the integral time scale deduced from the autocorrelation from time-series analyses. Both methods produced comparable values of eddy diffusivity for the cases with some foliage during late autumn, but some discrepancy in the upper canopy layer was observed when the trees did not have their leaves in early spring. It was also found that the eddy diffusivities generally take greater values at higher positions, where the wind speeds are large. Anisotropy of eddy diffusivities between the vertical and horizontal components was also observed, particularly in the cases when the canopy does not have leaves, when the horizontal eddy diffusivities are generally larger than the vertical ones. On the other hand, the anisotropy is less visible when the trees have some foliage during autumn. The effects of topography on the turbulent diffusion were also investigated, including evaluation of the non-zero time-averaged vertical wind velocities. The results show that the effects are marginal for both cases, and can be neglected as far as diffusion in the canopy is concerned

Localization length of a soliton from a non-magnetic impurity in a general double-spin-chain model

A localization length of a free-spin soliton from a non-magnetic impurity is deduced in a general double-spin-chain model ($J_0-J_1-J_2-J_3$ model). We have solved a variational problem which employs the nearest-neighbor singlet-dimer basis. The wave function of a soliton is expressed by the Airy function, and the localization length $(\xi)$ is found to obey a power law of the dimerization $(J_2-J_3)$ with an exponent -1/3; $\xi\sim (J_2-J_3)^{-1/3}$. This explains why NaV_2O_5 does not show the antiferromagnetic order, while CuGeO_3 does by impurity doping. When the gap exists by the bond-dimerization, a soliton is localized and no order is expected. Contrary, there is a possibility of the order when the gap is mainly due to frustration.Comment: 4 pages, REVTeX, Figures are in eps-file

The Minimum Total Mass of MACHOs and Halo Models of the Galaxy

If the density distribution \rho (r) of MACHOs is spherically symmetric with respect to the Galactic center, it is shown that the minimal total mass M_{min}^{{ MACHO}} of the MACHOs is 1.7\times 10^{10}\sol \tau_{-6.7}^{{ LMC}} where \tau_{-6.7}^{{ LMC}} is the optical depth (\tau^{{ LMC}}) toward the Large Magellanic Cloud (LMC) in the unit of 2\times 10^{-7}. If \rho (r) is a decreasing function of r, it is proved that M_{min}^{{ MACHO}} is 5.6\times 10^{10}\sol \tau_{-6.7}^{{ LMC}}. Several spherical and axially symmetric halo models of the Galaxy with a few free parameters are also considered. It is found that M_{min}^{{ MACHO}} ranges from 5.6\times 10^{10}\sol \tau_{-6.7}^{{ LMC}} to \sim 3 \times 10^{11}\sol \tau_{-6.7}^{{ LMC}}. For general case, the minimal column density \Sigma_{min}^{{ MACHO}} of MACHOs is obtained as \Sigma_{min}^{{ MACHO}} =25 \sol { pc}^{-2}\tau_{-6.7}^{{ LMC}}. If the clump of MACHOs exist only halfway between LMC and the sun, M_{min}^{{ MACHO}} is 1.5\times 10^9\sol. This shows that the total mass of MACHOs is smaller than 5 \times 10^{10}\sol , i.e. \sim 10\% of the mass of the halo inside LMC, either if the density distribution of MACHOs is unusual or \tau^{{ LMC}}\ll 2\times 10^{-7}.Comment: 5 pages, 5 Encapsulated PostScript figures, Latex, Accepted for publication in Apj. Letter