Coarse grained and fine dynamics in trapped ion Raman schemes

A novel result concerning Raman coupling schemes in the context of trapped ions is obtained. By means of an operator perturbative approach, it is shown that the complete time evolution of these systems (in the interaction picture) can be expressed, with a high degree of accuracy, as the product of two unitary evolutions. The first one describes the time evolution related to an effective coarse grained dynamics. The second is a suitable correction restoring the {\em fine} dynamics suppressed by the coarse graining performed to adiabatically eliminate the nonresonantly coupled atomic level.Comment: 12 pages, no figure

The Supercooling of a Nematic Liquid Crystal

We investigate the supercooling of a nematic liquid crystal using fluctuating non-linear hydrodynamic equations. The Martin-Siggia-Rose formalism is used to calculate renormalized transport coefficients to one-loop order. Similar theories for isotropic liquids have shown substantial increases of the viscosities as the liquid is supercooled or compressed due to feedback from the density fluctuations which are freezing. We find similar results here for the longitudinal and various shear viscosities of the nematic. However, the two viscosities associated with the nematic director motion do not grow in any dramatic way; i.e.\ there is no apparent freezing of the director modes within this hydrodynamic formalism. Instead a glassy state of the nematic may arise from a ``random anisotropy" coupling of the director to the frozen density.Comment: Late

Quantum mechanical counterpart of nonlinear optics

Raman-type laser excitation of a trapped atom allows one to realize the quantum mechanical counterpart of phenomena of nonlinear optics, such as Kerr-type nonlinearities, parametric amplification, and multi-mode mixing. Additionally, huge nonlinearities emerge from the interference of the atomic wave function with the laser waves. They lead to a partitioning of the phase space accompanied by a significantly different action of the time evolution in neighboring phase-space zones. For example, a nonlinearly modified coherent "displacement" of the motional quantum state may induce strong amplitude squeezing and quantum interferences.Comment: 6 pages, 4 figures, to be published in Phys. Rev. A 55 (June

Relation between positional specific heat and static relaxation length: Application to supercooled liquids

A general identification of the {\em positional specific heat} as the thermodynamic response function associated with the {\em static relaxation length} is proposed, and a phenomenological description for the thermal dependence of the static relaxation length in supercooled liquids is presented. Accordingly, through a phenomenological determination of positional specific heat of supercooled liquids, we arrive at the thermal variation of the static relaxation length $\xi$, which is found to vary in accordance with $\xi \sim (T-T_0)^{-\nu}$ in the quasi-equilibrium supercooled temperature regime, where $T_0$ is the Vogel-Fulcher temperature and exponent $\nu$ equals unity. This result to a certain degree agrees with that obtained from mean field theory of random-first-order transition, which suggests a power law temperature variation for $\xi$ with an apparent divergence at $T_0$. However, the phenomenological exponent $\nu = 1$, is higher than the corresponding mean field estimate (becoming exact in infinite dimensions), and in perfect agreement with the relaxation length exponent as obtained from the numerical simulations of the same models of structural glass in three spatial dimensions.Comment: Revised version, 7 pages, no figures, submitted to IOP Publishin

Testing the solar LMA region with KamLAND data

We investigate the potential of 3 kiloTon-years(kTy) of KamLAND data to further constrain the $\Delta m^2$ and $\tan^2\theta$ values compared to those presently allowed by existing KamLAND and global solar data. We study the extent, dependence and characteristics of this sensitivity in and around the two parts of the LMA region that are currently allowed. Our analysis with 3 kTy simulated spectra shows that KamLAND spectrum data by itself can constrain $\Delta m^2$ with high precision. Combining the spectrum with global solar data further tightens the constraints on allowed values of $\tan^2\theta$ and $\Delta m^2$. We also study the effects of future neutral current data with a total error of 7% from the Sudbury Neutrino Observatory. We find that these future measurements offer the potential of considerable precision in determining the oscillation parameters (specially the mass parameter).Comment: 16 pages, to appear in J Phys.

Muonium as a hydrogen analogue in silicon and germanium; quantum effects and hyperfine parameters

We report a first-principles theoretical study of hyperfine interactions, zero-point effects and defect energetics of muonium and hydrogen impurities in silicon and germanium. The spin-polarized density functional method is used, with the crystalline orbitals expanded in all-electron Gaussian basis sets. The behaviour of hydrogen and muonium impurities at both the tetrahedral and bond-centred sites is investigated within a supercell approximation. To describe the zero-point motion of the impurities, a double adiabatic approximation is employed in which the electron, muon/proton and host lattice degrees of freedom are decoupled. Within this approximation the relaxation of the atoms of the host lattice may differ for the muon and proton, although in practice the difference is found to be slight. With the inclusion of zero-point motion the tetrahedral site is energetically preferred over the bond-centred site in both silicon and germanium. The hyperfine and superhyperfine parameters, calculated as averages over the motion of the muon, agree reasonably well with the available data from muon spin resonance experiments.Comment: 20 pages, including 9 figures. To appear in Phys. Rev.

Determination of entangled quantum states of a trapped atom

We propose a method for measuring entangled vibronic quantum states of a trapped atom. It is based on the nonlinear dynamics of the system that appears by resonantly driving a weak electronic transition. The proposed technique allows the direct sampling of a Wigner-function matrix, displaying all knowable information on the quantum correlations of the motional and electronic degrees of freedom of the atom. It opens novel possibilities for testing fundamental predictions of the quantum theory concerning interaction phenomena.Comment: 7 pages, 3 figures, to be published in Phys. Rev. A 56 (Aug

The atmospheric neutrino anomaly without maximal mixing?

We consider a pattern of neutrino masses in which there is an approximate mass degeneracy between the two mass eigenstates most coupled to the $\nu_\mu$ and $\nu_\tau$ flavour eigenstates. Earth-matter effects can lift this degeneracy and induce an effectively maximal mixing between these two generations. This occurs if $\nu_e$'s contain comparable admixtures of the degenerate eigenstates, even rather small ones. This provides an explanation of the atmospheric neutrino anomaly in which the {\it ab initio} introduction of a large mixing angle is not required. To test this possibility we perform a novel and detailed analysis of the 52 kiloton-year SuperKamiokande data, and we find that in a large region of parameter space the corresponding confidence levels are excellent. The most recent results from the Chooz reactor experiment, however, severely curtail this region, so that the conventional scenario with nearly maximal mixing angles --which we also analyse in detail-- is supported by the data.Comment: Some relevant references added and a misprint correcte

High-Mass X-ray Binaries and the Spiral Structure of the Host Galaxy

We investigate the manifestation of the spiral structure in the distribution of high-mass X-ray binaries (HMXBs) over the host galaxy. We construct the simple kinematic model. It shows that the HMXBs should be displaced relative to the spiral structure observed in such traditional star formation rate indicators as the Halpha and FIR emissions because of their finite lifetimes. Using Chandra observations of M51, we have studied the distribution of X-ray sources relative to the spiral arms of this galaxy observed in Halpha. Based on K-band data and background source number counts, we have separated the contributions from high-mass and low-mass X-ray binaries and active galactic nuclei. In agreement with model predictions, the distribution of HMXBs is wider than that of bright HII regions concentrated in the region of ongoing star formation. However, the statistical significance of this result is low, as is the significance of the concentration of the total population of X-ray sources to the spiral arms. We also predict the distribution of HMXBs in our Galaxy in Galactic longitude. The distribution depends on the mean HMXB age and can differ significantly from the distributions of such young objects as ultracompact HII regions.Comment: 18 pages, 6 figures; Astronomy Letters, Vol. 33, No. 5, 2007, pp. 299-30