Quantum Field Theoretical Analysis on Unstable Behavior of Bose-Einstein Condensates in Optical Lattices

We study the dynamics of Bose-Einstein condensates flowing in optical lattices on the basis of quantum field theory. For such a system, a Bose-Einstein condensate shows a unstable behavior which is called the dynamical instability. The unstable system is characterized by the appearance of modes with complex eigenvalues. Expanding the field operator in terms of excitation modes including complex ones, we attempt to diagonalize the unperturbative Hamiltonian and to find its eigenstates. It turns out that although the unperturbed Hamiltonian is not diagonalizable in the conventional bosonic representation the appropriate choice of physical states leads to a consistent formulation. Then we analyze the dynamics of the system in the regime of the linear response theory. Its numerical results are consitent with as those given by the discrete nonlinear Schrodinger equation.Comment: 16pages, 4figure

Quantum Field Theoretical Description of Unstable Behavior of Trapped Bose-Einstein Condensates with Complex Eigenvalues of Bogoliubov-de Gennes Equations

The Bogoliubov-de Gennes equations are used for a number of theoretical works on the trapped Bose-Einstein condensates. These equations are known to give the energies of the quasi-particles when all the eigenvalues are real. We consider the case in which these equations have complex eigenvalues. We give the complete set including those modes whose eigenvalues are complex. The quantum fields which represent neutral atoms are expanded in terms of the complete set. It is shown that the state space is an indefinite metric one and that the free Hamiltonian is not diagonalizable in the conventional bosonic representation. We introduce a criterion to select quantum states describing the metastablity of the condensate, called the physical state conditions. In order to study the instability, we formulate the linear response of the density against the time-dependent external perturbation within the regime of Kubo's linear response theory. Some states, satisfying all the physical state conditions, give the blow-up and damping behavior of the density distributions corresponding to the complex eigenmodes. It is qualitatively consistent with the result of the recent analyses using the time-dependent Gross-Pitaevskii equation.Comment: 29 page

Fermi surface in BaNi2_2P2_2

We report measurements of the de Haas-van Alphen (dHvA) oscillation and a band structure calculation for the pnictide superconductor BaNi$_2$P$_2$, which is isostructural to BaFe$_2$As$_2$, the mother compound of the iron-pnictide high-$T_c$ superconductor (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$. Six dHvA-frequency branches with frequencies up to $\sim$8 kT were observed, and they are in excellent agreement with results of the band-structure calculation. The determined Fermi surface is large, enclosing about one electron and hole per formula unit, and three-dimensional. This is in contrast to the small two-dimensional Fermi surface expected for the iron-pnictide high-$T_c$ superconductors. The mass enhancement is about two.Comment: To appear in J. Phys. Soc. Jpn., Vol. 78, No.

Tau Neutrinos Favored over Sterile Neutrinos in Atmospheric Muon Neutrino Oscillations

The previously published atmospheric neutrino data did not distinguish whether muon neutrinos were oscillating into tau neutrinos or sterile neutrinos, as both hypotheses fit the data. Using data recorded in 1100 live-days of the Super-Kamiokande detector, we use three complementary data samples to study the difference in zenith angle distribution due to neutral currents and matter effects. We find no evidence favoring sterile neutrinos, and reject the hypothesis at the 99% confidence level. On the other hand, we find that oscillation between muon and tau neutrinos suffices to explain all the results in hand.Comment: 9 pages with 2 figures, submitted to PR

Search for Dark Matter WIMPs using Upward Through-going Muons in Super-Kamiokande

We present the results of indirect searches for Weakly Interacting Massive Particles (WIMPs) with 1679.6 live days of data from the Super-Kamiokande detector using neutrino-induced upward through-going muons. The search is performed by looking for an excess of high energy muon neutrinos from WIMP annihilations in the Sun, the core of the Earth, and the Galactic Center, as compared to the number expected from the atmospheric neutrino background. No statistically significant excess was seen. We calculate flux limits in various angular cones around each of the above celestial objects. We obtain conservative model-independent upper limits on WIMP-nucleon cross-section as a function of WIMP mass and compare these results with the corresponding results from direct dark matter detection experiments.Comment: 10 pages, 14 figures, Submitted to Phys. Rev.

Normal systems over ANR's, rigid embeddings and nonseparable absorbing sets

Most of results of Bestvina and Mogilski [\textit{Characterizing certain incomplete infinite-dimensional absolute retracts}, Michigan Math. J. \textbf{33} (1986), 291--313] on strong $Z$-sets in ANR's and absorbing sets is generalized to nonseparable case. It is shown that if an ANR $X$ is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and $w(U) = w(X)$ (where `$w$' is the topological weight) for each open nonempty subset $U$ of $X$,then $X$ itself is homotopy dense embeddable in a Hilbert manifold. It is also demonstrated that whenever $X$ is an AR, its weak product $W(X,*) = \{(x_n)_{n=1}^{\infty} \in X^{\omega}:\ x_n = * \textup{for almost all} n\}$ is homeomorphic to a pre-Hilbert space $E$ with $E \cong \Sigma E$. An intrinsic characterization of manifolds modelled on such pre-Hilbert spaces is given.Comment: 26 page

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO