Effective Medium Theory of Filamentous Triangular Lattice

We present an effective medium theory that includes bending as well as stretching forces, and we use it to calculate mechanical response of a diluted filamentous triangular lattice. In this lattice, bonds are central-force springs, and there are bending forces between neighboring bonds on the same filament. We investigate the diluted lattice in which each bond is present with a probability $p$. We find a rigidity threshold $p_b$ which has the same value for all positive bending rigidity and a crossover characterizing bending-, stretching-, and bend-stretch coupled elastic regimes controlled by the central-force rigidity percolation point at $p_{\textrm{CF}} \simeq 2/3$ of the lattice when fiber bending rigidity vanishes.Comment: 15 pages, 9 figure

Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations

A discrete stochastic Razumikhin-type theorem is established to investigate whether the Euler--Maruyama (EM) scheme can reproduce the moment exponential stability of exact solutions of stochastic functional differential equations (SFDEs). In addition, the Chebyshev inequality and the Borel-Cantelli lemma are applied to show the almost sure stability of the EM approximate solutions of SFDEs. To show our idea clearly, these results are used to discuss stability of numerical solutions of two classes of special SFDEs, including stochastic delay differential equations (SDDEs) with variable delay and stochastically perturbed equations

The Application of Micro-Raman Spectroscopy to Analysis and Identification of Minerals in Thin Section

Micro-Raman spectroscopy is a useful analytical tool for studying minerals in thin section. The advantages of this technique as a structural probe for analysis of micron-size minerals are demonstrated with a study of polymorphism of SiO2 and MgSiO3. Three polymorphs of silica, -quartz, coesite, and glass, in a thin section of Coconino sandstone were identified in situ with a Raman microprobe. The Raman spectra of these phases were compared to that measured for stishovite obtained from the same rock. Spectra of protoenstatite, orthoenstatite, and clinoenstatite, three polymorphs of MgSiO3, are consistent with their similar pyroxene chain structures but different space groups. The characteristic Raman spectra in each instance could be used for finger-printing identification of the phases and their orientations

The density, the cosmic microwave background and the proton-to-electron mass ratio in a cloud at redshift 0.9

Based on measurements with the Effelsberg 100-m telescope, a multi-line study of molecular species is presented toward the gravitational lens system PKS 1830–211, which is by far the best known target to study dense cool gas in absorption at intermediate redshift. Determining average radial velocities and performing Large Velocity Gradient radiative transfer calculations, the aims of this study are (1) to determine the density of the gas, (2) to constrain the temperature of the cosmic microwave background (CMB), and (3) to evaluate the proton-to-electron mass ratio at redshift z ∼ 0.89. Analyzing data from six rotational HC_3N transitions (this includes the J = 7 ← 6 line, which is likely detected for the first time in the interstellar medium) we obtain n(H_2) ∼ 2600 cm^(−3) for the gas density of the south-western absorption component, assuming a background source covering factor, which is independent of frequency. With a possibly more realistic frequency dependence proportional to ν^(0.5) (the maximal exponent permitted by observational boundary conditions), n(H2) ∼ 1700 cm^(−3). Again toward the south-western source, excitation temperatures of molecular species with optically thin lines and higher rotational constants are, on average, consistent with the expected temperature of the cosmic microwave background, T^(CMB) = 5.14 K. However, individually, there is a surprisingly large scatter which far surpasses expected uncertainties. A comparison of CS J = 1 ← 0 and 4 ← 3 optical depths toward the weaker north-western absorption component results in T_(ex) = 11 K and a 1-σ error of 3 K. For the main component, a comparison of velocities determined from ten optically thin NH_3 inversion lines with those from five optically thin rotational transitions of HC_3N, observed at similar frequencies, constrains potential variations of the proton-to-electron mass ratio μ to Δμ/μ < 1.4 × 10^(−6) with 3-σ confidence. Also including optically thin rotational lines from other molecular species, it is emphasized that systematic errors are ΔV < 1 kms^(−1), corresponding to Δμ/μ < 1.0 × 10^(−6)

Quantum Reciprocity Conjecture for the Non-Equilibrium Steady State

By considering the lack of history dependence in the non-equilibrium steady state of a quantum system we are led to conjecture that in such a system, there is a set of quantum mechanical observables whose retarded response functions are insensitive to the arrow of time, and which consequently satisfy a quantum analog of the Onsager reciprocity relations. Systems which satisfy this conjecture can be described by an effective Free energy functional. We demonstrate that the conjecture holds in a resonant level model of a multi-lead quantum dot.Comment: References revised to take account of related work on Onsager reciprocity in mesoscopics by Christen, and in hydrodynamics by Mclennan, Dufty and Rub

Spin dynamics from Majorana fermions

Using the Majorana fermion representation of spin-1/2 local moments, we show how it is possible to directly read off the dynamic spin correlation and susceptibility from the one-particle propagator of the Majorana fermion. We illustrate our method by applying it to the spin dynamics of a non-equilibrium quantum dot, computing the voltage-dependent spin relaxation rate and showing that, at weak coupling, the fluctuation-dissipation relation for the spin of a quantum dot is voltage-dependent. We confirm the voltage-dependent Curie susceptibility recently found by Parcollet and Hooley [Phys. Rev. B {\bf 66}, 085315 (2002)].Comment: Small modifications added to figure and tex

Large collective Lamb shift of two distant superconducting artificial atoms

Virtual photons can mediate interaction between atoms, resulting in an energy shift known as a collective Lamb shift. Observing the collective Lamb shift is challenging, since it can be obscured by radiative decay and direct atom-atom interactions. Here, we place two superconducting qubits in a transmission line terminated by a mirror, which suppresses decay. We measure a collective Lamb shift reaching 0.8% of the qubit transition frequency and exceeding the transition linewidth. We also show that the qubits can interact via the transmission line even if one of them does not decay into it.Comment: 7+5 pages, 4+2 figure

Same Sign WW Scattering Process as a Probe of Higgs Boson in pp Collision at s\sqrt{s} = 10 TeV

WW scattering is an important process to study electroweak symmetry breaking in the Standard Model at the LHC, in which the Higgs mechanism or other new physics processes must intervene to preserve the unitarity of the process below 1 TeV. This channel is expected to be one of the most sensitive to determine whether the Higgs boson exists. In this paper, the final state with two same sign Ws is studied, with a simulated sample corresponding to the integrated luminosity of 60 fb$^{-1}$ in pp collision at $\sqrt{s}=$10 TeV. Two observables, the invariant mass of $\mu\mu$ from W decays and the azimuthal angle difference between the two $\mu$s, are utilized to distinguish the Higgs boson existence scenario from the Higgs boson absence scenario. A good signal significance for the two cases can be achieved. If we define the separation power of the analysis as the distance, in the log-likelihood plane, of pseudo-experiments outcomes in the two cases, with the total statistics expected from the ATLAS and CMS experiments at the nominal centre-of-mass energy of 14 TeV, the separation power will be at the level of 4 $\sigma$.Comment: 5 pages, 4 figures, 3 table