How likely is Polya's drunkard to stay in x⩾ y⩾z?

In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inxyz. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844....     

Identification of transverse spin currents in noncollinear magnetic structures

In this Letter we construct a spinor transport theory and derive the equations of motion for the distribution functions for currents in noncollinear magnetic multilayers. We find the length scale which characterizes the transverse spin current is of the order of 3 nm for a ferromagnetic 3d transition metal such as Co; this alters one's prediction of the spin torque generated for free magnetic layers less than 3 nm. In the limit of large exchange splitting we reproduce the results previously found for spin currents across noncollinear multilayers inasmuch as there are no transverse spin currents in the layers themselves in this limit.     

Enhanced light‐vapor interactions and all optical switching in a chip scale micro‐ring resonator coupled with atomic vapor

The coupling of atomic and photonic resonances serves as an important tool for enhancing light‐matter interactions and enables the observation of multitude of fascinating and fundamental phenomena. Here, by exploiting the platform of atomic‐cladding wave guides, the resonant coupling of rubidium vapor and an atomic cladding micro ring resonator is experimentally demonstrated. Specifically, cavity‐atom coupling in the form of Fano resonances having a distinct dependency on the relative frequency detuning between the photonic and the atomic resonances is observed. Moreover, significant enhancement of the efficiency of all optical switching in the V‐type pump‐probe scheme is demonstrated. The coupled system of micro‐ring resonator and atomic vapor is a promising building block for a variety of light vapor experiments, as it offers a very small footprint, high degree of integration and extremely strong confinement of light and vapor. As such it may be used for important applications, such as all optical switching, dispersion engineering (e.g. slow and fast light) and metrology, as well as for the observation of important effects such as strong coupling, and Purcell enhancement.

     

The fluorescence excitation spectrum of s-tetrazine cooled in a supersonic free jet

The fluorescence excitation spectrum of the ${}^1\text{B}{}_{\mathrm{3u}}\text{(v′ = 0) ←}{}^1\text{A}{}_{\mathrm{g}}\text{(v″ = 0)}$ transition in s-tetrazine has been observed and measured. The sample was cooled to a rotational temperature of <1 K by expansion in a supersonic free jet. In this way the rotational structure arising from asymmetry split low J lines could be observed. The rotational A and B axes of the ²H₁¹²C₂¹⁴N₄ isotope were observed to interchange upon electronic excitation and a theory describing the effect of this interchange upon the optical selection rules has been developed. Analysis of the resolved rotational structure suggests that the geometry change upon electronic excitation is smaller than that deduced from previous analysis of the room temperature optical spectrum.     

Electrical properties study of multi-walled carbon nanotubes/hybrid-glass nanocomposites

Electrical properties of multi-walled carbon nanotubes (MWNTs)/hybrid-glass nanocomposites prepared by the fast-sol–gel reaction were investigated in light of percolation theory. A good correlation was found between the experimental results and the theory. We obtained a percolation threshold ? _c  = 0.22 wt%, and a critical exponent of t = 1.73. These values are reported for the first time for a silica-based system. The highest conductivity measured on the MWNT/hybrid-glass nanocomposites was σ ≈ 10^?3(Ω cm)^?1 for 2 wt% carbon nanotube (CNT) loading. The electrical conductivity was at least 12 orders of magnitude higher than that of pure silica. Electrostatic force microscopy and conductive-mode atomic force microscopy studies demonstrated conductivity at the micro-level, which was attributed to the CNT dispersed in the matrix. It appears that the dispersion in our MWNT/hybrid-glass system yields a particularly low percolation threshold compared with that of a MWNT/silica-glass system. Materials with electrical conductivities described in this work can be exploited for anti-static coating.     

Thermoluminescence and radiation-induced volume changes in CaF2 (Mn,RE) materials

The thermoluminescence properties of various CaF₂ materials (natural fluorite, CaF₂-glass ceramics and enamels) doped with RE oxides and Mn are investigated in details. Volumetric measurements show that γ-irradiation leads to a change in the volume density of powder samples of these materials. Depending on the character of the sample, positive (increased volume) or negative dilatation (decreased volume) can be observed during irradiation with doses within the range 1 C/kg–9 C/kg. As time elapses, the radiation-induced alteration of the sample volume is relaxed and after 2–3 months reaches again the initial volume density of the sample. The unexpected result of radiation-induced volume changes are discussed in details accounting for supplementary X-ray, electron microscopy and EPR studies.