Self-avoiding walk in five or more dimensions I. The critical behaviour

We use the lace expansion to study the standard self-avoiding walk in thed-dimensional hypercubic lattice, ford5. We prove that the numberc _n ofn-step self-avoiding walks satisfiesc _n ~A ⁿ , where is the connective constant (i.e. =1), and that the mean square displacement is asymptotically linear in the number of steps (i.e.v=1/2). A bound is obtained forc _n(x), the number ofn-step self-avoiding walks ending atx. The correlation length is shown to diverge asymptotically like (^––Z)^1/2. The critical two-point function is shown to decay at least as fast as x^–2, and its Fourier transform is shown to be asymptotic to a multiple ofk ^–2 ask0 (i.e. =0). We also prove that the scaling limit is Gaussian, in the sense of convergence in distribution to Brownian motion. The infinite self-avoiding walk is constructed. In this paper we prove these results assuming convergence of the lace expansion. The convergence of the lace expansion is proved in a companion paper.Supported by the Nishina Memorial Foundation and NSF grant PHY-8896163.Supported by NSERC grant A9351     

Recoil-limited laser cooling of 87Sr atoms near the Fermi temperature

A dynamic magneto-optical trap, which relies on the rapid randomization of population in Zeeman substates, has been demonstrated for fermionic strontium atoms on the 1S0-3P1 intercombination transition. The obtained sample, 1x10(6) atoms at a temperature of 2 microK in the trap, was further Doppler cooled and polarized in a far-off resonant optical lattice to achieve 2 times the Fermi temperature.     

Experimental demonstration and stochastic modeling of autonomous formation of nanophotonic droplets

We have previously demonstrated a novel technique for autonomously forming a nanophotonic droplet, which is micro-scale spherical polymer structure that contains paired heterogeneous nanometric components. The sort-selectivity and alignment accuracy of the nanometric components in each nanophotonic droplet, and the related homogeneity of the optical function, are due to a characteristic pairing process based on a phonon-assisted photo-curing method. The proposed method requires irradiating a mixture of components with light to induce optical near-field interactions between each component, and subsequent processes based on these interactions. The pairing yield of components via the interactions is considered to mainly depend on the frequency of their encounters and the size-resonance effect between encountered components. In this paper, we model these two factors by individual stochastic procedures and construct a numerical model to describe the pairing process. Agreement between the results of numerical and experimental demonstrations shows the validity of our stochastic modeling.     

One-dimensional surface reconstruction as an atomic-scale template for the growth of periodically striped Ag films

The role of the In/Si(111)-(4 x 1)-In surface as an atomic-scale geometrical template for the growth of Ag thin films is clarified by scanning tunneling microscopy and low energy electron diffraction. Low-temperature grown Ag films are found to have stripe structures with a transverse periodicity equal to that of indium chains of the In/Si(111)-(4 x 1)-In. The stripes exhibit a structural transformation at the thickness of 6 monolayers (ML); this relaxation allows the stripes to persist up to a thickness as large as 30 ML (approximately = 7 nm) while maintaining their mean periodicity. We attribute this stability to a coincidental matching of the periodicity and the corrugation amplitude between the Ag film and the substrate, which is realized by periodic insertion of stacking faults into a Ag fcc crystal.     

Study of alkyl chain length dependent characteristics of imidazolium based ionic liquids [CnMIM]+[TFSA]− by Brillouin and dielectric loss spectroscopy

This study examined the acoustic phonon mode of ionic liquids consisting of 1-alkyl-3-methyl-imidazolium family (C_nMIM) cations with n values ranging from 2 to 10 and bis(trifluoromethylsulfonyl)amide (TFSA) anion in the temperature range from 300 K to 100 K. [C_nMIM]⁺[TFSA]^? showed depolarized (VH) components of Brillouin peaks at temperatures below the glass transition temperature when n is larger than 4. On the other hand, in the case of ionic liquids with different anions, such as [C₄MIM]⁺[BF₄]^?, [C₄MIM]⁺[PF₆]^? and [C₈MIM]⁺[BF₄]^?, the VH component of Brillouin peaks was not observed in the temperature range investigated. The dielectric loss spectra showed that the temperature dependence of alkyl chain domain relaxation of all ionic liquids followed the Arrhenius law and showed an increase in activation energy at the temperature where the VH component of Brillouin peak appeared. These results suggest that the observed depolarized component of Brillouin peak might originate from uniquely induced polarization in the 2nd domain composed of head groups of cations and anions.     

Interfaces of correlated electron systems: proposed mechanism for colossal electroresistance

Mott's metal-insulator transition at an interface due to band bending is studied by the density matrix renormalization group approach. We show that the result can be recovered by a simple modification of the conventional Poisson's equation approach used in semiconductor heterojunctions. A novel mechanism of colossal electroresistance is proposed, which incorporates the hysteretic behavior of the transition in higher dimensions.     

Propagating beam analysis of fiber wavelength filters with a depressed-index section

A wavelength filter consisting of single-mode and few-mode fibers is investigated numerically. A simple finite-difference beam-propagation method, in which a transparent boundary condition can be imposed, is developed for circularly symmetric waveguides. After confirming the validity of the numerical method by the mode-mismatch loss, we calculate the propagating field in the fiber wavelength filter, in which interference between LP₀₁, and LP₀₂ modes occurs. To improve the filtering operation, a depressed-index fiber is employed for the few-mode fiber. The effects of the radius and refractive index of the depressed section on the transmission power are revealed and discussed. Power is suppressed to less than 0.1% at 1.3 μm, while maintaining power transmission of more than 85% at 1.55 μm. It is also found that the filtering operation shifts to higher wavelengths as the input power is increased when we choose a self-focusing nonlinear material in the depressed section.     

Mid-infrared emissions from Ho3+ in Ga2S3-GeS2-Sb2S3 glass

Emission properties were investigated in the infrared region for Ga₂S₃-GeS₂-Sb₂S₃ glasses doped with Ho³⁺. We performed Judd–Ofelt analysis and lifetime measurements of the ⁵I₄, ⁵I₅, and ⁵I₆ levels, which are the initial levels of the mid-infrared emissions between 3 to 5 μm of Ho³⁺. The quantum efficiencies reached approximately 18%, 64%, and ～100% for the ⁵I₄, ⁵I₅, and ⁵I₆, respectively. Population analyses were carried out from the relative intensities of the emissions in the near-infrared region. We investigated the dependences on the Ho³⁺ ion concentration of the population ratio of the initial levels to the final levels, [initial]/[final], of the mid-infrared emissions. The population ratio of [⁵I₅]/[⁵I₆] decreased with increase of the Ho³⁺ concentration while those of [⁵I₄]/[⁵I₅] and [⁵I₆]/[⁵I₇] increased. Particularly, the former, [⁵I₄]/[⁵I₅], rapidly increased because of the strong concentration quenching of the ⁵I₅ level through cross relaxation. It was found that the population inversion for the 4.8 μm emission due to the transition, ⁵I₄→⁵I₅, was achieved at high Ho³⁺ concentration in the present experiments.