2,061 research outputs found

    Existence and uniqueness of the integrated density of states for Schr\"odinger operators with magnetic fields and unbounded random potentials

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    The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal. {\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first version of math-ph/0010013. For a revised version of the second part, see math-ph/0105046. To appear in Reviews in Mathematical Physic

    Low lying spectrum of weak-disorder quantum waveguides

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    We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis.Comment: Accepted for publication in Journal of Statistical Physics http://www.springerlink.com/content/0022-471

    A New Experimental Approach to Evaluate Plasma-induced Damage in Microcantilever

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    Plasma  etching,  during  micro-fabrication  processing  is  indispensable  for  fabricating  MEMS  structures.  During  the plasma  processes,  two  major matters,  charged  ions  and  vacuum–ultraviolet  (VUV)  irradiation  damage,  take  charge  of reliability  degradation.  The  charged  ions  induce  unwanted  sidewall  etching,  generally  called  as  “notching”,  which causes  degradation  in  brittle  strength.  Furthermore,  the  VUV  irradiation  gives  rise  to  crystal  defects  on  the  etching surface.  To  overcome  the  problem,  neutral  beam  etching  (NBE),  which  use  neutral  particles  without  the  VUV irradiation,  has  been  developed.  In  order  to  evaluate  the  effect  of  the  NBE  quantitatively,  we  measured  the  resonance property of a micro-cantilever before and after NBE treatment. The thickness of damage layer (δ) times the imaginary part  of  the  complex  Young's  modulus  (Eds)  were  then  compared,  which  is  a  parameter  of  surface  damage.  Although plasma processes  make the initial surface of cantilevers damaged during their fabrication, the removal of that damage by NBE was confirmed as the reduction in δEds. NBE will realize a damage-free surface for microstructures

    Wettability characteristics of an Al2O3/SiO2-based ceramic modified with CO2, Nd:YAG, excimer and high-power diode lasers

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    Interaction of CO2, Nd:YAG, excimer and high power diode laser (HPDL) radiation with the surface of an Al2O3/SiO2 based ceramic was found to effect significant changes in the wettability characteristics of the material. It was observed that interaction with CO2, Nd:YAG and HPDL radiation reduced the enamel contact angle from 1180 to 310, 340 and 330 respectively. In contrast, interaction with excimer laser radiation resulted an increase in the contact angle to 1210. Such changes were identified as being due to: (i) the melting and partial vitrification of the Al2O3/SiO2 based ceramic surface as a result of interaction with CO2, Nd:YAG HPDL radiation. (ii) the surface roughness of the Al2O3/SiO2 based ceramic increasing after interaction with excimer laser radiation. (iii) the surface oxygen content of the Al2O3/SiO2 based ceramic increasing after interaction with CO2, Nd:YAG and HPDL radiation. The work has shown that the wettability characteristics of the Al2O3/SiO2 based ceramic could be controlled and/or modified with laser surface treatment. In particular, whether the laser radiation had the propensity to cause surface melting. However, a wavelength dependance of the change of the wetting properties could not be deduced from the findings of this work
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