Low noise 80–115 GHz quasiparticle mixer with small Nb/Al-Oxide/Nb tunnel junctions

Millimeter-wave characterization of a heterodyne receiver using (2 m²) Nb/Al-Ox/Nb Superconducting-Insulator-Superconducting (SIS) junctions arrays is reported. The fabrication of the Nb/Al-Ox/Nb SIS junction arrays as a heterodyne mixer is described. The leakage current of these junctions is below 2A at 4.2K and unmeasurable at 2.5K. The receiver gave a noise temperature Double Side Band (DSB) between 63K and 187K over the frequency range 80 to 115 GHz at the first conversion peak. The results are comparable to those obtained with SIS receivers using well researched lead junctions. Contrary to the lead junctions, our mixer using all Nb junctions have proven remarkably stable with respect to thermal cycling, characteristics which are required for space applications. To our knowledge, this is the most reliable low noise receiver operating in this frequency range.     

Comparison theorems for weak splittings of bounded operators

Summary Comparison theorems for weak splittings of bounded operators are presented. These theorems extend the classical comparison theorem for regular splittings of matrices by Varga, the less known result by Wonicki, and the recent results for regular and weak regular splittings of matrices by Neumann and Plemmons, Elsner, and Lanzkron, Rose and Szyld. The hypotheses of the theorems presented here are weaker and the theorems hold for general Banach spaces and rather general cones. Hypotheses are given which provide strict inequalities for the comparisons. It is also shown that the comparison theorem by Alefeld and Volkmann applies exclusively to monotone sequences of iterates and is not equivalent to the comparison of the spectral radius of the iteration operators.This work was supported by the National Science Foundation grants DMS-8807338 and INT-8918502     

First passage percolation: The stationary case

Summary If the passage time of the edges of the ^d lattice are stationary, ergodic and have finite moment of orderp>d, then a.s. the set of vertices that can be reached within timet, has an asymptotic shape ast.     

Multiple ergodic theorems

Given measure preserving transformationsT ₁,T ₂,...,T _s of a probability space (X,B, μ) we are interested in the asymptotic behaviour of ergodic averages of the form $$\frac{1}{N}\sum\limits_{n = 0}^{N - 1} {T_1^n f_1 \cdot T_2^n f_2 } \cdot \cdots \cdot T_s^n f_s $$ wheref ₁,f ₂,...,f _s ?L ^∞(X,B,μ). In the general case we study, mainly for commuting transformations, conditions under which the limit of (1) inL ²-norm is ∫ _x f ₁ dμ·∫ _x f ₂ dμ...∫ _x f _s dμ for anyf ₁,f ₂...,f _s ?L ^∞(X,B,μ). If the transformations are commuting epimorphisms of a compact abelian group, then this limit exists almost everywhere. A few results are also obtained for some classes of non-commuting epimorphisms of compact abelian groups, and for commuting epimorphisms of arbitrary compact groups.     

ℤ/k-manifolds and families of Dirac operators

Summary The index of a family of a family of Dirac operators is aK-Theory element in the parameter space. Sullivan's/k-manifolds are used to detect this index completely. For the first Chern class this gives a topological interpretation of Witten's global anomaly. The relationship with the geometry of the index bundle is considered.To my teacher Isadore M. SingerThe author is partially supported by an NSF Postdoctoral Research Fellowship     

Optical reference geometry for stationary and static dynamics

Attention is drawn to the advantages of representing dynamical behavior in a stationary or static background spacetime in terms of a fixed reference 3-geometry that differs from the usual one by a certain conformal rescaling factor. The resulting Riemannian metric may be appropriately described as the optical geometry in recognition of the fact that line-of-sight trajectories are faithfully represented within it as geodesic, at least in the strictly static case for which such lines-of-sight are unambiguously defined. (In more general stationary examples the geodesies represent what amounts to the result of a cancellation between the Coriolis-type effects that would cause a physical light path to deviate to one side or the other depending on the sense of propagation.) The application to the particular case of the Schwarzschild solution is discussed: In this example the optical 3-geometry has a throat that occurs not on the horizon (as in the directly projected 3-geometry) but at the radius of the circular null geodesic orbit.     

Correlation length bounds for disordered Ising ferromagnets

Thed-dimensional, nearest-neighbor disordered Ising ferromagnet: $$H = - \sum {J_{ij} \sigma _i \sigma _j }$$ is studied as a function of both temperature,T, and a disorder parameter,λ, which measures the size of fluctuations of couplingsJ _ij ≧0. A finite-size scaling correlation length,ζ _f (T, λ), is defined in terms of the magnetic response of finite samples. This correlation length is shown to be equivalent, in the scaling sense, to the quenched average correlation lengthζ(T, λ), defined as the asymptotic decay rate of the quenched average two-point function. Furthermore, the magnetic response criterion which definesζ _f is shown to have a scale-invariant property at the critical point. The above results enable us to prove that the quenched correlation length satisfies: $$C\left| {\log \xi (T)} \right|\xi (T) \geqq \left| {T - T_c } \right|^{ - {2 \mathord{\left/ {\vphantom {2 d}} \right. \kern-\nulldelimiterspace} d}}$$ which implies the boundv≧2/d for the quenched correlation length exponent.