Bethe ansatz approach to the Kondo effect within density-functional theory

Transport through an Anderson junction (two macroscopic electrodes coupled to an Anderson impurity) is dominated by a Kondo peak in the spectral function at zero temperature. We show that the single-particle Kohn-Sham potential of density-functional theory reproduces the linear transport, despite the lack of a Kondo peak in its spectral function. Using Bethe ansatz techniques, we calculate this potential for all coupling strengths, including the crossover from mean-field behavior to charge quantization caused by the derivative discontinuity. A simple and accurate interpolation formula is also given.     

Determining the energy barrier for decay out of superdeformed bands

An asymptotically exact quantum mechanical calculation of the matrix elements for tunneling through an asymmetric barrier is combined with the two-state statistical model for decay out of superdeformed bands to determine the energy barrier (as a function of spin) separating the superdeformed and normal-deformed wells for several nuclei in the 190 and 150 mass regions. The spin-dependence of the barrier leading to sudden decay out is shown to be consistent with the decrease of a centrifugal barrier with decreasing angular momentum. Values of the barrier frequency in the two mass regions are predicted.     

Naïve noncommutative blowups at zero-dimensional schemes

In an earlier paper [D.S. Keeler, D. Rogalski, J.T. Stafford, Naïve noncommutative blowing up, Duke Math. J. 126 (2005) 491–546, MR 2120116], we defined and investigated the properties of the naïve blowup of an integral projective scheme X at a single closed point. In this paper we extend those results to the case when one naïvely blows up X at any suitably generic zero-dimensional subscheme Z. The resulting algebra A has a number of curious properties; for example it is noetherian but never strongly noetherian and the point modules are never parametrized by a projective scheme. This is despite the fact that the category of torsion modules in qgr-A is equivalent to the category of torsion coherent sheaves over X. These results are used in the companion paper [D. Rogalski, J.T. Stafford, A class of noncommutative projective surfaces, in press] to prove that a large class of noncommutative surfaces can be written as naïve blowups.     

Simplicity of noncommutative Dedekind domains

The following dichotomy is established: A finitely generated, complex Dedekind domain that is not commutative is a simple ring. Weaker versions of this dichotomy are proved for Dedekind prime rings and hereditary noetherian prime rings.

     

Intra-cavity power effects in singly resonant cw OPOs

A continuous wave singly resonant optical parametric oscillator (cw SRO) has been developed that can be pumped at a level of up to 15 times its oscillation threshold by a single frequency fiber laser pump source. We report the observation of extremely high intra-cavity circulating powers of over 1 kW at the signal wavelength, and associated effects including heating of the nonlinear crystal, and beam quality degradation. Furthermore we show that these effects may be mitigated by implementing output coupling, while also extracting multi-Watt single frequency power output at both signal and idler wavelengths. PACS 42.65.Yj; 42.55.Wd; 42.62.Fi     

Manipulating morphology and orientation in thermally responsive block copolymer thin films

We demonstrate the use of combined thermal annealing and solvent vapor annealing (SVA) to tune the morphology of thermally responsive block copolymer (BCP) thin films. The BCP, poly(styrene‐b‐tert‐butyl acrylate) (PS‐b‐PtBA), undergoes a chemical deprotection to poly(styrene‐b‐acrylic anhydride) (PS‐b‐PAH) above a temperature threshold, giving rise to a structural and morphological transition. Our experiments systematically examine different thermal annealing and SVA protocols with two solvents (tetrahydrofuran and acetone) and map the resulting morphologies. Assessments of these processing protocols were accelerated using temperature gradients. Our results demonstrate that the final nanoscale morphologies after SVA are determined by the changes in the relative solvent/polymer interactions and surface tensions of the polymer blocks that accompany deprotection. Because of these driving forces, certain processing combinations led to irreversible morphological states, whereas others present opportunities for further manipulation. Accordingly, our study reveals that the morphology of this thermally sensitive BCP can be altered through judicious choice of annealing protocol. The protocols that combine equal numbers of SVA and thermal annealing (TA) steps are not necessarily equivalent, and the order of the SVA relative to TA is a deciding factor in the final morphology. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Trifunctional polycondensation: A cumulative distribution function

A trifunctional polycondensation, cumulative-weight-fraction distribution function has been derived. The equation is exact and yields cumulative-weight fractions that are the same as those calculated by summation of the differential distribution function. The cumulative distribution function still contains factorials, which renders computation difficult for high values of i. The cumulative distribution function is derived in a form that allows inferences to be drawn on whether mass is conserved past an extent of reaction of p = 0.5 or whether a material loss to what is considered a gel phase occurs. The inferences that can be drawn indicate that mass is conserved up to p = 1. The discrepancy between this finding and the requirements of the Flory gel–sol theory are discussed.