Analyticity properties of eigenfunctions and scattering matrix

For potentialsV=V(x)=O(|x|^–2–) for |x|,x³ we prove that if theS-matrix of (–, –+V) has an analytic extension to a regionO in the lower half-plane, then the family of generalized eigenfunctions of –+V has an analytic extension toO such that for |Imk|<b. Consequently, the resolvent (–+V–z ²)^–1 has an analytic continuation from ⁺ to {kOImk|<b} as an operator from _b ={f=e ^–b|x| g|gL ₂(³)} to _–b . Based on this, we define for potentialsW=o(e ^–2b|x|) resonances of (–+V, –+V+W) as poles of and identify these resonances with poles of the analytically continuedS-matrix of (–+V, –+V+W).The author would like to thank the Institute for Advanced Study for its hospitality and the National Science Foundation for financial support under Grant No. DMS-8610730(1)     

C=1 conformal field theories on Riemann surfaces

We study the theory ofc=1 torus and ₂-orbifold models on general Riemann surfaces. The operator content and occurrence of multi-critical points in this class of theories is discussed. The partition functions and correlation functions of vertex operators and twist fields are calculated using the theory of double covered Riemann surfaces. It is shown that orbifold partition functions are sensitive to the Torelli group. We give an algebraic construction of the operator formulation of these nonchiral theories on higher genus surfaces. Modular transformations are naturally incorporated as canonical transformations in the Hilbert space.     

On the metric properties of the Feigenbaum attractor

The two standard literature definitions of the function associated with the Feigenbaum attractor are not equivalent. The method due to Vulet al. and Feigenbaum is used to calculate the Haussdorff dimension of the Feigenbaum attractor, using as input the trajectory scaling functions. The two calculations yield the same Hausdorff dimensionD=0.5380451435 to within the accuracy of the computation.     

Anomalous capacitance of quantum well double-barrier diodes

The S-parameters of several different quantum well double barrier diodes have been measured. A technique has been developed for measuring whisker contacted diodes with and HP 8510B automatic network analyzer. Special coaxial mounts using K-connectors were designed to enable measurements up to 20 GHz. The voltage-dependent conductance and capacitance were derived from the measured reflection coefficient of each device. The C/V characteristics were observed to exhibit an anomalous increase at voltages corresponding the the negative differential resistance region (NDR). These are the first reported S-parameter measurements in the negative differential resistance region of quantum well double barrier diodes. A theory is presented that explains, in part, the observed results.     

State tomography of capacitively shunted phase qubits with high fidelity

We introduce a new design concept for superconducting phase quantum bits (qubits) in which we explicitly separate the capacitive element from the Josephson tunnel junction for improved qubit performance. The number of two-level systems that couple to the qubit is thereby reduced by an order of magnitude and the measurement fidelity improves to 90%. This improved design enables the first demonstration of quantum state tomography with superconducting qubits using single-shot measurements.     

Single-molecule pump-probe detection resolves ultrafast pathways in individual and coupled quantum systems

We report the first experimental study of individual molecules with femtosecond time resolution using a novel ultrafast single-molecule pump-probe method. A wide range of relaxation times from below 100 up to 400 fs is found, revealing energy redistribution over different vibrational modes and phonon coupling to the nanoenvironment. Addressing quantum-coupled molecules we find longer decay times, pointing towards inhibited intramolecular decay due to delocalized excitation. Interestingly, each individual system shows discrete jumps in femtosecond response, reflecting sudden breakup of the coupled superradiant state.     

Quantum diffusion of positive muons

Recent studies of the diffusion of positive muons in metals, particularly aluminium, are reviewed. At low temperatures, quantum tunnelling is an important process for the mobility of the muons and experiments aimed at the study of tunnelling in the presence of phonons and conduction electrons are discussed. The concept of quantum diffusion is introduced and the conditions for quantum diffusion and quantum propagation (i.e. band-like motion) in normal and superconducting metals are compared.     

A multigrid method with unstructured adaptive grids for steady Euler equations

The multigrid method based on multi-stage Jacobi relaxation, earlier developed by the authors for structured grid calculations with Euler equations, is extended to unstructured grid applications. The meshes are generated with Delaunay triangulation algorithms and are adapted to the flow solution.     

Tabu search for graph partitioning

In this paper, we develop a tabu search procedure for solving the uniform graph partitioning problem. Tabu search, an abstract heuristic search method, has been shown to have promise in solving several NP-hard problems, such as job shop and flow shop scheduling, vehicle routing, quadratic assignment, and maximum satisfiability. We compare tabu search to other heuristic procedures for graph partitioning, and demonstrate that tabu search is superior to other solution approaches for the uniform graph partitioning problem both with respect to solution quality and computational requirements.