The Happer's puzzle degeneracies and Yangian

We find operators distinguishing the degenerate states for the Hamiltonian $H= x(K+{1/2})S_z +{\bf K}\cdot {\bf S}$ at $x=\pm 1$ that was given by Happer et al$^{[1,2]}$ to interpret the curious degeneracies of the Zeeman effect for condensed vapor of $^{87}$Rb. The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of $Y(sl(2))$.Comment: 8 pages, Latex fil

Photon-Assisted Quasiparticle Transport and Andreev Transport through an Interacting Quantum Dot

Resonant tunneling through a quantum dot coupled to superconducting reservoirs in the presence of time-dependent external voltage has been studied. A general formula of the current is derived based on the nonequilibrium Green's function technique. Using this formula photon-assisted quasiparticle transport has been investigated for the quantum dot connected to superconductors. In addition, resonant Andreev transport through a strongly correlated quantum dot connected to a normal metallic lead and a superconducting lead is studied.Comment: 9 pages(1 column) with 3 figure

An experimental study of coupling between combustor pressure, fuel/air mixing, and the flame

Fuel-air mixing behavior under the influence of imposed acoustic oscillations has been studied by investigating the response of the fuel mixture fraction field. The distribution of local fuel mixture fraction inside the mixing zone, which is expected to evolve into the local equivalence ratio in the flame zone, is closely coupled to unstable and oscillatory flame behavior. The Experiment was performed with an aerodynamically-stabilized non-premixed burner. In this study, acoustic oscillations were imposed at 22, 27, 32, 37, and 55Hz. Phase-resolved acetone PLIF was used to image the flow field of both isothermal and reacting flow cases and this data along with the derived quantities of temporal and spatial unmixedness were employed for analysis. The behavior of the unmixedness factor is compared with the previous measurements of oscillations in the flame zone. This comparison shows that local oscillations (of order millimeters or smaller) in fuel/air mixing are closely related to the oscillatory behavior of the flame. For each driving frequency, the mixture fraction oscillates at that frequency but with a slight phase difference between it and the pressure field/flame intensity, indicating that the fuel mixture fraction oscillation are likely the major reason for oscillatory behaviors of this category of flames and combustor geometry

Two essays on managerial risk-seeking activities and compensation contracts

textThis dissertation examines how the structures of compensation for executives and directors are affected by the possibility that managers can influence the risk of a firm's cash flows. In chapter 1, I consider a moral hazard model which shows that a strong pay-for-performance sensitivity in managerial compensation may deteriorate shareholder value when shareholders cannot monitor managerial risk-seeking activities. Intuitively, while high-powered managerial compensation provides the manager with incentives to increase the firm's value by exerting effort, it also creates managerial incentive to engage in (unproductive) risk-seeking activities. To test this prediction, I consider a regulatory change that makes it more difficult for managers to conceal information about the (speculative) use of derivative instruments. Specifically, I examine how the structures of compensation for executives and managers are affected by the adoption of a new accounting standard, the Statement of Financial Accounting Standard No. 133 Accounting for Derivative Instruments and Hedging Activities (FAS 133) which mandates the fair value accounting for derivative holdings. Consistent with the model prediction, I find that relative to other firms, derivative users (firms that traded derivatives before adopting FAS 133) increase the pay-for-performance sensitivity of CEO/CFO compensation. In Chapter 2, I extend the model by incorporating the realistic features that shareholders delegate to the (self-interested) board the tasks of monitoring managers and of setting their compensation contracts. My analysis shows that while high-powered board compensation induces the board to monitor the firm and to properly design managerial compensation, it also provides the board with incentives to misreport managerial risk-seeking activities and to engage in collusive behavior with the manager at the expense of shareholders. From these trade-offs, I develop a number of testable hypotheses and take them to the data. Consistent with the model predictions, I find that firms in which (i) managerial risk-seeking activities are more likely to occur (e.g., high R&D firms or banks) and (ii) board monitoring costs are likely to be lower (e.g., firms that have non-officer blockholders on the board) show weaker pay-for-performance sensitivity of board compensation and stronger pay-for-performance sensitivity of CEO compensation.Financ