Retarded Green's Functions In Perturbed Spacetimes For Cosmology and Gravitational Physics

Electromagnetic and gravitational radiation do not propagate solely on the null cone in a generic curved spacetime. They develop "tails," traveling at all speeds equal to and less than unity. If sizeable, this off-the-null-cone effect could mean objects at cosmological distances, such as supernovae, appear dimmer than they really are. Their light curves may be distorted relative to their flat spacetime counterparts. These in turn could affect how we infer the properties and evolution of the universe or the objects it contains. Within the gravitational context, the tail effect induces a self-force that causes a compact object orbiting a massive black hole to deviate from an otherwise geodesic path. This needs to be taken into account when modeling the gravitational waves expected from such sources. Motivated by these considerations, we develop perturbation theory for solving the massless scalar, photon and graviton retarded Green's functions in perturbed spacetimes, assuming these Green's functions are known in the background spacetime. In particular, we elaborate on the theory in perturbed Minkowski spacetime in significant detail; and apply our techniques to compute the retarded Green's functions in the weak field limit of the Kerr spacetime to first order in the black hole's mass and angular momentum. Our methods build on and generalizes work appearing in the literature on this topic to date, and lays the foundation for a thorough, first principles based, investigation of how light propagates over cosmological distances, within a spatially flat inhomogeneous Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) universe. This perturbative scheme applied to the graviton Green's function, when pushed to higher orders, may provide approximate analytic (or semi-analytic) results for the self-force problem in the weak field limits of the Schwarzschild and Kerr black hole geometries.Comment: 23 pages, 5 figures. Significant updates in v2: Scalar, photon and graviton Green's functions calculated explicitly in Kerr black hole spacetime up to first order in mass and angular momentum (Sec. V); Visser's van Vleck determinant result shown to be equivalent to ours in Sec. II. v3: JWKB discussion moved to introduction; to be published in PR

Initial overview of disconnection events in Halley's Comet 1986

We present an initial overview of the disconnection events (DE's) in Comet Halley in 1986. Although disconnection events are arguably the most spectacular of all dynamic comet phenomena, the mechanisms by which they occur are not fully understood. It is generally believed that the solar wind plays a major role in determining when disconnection events occur, but the details of the solar wind/cometary interactions responsible for initiating the tail disconnection are still under debate. The three most widely accepted models are: (1) high speed streams in the solar wind cause the tail to disconnect due to pressure effects; (2) decreased production of cometary ions in a high speed stream allows magnetic field to slip away from the comet; and (3) the tail disconnects after frontside reconnection of the interplanetary magnetic field (IMF) as the comet crosses a magnetic field sector boundary. We find that the front-side magnetic reconnection model is the best explanation for the DE's we have considered

Atom-molecule conversion with particle losses

Based on the mean-field approximation and the phase space analysis, we study the dynamics of an atom-molecule conversion system subject to particle loss. Starting from the many-body dynamics described by a master equation, an effective nonlinear Schr\"odinger equation is introduced. The classical phase space is then specified and classified by fixed points. The boundary, which separate different dynamical regimes have been calculated and discussed. The effect of particle loss on the conversion efficiency and the self-trapping is explored.Comment: 6 pages, 5 figure

Effective Hamiltonian approach to adiabatic approximation in open systems

The adiabatic approximation in open systems is formulated through the effective Hamiltonian approach. By introducing an ancilla, we embed the open system dynamics into a non-Hermitian quantum dynamics of a composite system, the adiabatic evolution of the open system is then defined as the adiabatic dynamics of the composite system. Validity and invalidity conditions for this approximation are established and discussed. A High-order adiabatic approximation for open systems is introduced. As an example, the adiabatic condition for an open spin-$\frac 1 2$ particle in time-dependent magnetic fields is analyzed.Comment: 6 pages, 2 figure

Shock wave propagation in vibrofluidized granular materials

Shock wave formation and propagation in two-dimensional granular materials under vertical vibration are studied by digital high speed photography. The steepen density and temperature wave fronts form near the plate as granular layer collides with vibrating plate and propagate upward through the layer. The temperature front is always in the transition region between the upward and downward granular flows. The effects of driving parameters and particle number on the shock are also explored.Comment: 9 pages, 4 figures, submitted to PR

Phosphofructokinase 1 Glycosylation Regulates Cell Growth and Metabolism

Cancer cells must satisfy the metabolic demands of rapid cell growth within a continually changing microenvironment. We demonstrated that the dynamic posttranslational modification of proteins by O-linked β-N-acetylglucosamine (O-GlcNAcylation) is a key metabolic regulator of glucose metabolism. O-GlcNAcylation was induced at serine 529 of phosphofructokinase 1 (PFK1) in response to hypoxia. Glycosylation inhibited PFK1 activity and redirected glucose flux through the pentose phosphate pathway, thereby conferring a selective growth advantage on cancer cells. Blocking glycosylation of PFK1 at serine 529 reduced cancer cell proliferation in vitro and impaired tumor formation in vivo. These studies reveal a previously uncharacterized mechanism for the regulation of metabolic pathways in cancer and a possible target for therapeutic intervention

Effect of feedback on the control of a two-level dissipative quantum system

We show that it is possible to modify the stationary state by a feedback control in a two-level dissipative quantum system. Based on the geometric control theory, we also analyze the effect of the feedback on the time-optimal control in the dissipative system governed by the Lindblad master equation. These effects are reflected in the function $\Delta_A(\vec{x})$ and $\Delta_B(\vec{x})$ that characterize the optimal trajectories, as well as the switching function $\Phi(t)$ and $\theta(t),$ which characterize the switching point in time for the time-optimal trajectory.Comment: 5 pages, 5 figure