Normalized Ricci flow on Riemann surfaces and determinants of Laplacian

In this note we give a simple proof of the fact that the determinant of Laplace operator in smooth metric over compact Riemann surfaces of arbitrary genus $g$ monotonously grows under the normalized Ricci flow. Together with results of Hamilton that under the action of the normalized Ricci flow the smooth metric tends asymptotically to metric of constant curvature for $g\geq 1$, this leads to a simple proof of Osgood-Phillips-Sarnak theorem stating that that within the class of smooth metrics with fixed conformal class and fixed volume the determinant of Laplace operator is maximal on metric of constant curvatute.Comment: a reference to paper math.DG/9904048 by W.Mueller and K.Wendland where the main theorem of this paper was proved a few years earlier is adde

Stability analysis of the Witten black hole (cigar soliton) under world-sheet RG flow

We analyze the stability of the Euclidean Witten black hole (the cigar soliton in mathematics literature) under first-order RG (Ricci) flow of the world-sheet sigma model. This analysis is from the target space point of view. We find that the Witten black hole has no unstable normalizable perturbative modes in a linearized mode analysis in which we consider circularly symmetric perturbations. Finally, we discuss a result from mathematics that implies the existence of a non-normalizable mode of the Witten black hole under which the geometry flows to the sausage solution studied by Fateev, Onofri and Zamolodchikov.Comment: 17 pages, version to appear in Physical Review D, and now has complete proof of stability for circularly symmetric perturbations, in response to referee comment

Single-charge rotating black holes in four-dimensional gauged supergravity

We consider four-dimensional U(1)^4 gauged supergravity, and obtain asymptotically AdS_4, non-extremal, charged, rotating black holes with one non-zero U(1) charge. The thermodynamic quantities are computed. We obtain a generalization that includes a NUT parameter. The general solution has a discrete symmetry involving inversion of the rotation parameter, and has a string frame metric that admits a rank-2 Killing-Stackel tensor.Comment: 9 page

Symmetries of supergravity black holes

We investigate Killing tensors for various black hole solutions of supergravity theories. Rotating black holes of an ungauged theory, toroidally compactified heterotic supergravity, with NUT parameters and two U(1) gauge fields are constructed. If both charges are set equal, then the solutions simplify, and then there are concise expressions for rank-2 conformal Killing-Stackel tensors. These are induced by rank-2 Killing-Stackel tensors of a conformally related metric that possesses a separability structure. We directly verify the separation of the Hamilton-Jacobi equation on this conformally related metric, and of the null Hamilton-Jacobi and massless Klein-Gordon equations on the "physical" metric. Similar results are found for more general solutions; we mainly focus on those with certain charge combinations equal in gauged supergravity, but also consider some other solutions.Comment: 36 pages; v2: minor changes; v3: slightly shorte

Extremal Black Hole/CFT Correspondence in (Gauged) Supergravities

We extend the investigation of the recently proposed Kerr/CFT correspondence to large classes of rotating black hole solutions in gauged and ungauged supergravities. The correspondence, proposed originally for four-dimensional Kerr black holes, asserts that the quantum states in the near-horizon region of an extremal rotating black hole are holographically dual to a two-dimensional chiral theory whose Virasoro algebra arises as an asymptotic symmetry of the near-horizon geometry. In fact in dimension D there are [(D-1)/2] commuting Virasoro algebras. We consider a general canonical class of near-horizon geometries in arbitrary dimension D, and show that in any such metric, the [(D-1)/2] central charges each imply, via the Cardy formula, a microscopic entropy that agrees with the Bekenstein-Hawking entropy of the associated extremal black hole. In the remainder of the paper we show for most of the known rotating black hole solutions of gauged supergravity, and for the ungauged supergravity solutions with four charges in D=4 and three charges in D=5, that their extremal near-horizon geometries indeed lie within the canonical form. This establishes that in all these examples, the microscopic entropies of the dual CFTs agree with the Bekenstein-Hawking entropies of the extremal rotating black holes.Comment: 32 pages, references added and minor typos fixe

Giant Modal Gain, Amplified Surface Plasmon Polariton Propagation, and Slowing Down of Energy Velocity in a Metal-Semiconductor-Metal Structure

We investigated surface plasmon polariton (SPP) propagation in a metal-semiconductor-metal structure where semiconductor is highly excited to have optical gain. We show that near the SPP resonance, the imaginary part of the propagation wavevector changes from positive to hugely negative, corresponding to an amplified SPP propagation. The SPP experiences a giant gain that is 1000 times of material gain in the excited semiconductor. We show that such a giant gain is related to the slowing down of average energy propagation in the structur

Electron tunneling time measured by photoluminescence excitation correlation spectroscopy

The tunneling time for electrons to escape from the lowest quasibound state in the quantum wells of GaAs/AlAs/GaAs/AlAs/GaAs double-barrier heterostructures with barriers between 16 and 62 Å has been measured at 80 K using photoluminescence excitation correlation spectroscopy. The decay time for samples with barrier thicknesses from 16 Å (≈12 ps) to 34 Å(≈800 ps) depends exponentially on barrier thickness, in good agreement with calculations of electron tunneling time derived from the energy width of the resonance. Electron and heavy hole carrier densities are observed to decay at the same rate, indicating a coupling between the two decay processes

Twisted and Nontwisted Bifurcations Induced by Diffusion

We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution represents a stable, spatially homogeneous time-periodic solution of the PDE. We show that when the diffusion coefficients become small, the spatially homogeneous periodic solution becomes unstable and bifurcates into spatially nonhomogeneous periodic solutions. The nature of the bifurcation is determined by the twistedness of an equilibrium/homoclinic bifurcation that occurs as the diffusion coefficients decrease. In the nontwisted case two spatially nonhomogeneous simple periodic solutions of equal period are generated, while in the twisted case a unique spatially nonhomogeneous double periodic solution is generated through period-doubling. Key Words: Reaction-diffusion equations; predator-prey systems; homoclinic bifurcations; periodic solutions.Comment: 42 pages in a tar.gz file. Use ``latex2e twisted.tex'' on the tex files. Hard copy of figures available on request from [email protected]

A KINEMATIC ANALYSIS OF TRUNK ABILITY IN WHEELCHAIR FENCING: A PILOT STUDY

The purpose of this study was to explore the trunk ability differences between category A and B participants in wheelchair fencing. The result showed that category B participants might perform similar performance as category A participants in maximum lunge velocity, maximum lunge angle and maximum fast return velocity. This result may provide information to International Wheelchair Fencing Committee (IWFC) for the need of research on Wheelchair Fencing Classification (WFC) to clarify the differences between these two categories of participants