Late-time decay of perturbations outside extremal charged black hole

We analyze the late-time decay of scalar perturbations in extremal Reissner-Nordstrom spacetime. We consider individual spherical-harmonic modes $l$ of a test massless scalar field, restricting our attention to initial data of compact support, with generic regular behavior across the horizon. We obtain a decay rate $\propto t^{-(2l+3)}$ (just like in Schwarzschild) for incident waves scattered by the black hole. However, for waves originating at the horizon's neighborhood we obtain a slightly slower decay, $\propto t^{-(2l+2)}$. We discuss relations to previous works.Comment: 24 pages. Minor correction

Limit groups for relatively hyperbolic groups, I: The basic tools

We begin the investigation of Gamma-limit groups, where Gamma is a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. Using the results of Drutu and Sapir, we adapt the results from math.GR/0404440 to this context. Specifically, given a finitely generated group G, and a sequence of pairwise non-conjugate homomorphisms {h_n : G -> Gamma}, we extract an R-tree with a nontrivial isometric G-action. We then prove an analogue of Sela's shortening argument.Comment: 41 pages. The new version of this paper has been substantially rewritten. It now includes all of the results of the previous version, and also of math.GR/0408080. The exception to this is the proof of the Hopf property, which follows imediately from Theorem 5.2 of math.GR/0503045 (and does not use anything omitted from this version

One against all in the fictitious play process

There are only few "positive" results concerning multi-person games with the fictitious play property, that is, games in which every fictitious play process approaches the set of equilibria. In this paper we chararcterize classes of multi-person games with the fictitious play property. We consider an (n+1) player game {0,1,2,...,n} based on n two-person sub-games. In each of these sub-games player 0 plays against one of the other players. Player 0 is regulated, so that he must choose the same strategy in all n sub-games. we show that if all sub-games are either zero-sum ganes, weighted potential games, or games with identical payoff functions, then the fictitious play property holds for the associated game.

Sequential Two-Prize Contests

We study two-stage all-pay auctions with two identical prizes. In each stage, players compete for one prize. Each player may win either one or two prizes. We analyze the equilibrium strategies where players’ marginal values for the prizes are either declining or incliningMulti-prize contests, All-pay auctions

Operating a quantum pump in a closed circuit

During an adiabatic pumping cycle a conventional two barrier quantum device takes an electron from the left lead and ejects it to the right lead. Hence the pumped charge per cycle is naively expected to be $Q \le e$. This zero order adiabatic point of view is in fact misleading. For a closed device we can get ${Q > e}$ and even ${Q \gg e}$. In this paper a detailed analysis of the quantum pump operation is presented. Using the Kubo formula for the geometric conductance, and applying the Dirac chains picture, we derive practical estimates for~$Q$.Comment: 19 pages, 8 figs, minor textual corretions, to be published in JP

Symmetry-resolved entanglement in many-body systems

Similarly to the system Hamiltonian, a subsystem's reduced density matrix is composed of blocks characterized by symmetry quantum numbers (charge sectors). We present a geometric approach for extracting the contribution of individual charge sectors to the subsystem's entanglement measures within the replica trick method, via threading appropriate conjugate Aharonov-Bohm fluxes through a multi-sheet Riemann surface. Specializing to the case of 1+1D conformal field theory, we obtain general exact results for the entanglement entropies and spectrum, and apply them to a variety of systems, ranging from free and interacting fermions to spin and parafermion chains, and verify them numerically. We find that the total entanglement entropy, which scales as $\ln L$, is composed of $\sqrt{\ln L}$ contributions of individual subsystem charge sectors for interacting fermion chains, or even $\mathcal{O} (L^0)$ contributions when total spin conservation is also accounted for. We also explain how measurements of the contribution to the entanglement from separate charge sectors can be performed experimentally with existing techniques.Comment: 5+1 pages, 3 figures; v2: published versio

Spin-charge coupling in quantum wires at zero magnetic field

We discuss an approximation for the dynamic charge response of nonlinear spin-1/2 Luttinger liquids in the limit of small momentum. Besides accounting for the broadening of the charge peak due to two-holon excitations, the nonlinearity of the dispersion gives rise to a two-spinon peak, which at zero temperature has an asymmetric line shape. At finite temperature the spin peak is broadened by diffusion. As an application, we discuss the density and temperature dependence of the Coulomb drag resistivity due to long-wavelength scattering between quantum wires.Comment: 16 pages, 5 figures. This is an extended version of "Coulomb drag from spin-charge coupling at zero magnetic field

Condensation of Photons coupled to a Dicke Field in an Optical Microcavity

Motivated by recent experiments reporting Bose-Einstein condensation (BEC) of light coupled to incoherent dye molecules in a microcavity, we show that due to a dimensionality mismatch between the 2D cavity-photons and the 3D arrangement of molecules, the relevant molecular degrees of freedom are collective Dicke states rather than individual excitations. For sufficiently high dye concentration the coupling of the Dicke states with light will dominate over local decoherence. This system also shows Mott criticality despite the absence of an underlying lattice in the limit when all dye molecules become excited.Comment: 4 pages + supplementary materia

Fictitious play and- no-cycling conditions

We investigate the paths of pure strategy profiles induced by the fictitious play process. We present rules that such paths must follow. Using these rules we prove that every non-degenerate 2*3 game has the continuous fictitious play property, that is, every continuous fictitious play process, independent of initial actions and beliefs, approaches equilibrium in such games.