Explicit reconstruction of the entanglement wedge

The problem of how the boundary encodes the bulk in AdS/CFT is still a subject of study today. One of the major issues that needs more elucidation is the problem of subregion duality; what information of the bulk a given boundary subregion encodes. Although the proof given by Dong, Harlow, and Wall states that the entanglement wedge of the bulk should be encoded in boundary subregions, no explicit procedure for reconstructing the entanglement wedge was given so far. In this paper, mode sum approach to obtaining smearing functions for a single bulk scalar is generalised to include bulk reconstruction in the entanglement wedge of boundary subregions. It is generally expectated that solutions to the wave equation on a complicated coordinate patch are needed, but this hard problem has been transferred to a less hard but tractable problem of matrix inversion.Comment: version accepted by JHEP; added references and discussions on covarianc

Statistical properties of chaotic microcavities in small and large opening cases

We study the crossover behavior of statistical properties of eigenvalues in a chaotic microcavity with different refractive indices. The level spacing distributions change from Wigner to Poisson distributions as the refractive index of a microcavity decreases. We propose a non-hermitian matrix model with random elements describing the spectral properties of the chaotic microcavity, which exhibits the crossover behaviors as the opening strength increases.Comment: 22 pages, 6 figure

Quantum corrections to frame-dragging in scattering amplitudes

Frame-dragging effect manifests itself as polarization direction rotation when linearly polarized electromagnetic/gravitational wave scatters from a spinning point source through gravitational interactions. Treating general relativity as an effective field theory, the polarization rotation angle and its quantum corrections are computed using scattering amplitudes. While the classical angle is universal as expected from the equivalence principle, the quantum corrections are found to be different between electromagnetic and gravitational waves, supporting earlier studies that some formulations of the equivalence principle seem to be violated in the quantum regime.Comment: more accessible discussions, shortened abstract, updated references; 7 pages, 1 TikZ figure, 1 ancillary fil

Quasiattractors in coupled maps and coupled dielectric cavities

We study the origin of attracting phenomena in the ray dynamics of coupled optical microcavities. To this end we investigate a combined map that is composed of standard and linear map, and a selection rule that defines when which map has to be used. We find that this system shows attracting dynamics, leading exactly to a quasiattractor, due to collapse of phase space. For coupled dielectric disks, we derive the corresponding mapping based on a ray model with deterministic selection rule and study the quasiattractor obtained from it. We also discuss a generalized Poincar\'e surface of section at dielectric interfaces.Comment: 7 pages, 7 figure

Heterogeneous Investors and their Changing Demand and Supply Schedules for Individual Common Stocks

Using 550 million limit orders submitted in the Korea Stock Exchange, we estimate demand and supply elasticities of heterogeneous investor types and their changes around the Asian financial crisis. We find that domestic individuals have substantially more inelastic demand and supply curves than domestic institutions and foreign investors. The crisis permanently reduced price elasticities of domestic individuals by 50% but had no effect on those of foreign investors. Institutional changes restricting margin purchases, implemented after the crisis, seem particularly important in explaining the dramatic drop. Information heterogeneity, availability of close substitutes and arbitrage risk also explain time-series variations in elasticities.