Black holes as mirrors: quantum information in random subsystems

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the "half-way" point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.Comment: 18 pages, 2 figures. (v2): discussion of decoding complexity clarifie

Modulated spin and charge densities in cuprate superconductors

Neutron scattering experiments have played a crucial role in characterizing the spin and charge correlations in copper-oxide superconductors. While the data are often interpreted with respect to specific theories of the cuprates, an attempt is made here to distinguish those facts that can be extracted empirically, and the connections that can be made with minimal assumptions.Comment: 6 pp., LaTeX, 2 col., uses espcrc2.sty + psfig.sty, 2 eps figures; Proc. of the International Conf. on Neutron Scattering, Toronto, Aug. 1997, to be published in Physica

Spin dynamics in stripe-ordered La5/3Sr1/3NiO4

Polarized and unpolarized neutron inelastic scattering has been used to measure the spin excitations in the spin-charge-ordered stripe phase of La5/3Sr1/3NiO4. At high energies, sharp magnetic modes are observed characteristic of a static stripe lattice. The energy spectrum is described well by a linear spin wave model with intra- and inter-stripe exchange interactions between neighbouring Ni spins given by J = 15 +/- 1.5 meV and J' = 7.5 +/- 1.5 meV respectively. A pronounced broadening of the magnetic fluctuations in a band between 10 meV and 25 meV is suggestive of coupling to collective motions of the stripe domain walls.Comment: ReVTeX 4, 4 pages inc. 4 Fig

Charge Stripes and Antiferromagnetism in Insulating Nickelates and Superconducting Cuprates

Neutron and X-ray scattering studies have provided strong evidence for coupled spatial modulations of charge and spin densities in layered nickelates and cuprates. The accumulated results for La(2-x)Sr(x)NiO(4+d) are consistent with the strongly-modulated topological-stripe concept. Clues from Nd-doped La(2-x)Sr(x)CuO(4) suggest similar behavior for the cuprates. The experimental results are summarized, and features that conflict with an interpretation based on a Fermi-surface instability are emphasized. A rationalization for the differences in transport properties between the cuprates and nickelates is given.Comment: 10pp., uses elsart.sty, 3 eps figures embedded with psfig; for proceedings of Spectroscopies in Novel Superconductors '97, J. Phys. Chem. Solid

Magnetic Coherence in Cuprate Superconductors

Recent inelastic neutron scattering (INS) experiments on La$_{2-x}$Sr$_x$CuO$_4$ observed a {\it magnetic coherence effect}, i.e., strong frequency and momentum dependent changes of the spin susceptibility, $\chi''$, in the superconducting phase. We show that this effect is a direct consequence of changes in the damping of incommensurate antiferromagnetic spin fluctuations due to the appearance of a d-wave gap in the fermionic spectrum. Our theoretical results provide a quantitative explanation for the weak momentum dependence of the observed spin-gap. Moreover, we predict {\bf (a)} a Fermi surface in La$_{2-x}$Sr$_x$CuO$_4$ which is closed around $(\pi,\pi)$ up to optimal doping, and {\bf (b)} similar changes in $\chi''$ for all cuprates with an incommensurate magnetic response.Comment: 5 pages, 4 figures, Fig.3 is in colo

Stability of homogeneous magnetic phases in a generalized t-J model

We study the stability of homogeneous magnetic phases in a generalized t-J model including a same-sublattice hopping t' and nearest-neighbor repulsion V by means of the slave fermion-Schwinger boson representation of spin operators. At mean-field order we find, in agreement with other authors, that the inclusion of further-neighbor hopping and Coulomb repulsion makes the compressibility positive, thereby stabilizing at this level the spiral and Neel orders against phase separation. However, the consideration of Gaussian fluctuation of order parameters around these mean-field solutions produces unstable modes in the dynamical matrix for all relevant parameter values, leaving only reduced stability regions for the Neel phase. We have computed the one-loop corrections to the energy in these regions, and have also briefly considered the effects of the correlated hopping term that is obtained in the reduction from the Hubbard to the t-J model.Comment: 5 pages, 5 figures, Revte

Brownian motion in AdS/CFT

We study Brownian motion and the associated Langevin equation in AdS/CFT. The Brownian particle is realized in the bulk spacetime as a probe fundamental string in an asymptotically AdS black hole background, stretching between the AdS boundary and the horizon. The modes on the string are excited by the thermal black hole environment and consequently the string endpoint at the boundary undergoes an erratic motion, which is identified with an external quark in the boundary CFT exhibiting Brownian motion. Semiclassically, the modes on the string are thermally excited due to Hawking radiation, which translates into the random force appearing in the boundary Langevin equation, while the friction in the Langevin equation corresponds to the excitation on the string being absorbed by the black hole. We give a bulk proof of the fluctuation-dissipation theorem relating the random force and friction. This work can be regarded as a step toward understanding the quantum microphysics underlying the fluid-gravity correspondence. We also initiate a study of the properties of the effective membrane or stretched horizon picture of black holes using our bulk description of Brownian motion.Comment: 54 pages (38 pages + 5 appendices), 5 figures. v2: references added, clarifications in 6.2. v3: clarifications, version submitted to JHE

Charge Segregation and Antiferromagnetism in High-Tc Superconductors

Local antiferromagnetism coexists with superconductivity in the cuprates. Charge segregation provides a way to reconcile these properties. Direct evidence for modulated spin and charge densities has been found in neutron and X-ray scattering studies of Nd-doped La(2-x)Sr(x)CuO(4). Here we discuss the nature of the modulation, and present some new results for a Zn-doped sample. Some of the open questions concerning the connections between segregation and superconductivity are described.Comment: 9 pp using elsart.sty, 3 eps figures included with psfig.sty, for Proc. of ISSP-7, to be published in J. Phys. Chem. Solid

Membrane paradigm realized?

Are there any degrees of freedom on the black hole horizon? Using the `membrane paradigm' we can reproduce coarse-grained physics outside the hole by assuming a fictitious membrane just outside the horizon. But to solve the information puzzle we need `real' degrees of freedom at the horizon, which can modify Hawking's evolution of quantum modes. We argue that recent results on gravitational microstates imply a set of real degrees of freedom just outside the horizon; the state of the hole is a linear combination of rapidly oscillating gravitational solutions with support concentrated just outside the horizon radius. The collective behavior of these microstate solutions may give a realization of the membrane paradigm, with the fictitious membrane now replaced by real, explicit degrees of freedom.Comment: 8 pages, Latex, 3 figures (Essay given second place in Gravity Research Foundation essay competition 2010

Glassy nature of stripe ordering in La(1.6-x)Nd(0.4)Sr(x)CuO(4)

We present the results of neutron-scattering studies on various aspects of crystalline and magnetic structure in single crystals of La(1.6-x)Nd(0.4)Sr(x)CuO(4) with x=0.12 and 0.15. In particular, we have reexamined the degree of stripe order in an x=0.12 sample. Measurements of the width for an elastic magnetic peak show that it saturates at a finite value below 30 K, corresponding to a spin-spin correlation length of 200 A. A model calculation indicates that the differing widths of magnetic and (previously reported) charge-order peaks, together with the lack of commensurability, can be consistently explained by disorder in the stripe spacing. Above 30 K, the width of the nominally elastic signal begins to increase. Interpreting the signal as critical scattering from slowly fluctuating spins, the temperature dependence of the width is consistent with renormalized classical behavior of a 2-dimensional anisotropic Heisenberg antiferromagnet. Inelastic scattering measurements show that incommensurate spin excitations survive at and above 50 K, where the elastic signal is neglible. We also report several results related to the LTO-to-LTT transition.Comment: 13 pp, 2-col. REVTeX, 11 figures embedded with psfig; expanded discussion of T-dep. of magnetic peak width; version to appear in Phys. Rev. B (01Jun99