687 research outputs found
Temperature Dependence of Thermopower in Strongly Correlated Multiorbital Systems
Temperature dependence of thermopower in the multiorbital Hubbard model is
studied by using the dynamical mean-field theory with the non-crossing
approximation impurity solver. It is found that the Coulomb interaction, the
Hund coupling, and the crystal filed splitting bring about non-monotonic
temperature dependence of the thermopower, including its sign reversal. The
implication of our theoretical results to some materials is discussed.Comment: 3 pages, 3 figure
Triple-horizon spherically symmetric spacetime and holographic principle
We present a family of spherically symmetric spacetimes, specified by the
density profile of a vacuum dark energy, which have the same global structure
as the de Sitter spacetime but the reduced symmetry which leads to a
time-evolving and spatially inhomogeneous cosmological term. It connects
smoothly two de Sitter vacua with different values of cosmological constant and
corresponds to anisotropic vacuum dark fluid defined by symmetry of its
stress-energy tensor which is invariant under the radial boosts. This family
contains a special class distinguished by dynamics of evaporation of a
cosmological horizon which evolves to the triple horizon with the finite
entropy, zero temperature, zero curvature, infinite positive specific heat, and
infinite scrambling time. Non-zero value of the cosmological constant in the
triple-horizon spacetime is tightly fixed by quantum dynamics of evaporation of
the cosmological horizon.Comment: Honorable Mentioned Essay - Gravity Research Foundation 2012;
submitted to Int. J. Mod. Phys.
Semidefinite Representation of the -Ellipse
The -ellipse is the plane algebraic curve consisting of all points whose
sum of distances from given points is a fixed number. The polynomial
equation defining the -ellipse has degree if is odd and degree
if is even. We express this polynomial equation as
the determinant of a symmetric matrix of linear polynomials. Our representation
extends to weighted -ellipses and -ellipsoids in arbitrary dimensions,
and it leads to new geometric applications of semidefinite programming.Comment: 16 pages, 5 figure
Future Foam
We study pocket universes which have zero cosmological constant and
non-trivial boundary topology. These arise from bubble collisions in eternal
inflation. Using a simplified dust model of collisions we find that boundaries
of any genus can occur. Using a radiation shell model we perform analytic
studies in the thin wall limit to show the existence of geometries with a
single toroidal boundary. We give plausibility arguments that higher genus
boundaries can also occur. In geometries with one boundary of any genus a
timelike observer can see the entire boundary. Geometries with multiple
disconnected boundaries can also occur. In the spherical case with two
boundaries the boundaries are separated by a horizon. Our results suggest that
the holographic dual description for eternal inflation, proposed by Freivogel,
Sekino, Susskind and Yeh, should include summation over the genus of the base
space of the dual conformal field theory. We point out peculiarities of this
genus expansion compared to the string perturbation series.Comment: 23 pages, 6 figure
Scalar Three-point Functions in a CDL Background
Motivated by the FRW-CFT proposal by Freivogel, Sekino, Susskind and Yeh, we
compute the three-point function of a scalar field in a Coleman-De Luccia
instanton background. We first compute the three-point function of the scalar
field making only very mild assumptions about the scalar potential and the
instanton background. We obtain the three-point function for points in the FRW
patch of the CDL instanton and take two interesting limits; the limit where the
three points are near the boundary of the hyperbolic slices of the FRW patch,
and the limit where the three points lie on the past lightcone of the FRW
patch. We expand the past lightcone three-point function in spherical
harmonics. We show that the near boundary limit expansion of the three-point
function of a massless scalar field exhibits conformal structure compatible
with FRW-CFT when the FRW patch is flat. We also compute the three-point
function when the scalar is massive, and explain the obstacles to generalizing
the conjectured field-operator correspondence of massless fields to massive
fields.Comment: 42 pages + appendices, 10 figures; v2, v3: minor correction
- …