Relative information entropy of an inhomogeneous universe

In the context of averaging an inhomogeneous cosmological model, we propose a natural measure identical to the Kullback-Leibler relative information entropy, which expresses the distinguishability of the local inhomogeneous density field from its spatial average on arbitrary compact domains. This measure is expected to be an increasing function in time and thus to play a significant role in studying gravitational entropy. To verify this conjecture, we explore the time evolution of the measure using the linear perturbation theory of a spatially flat FLRW model and a spherically symmetric nonlinear solution. We discuss the generality and conditions for the time-increasing nature of the measure, and also the connection to the backreaction effect caused by inhomogeneities.Comment: 9 pages, 4 figures, LaTeX 2e using aipproc.cls, published in AIP Conf. Proc., minor corrections mad

Complementarity of Entanglement and Interference

A complementarity relation is shown between the visibility of interference and bipartite entanglement in a two qubit interferometric system when the parameters of the quantum operation change for a given input state. The entanglement measure is a decreasing function of the visibility of interference. The implications for quantum computation are briefly discussed.Comment: Final version, to appear on IJMPC; minor revision

Comments on Closed Bianchi Models

We show several kinematical properties that are intrinsic to the Bianchi models with compact spatial sections. Especially, with spacelike hypersurfaces being closed, (A) no anisotropic expansion is allowed for Bianchi type V and VII(A\not=0), and (B) type IV and VI(A\not=0,1) does not exist. In order to show them, we put into geometric terms what is meant by spatial homogeneity and employ a mathematical result on 3-manifolds. We make clear the relation between the Bianchi type symmetry of space-time and spatial compactness, some part of which seem to be unnoticed in the literature. Especially, it is shown under what conditions class B Bianchi models do not possess compact spatial sections. Finally we briefly describe how this study is useful in investigating global dynamics in (3+1)-dimensional gravity.Comment: 14 pages with one table, KUCP-5

Compact Three Dimensional Black Hole: Topology Change and Closed Timelike Curve (minor changes)

We present a compactified version of the 3-dimensional black hole recently found by considering extra identifications and determine the analytical continuation of the solution beyond its coordinate singularity by extending the identifications to the extended region of the spacetime. In the extended region of the spacetime, we find a topology change and non-trivial closed timelike curves both in the ordinary 3-dimensional black hole and in the compactified one. Especially, in the case of the compactified 3-dimensional black hole, we show an example of topology change from one double torus to eight spheres with three punctures.Comment: 20 pages revtex.sty 8 figures contained, TIT/HEP-245/COSMO-4

A Modular Invariant Quantum Theory From the Connection Formulation of (2+1)-Gravity on the Torus

By choosing an unconventional polarization of the connection phase space in (2+1)-gravity on the torus, a modular invariant quantum theory is constructed. Unitary equivalence to the ADM-quantization is shown.Comment: Latex, 4 page

Information Entropy in Cosmology

The effective evolution of an inhomogeneous cosmological model may be described in terms of spatially averaged variables. We point out that in this context, quite naturally, a measure arises which is identical to a fluid model of the `Kullback-Leibler Relative Information Entropy', expressing the distinguishability of the local inhomogeneous mass density field from its spatial average on arbitrary compact domains. We discuss the time-evolution of `effective information' and explore some implications. We conjecture that the information content of the Universe -- measured by Relative Information Entropy of a cosmological model containing dust matter -- is increasing.Comment: LateX, PRLstyle, 4 pages; to appear in PR

Time Optimal Unitary Operations

Extending our previous work on time optimal quantum state evolution, we formulate a variational principle for the time optimal unitary operation, which has direct relevance to quantum computation. We demonstrate our method with three examples, i.e. the swap of qubits, the quantum Fourier transform and the entangler gate, by choosing a two-qubit anisotropic Heisenberg model.Comment: 4 pages, 1 figure. References adde

Generating derivative structures: Algorithm and applications

We present an algorithm for generating all derivative superstructures--for arbitrary parent structures and for any number of atom types. This algorithm enumerates superlattices and atomic configurations in a geometry-independent way. The key concept is to use the quotient group associated with each superlattice to determine all unique atomic configurations. The run time of the algorithm scales linearly with the number of unique structures found. We show several applications demonstrating how the algorithm can be used in materials design problems. We predict an altogether new crystal structure in Cd-Pt and Pd-Pt, and several new ground states in Pd-rich and Pt-rich binary systems

Global constants in (2+1)--dimensional gravity

The extended conformal algebra (so)(2,3) of global, quantum, constants of motion in 2+1 dimensional gravity with topology R x T^2 and negative cosmological constant is reviewed. It is shown that the 10 global constants form a complete set by expressing them in terms of two commuting spinors and the Dirac gamma matrices. The spinor components are the globally constant holonomy parameters, and their respective spinor norms are their quantum commutators.Comment: 14 pages, to appear in Classical and Quantum Gravity, Spacetime Safari: Essays in Honor of Vincent Moncrief on the Classical Physics of Strong Gravitational Field