Constants of motion and the conformal anti - de Sitter algebra in (2+1)-Dimensional Gravity

Constants of motion are calculated for 2+1 dimensional gravity with topology R x T^2 and negative cosmological constant. Certain linear combinations of them satisfy the anti - de Sitter algebra so(2,2) in either ADM or holonomy variables. Quantisation is straightforward in terms of the holonomy parameters. On inclusion of the Hamiltonian three new global constants are derived and the quantum algebra extends to that of the conformal algebra so(2,3). The modular group appears as a discrete subgroup of the conformal group. Its quantum action is generated by these conserved quantities.Comment: 22 pages, Plain Tex, No Figure

Status Buying Responses in a Survey of Students and Variations in Informational Levels.

This article reports on a survey of a large number of undergraduate students in the U.S. They were queried about whether they preferred living in a society where they had high relative income (status) but low purchasing power or a society where they have low status, but high purchasing power.While the overwhelming majority indicate a desire to buy status, the information given about intergenerational mobilty and amenities like health available in the different socities makes a big difference in the responses. The data indicate that that the majority desiring to buy status disappears with better information.

How mobile are dye adsorbates and acetonitrile molecules on the surface of TiO2 nanoparticles? A quasi-elastic neutron scattering study

Motions of molecules adsorbed to surfaces may control the rate of charge transport within monolayers in systems such as dye sensitized solar cells. We used quasi-elastic neutron scattering (QENS) to evaluate the possible dynamics of two small dye moieties, isonicotinic acid (INA) and bis-isonicotinic acid (BINA), attached to TiO2 nanoparticles via carboxylate groups. The scattering data indicate that moieties are immobile and do not rotate around the anchoring groups on timescales between around 10 ps and a few ns (corresponding to the instrumental range). This gives an upper limit for the rate at which conformational fluctuations can assist charge transport between anchored molecules. Our observations suggest that if the conformation of larger dye molecules varies with time, it does so on longer timescales and/or in parts of the molecule which are not directly connected to the anchoring group. The QENS measurements also indicate that several layers of acetonitrile solvent molecules are immobilized at the interface with the TiO2 on the measurement time scale, in reasonable agreement with recent classical molecular dynamics results

The Quantum Modular Group in (2+1)-Dimensional Gravity

The role of the modular group in the holonomy representation of (2+1)-dimensional quantum gravity is studied. This representation can be viewed as a "Heisenberg picture", and for simple topologies, the transformation to the ADM "Schr{\"o}dinger picture" may be found. For spacetimes with the spatial topology of a torus, this transformation and an explicit operator representation of the mapping class group are constructed. It is shown that the quantum modular group splits the holonomy representation Hilbert space into physically equivalent orthogonal ``fundamental regions'' that are interchanged by modular transformations.Comment: 23 pages, LaTeX, no figures; minor changes and clarifications in response to referee (basic argument and conclusions unaffected

Randomized benchmarking of atomic qubits in an optical lattice

We perform randomized benchmarking on neutral atomic quantum bits (qubits) confined in an optical lattice. Single qubit gates are implemented using microwaves, resulting in a measured error per randomized computational gate of 1.4(1) x 10^-4 that is dominated by the system T2 relaxation time. The results demonstrate the robustness of the system, and its viability for more advanced quantum information protocols.Comment: 11 pages, 4 figure

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

Comparative Quantizations of (2+1)-Dimensional Gravity

We compare three approaches to the quantization of (2+1)-dimensional gravity with a negative cosmological constant: reduced phase space quantization with the York time slicing, quantization of the algebra of holonomies, and quantization of the space of classical solutions. The relationships among these quantum theories allow us to define and interpret time-dependent operators in the ``frozen time'' holonomy formulation.Comment: 24 pages, LaTeX, no figure