Intrinsic time gravity and the Lichnerowicz-York equation

We investigate the effect on the Hamiltonian structure of general relativity of choosing an intrinsic time to fix the time slicing. 3-covariance with momentum constraint is maintained, but the Hamiltonian constraint is replaced by a dynamical equation for the trace of the momentum. This reveals a very simple structure with a local reduced Hamiltonian. The theory is easily generalised; in particular, the square of the Cotton-York tensor density can be added as an extra part of the potential while at the same time maintaining the classic 2 + 2 degrees of freedom. Initial data construction is simple in the extended theory; we get a generalised Lichnerowicz-York equation with nice existence and uniqueness properties. Adding standard matter fields is quite straightforward.Comment: 4 page

Andreev Bound States in the Kondo Quantum Dots Coupled to Superconducting Leads

We have studied the Kondo quantum dot coupled to two superconducting leads and investigated the subgap Andreev states using the NRG method. Contrary to the recent NCA results [Clerk and Ambegaokar, Phys. Rev. B 61, 9109 (2000); Sellier et al., Phys. Rev. B 72, 174502 (2005)], we observe Andreev states both below and above the Fermi level.Comment: 5 pages, 5 figure

Anomalous Transmission Phase of a Kondo-Correlated Quantum Dot

We study phase evolution of transmission through a quantum dot with Kondo correlations. By considering a model that includes nonresonant transmission as well as the Anderson impurity, we explain unusually large phase evolution of about $\pi$ in the Kondo valley observed in recent experiments. We argue that this anomalous phase evolution is a universal property that can be found in the high-temperature Kondo phase in the presence of the time-reversal symmetry.Comment: 5 pages, 3 figure

Affine group representation formalism for four dimensional, Lorentzian, quantum gravity

Within the context of the Ashtekar variables, the Hamiltonian constraint of four-dimensional pure General Relativity with cosmological constant, $\Lambda$, is reexpressed as an affine algebra with the commutator of the imaginary part of the Chern-Simons functional, $Q$, and the positive-definite volume element. This demonstrates that the affine algebra quantization program of Klauder can indeed be applicable to the full Lorentzian signature theory of quantum gravity with non-vanishing cosmological constant; and it facilitates the construction of solutions to all of the constraints. Unitary, irreducible representations of the affine group exhibit a natural Hilbert space structure, and coherent states and other physical states can be generated from a fiducial state. It is also intriguing that formulation of the Hamiltonian constraint or Wheeler-DeWitt equation as an affine algebra requires a non-vanishing cosmological constant; and a fundamental uncertainty relation of the form $\frac{\Delta{V}}{}\Delta {Q}\geq 2\pi \Lambda L^2_{Planck}$ (wherein $V$ is the total volume) may apply to all physical states of quantum gravity.Comment: 13 pages. Revised versio

The linearization of the Kodama state

We study the question of whether the linearization of the Kodama state around classical deSitter spacetime is normalizable in the inner product of the theory of linearized gravitons on deSitter spacetime. We find the answer is no in the Lorentzian theory. However, in the Euclidean theory the corresponding linearized Kodama state is delta-functional normalizable. We discuss whether this result invalidates the conjecture that the full Kodama state is a good physical state for quantum gravity with positive cosmological constant.Comment: 14 pages, statement on the corresponding Yang-Mills case correcte

Josephson current in strongly correlated double quantum dots

We study the transport properties of a serial double quantum dot (DQD) coupled to two superconducting leads, focusing on the Josephson current through the DQD and the associated 0-$\pi$ transitions which result from the subtle interplay between the superconductivity, the Kondo physics, and the inter-dot superexchange interaction. We examine the competition between the superconductivity and the Kondo physics by tuning the relative strength $\Delta/T_K$ of the superconducting gap $\Delta$ and the Kondo temperature $T_K$, for different strengths of the superexchange coupling determined by the interdot tunneling $t$ relative to the dot level broadening $\Gamma$. We find strong renormalization of $t$, a significant role of the superexchange coupling $J$, and a rich phase diagram of the 0 and $\pi$-junction regimes. In particular, when both the superconductivity and the exchange interaction are in close competion with the Kondo physics ($\Delta\sim J\sim T_K$), there appears an island of $\pi'$-phase at large values of the superconducting phase difference.Comment: 4 pages, 4 figure

Three-geometry and reformulation of the Wheeler-DeWitt equation

A reformulation of the Wheeler-DeWitt equation which highlights the role of gauge-invariant three-geometry elements is presented. It is noted that the classical super-Hamiltonian of four-dimensional gravity as simplified by Ashtekar through the use of gauge potential and densitized triad variables can furthermore be succinctly expressed as a vanishing Poisson bracket involving three-geometry elements. This is discussed in the general setting of the Barbero extension of the theory with arbitrary non-vanishing value of the Immirzi parameter, and when a cosmological constant is also present. A proposed quantum constraint of density weight two which is polynomial in the basic conjugate variables is also demonstrated to correspond to a precise simple ordering of the operators, and may thus help to resolve the factor ordering ambiguity in the extrapolation from classical to quantum gravity. Alternative expression of a density weight one quantum constraint which may be more useful in the spin network context is also discussed, but this constraint is non-polynomial and is not motivated by factor ordering. The article also highlights the fact that while the volume operator has become a preeminient object in the current manifestation of loop quantum gravity, the volume element and the Chern-Simons functional can be of equal significance, and need not be mutually exclusive. Both these fundamental objects appear explicitly in the reformulation of the Wheeler-DeWitt constraint.Comment: 10 pages, LaTeX fil

Selenium Biotransformations in an Engineered Aquatic Ecosystem for Bioremediation of Agricultural Wastewater via Brine Shrimp Production

An engineered aquatic ecosystem was specifically designed to bioremediate selenium (Se), occurring as oxidized inorganic selenate from hypersalinized agricultural drainage water while producing brine shrimp enriched in organic Se and omega-3 and omega-6 fatty acids for use in value added nutraceutical food supplements. Selenate was successfully bioremediated by microalgal metabolism into organic Se (seleno-amino acids) and partially removed via gaseous volatile Se formation. Furthermore, filterfeeding brine shrimp that accumulated this organic Se were removed by net harvest. Thriving in this engineered pond system, brine shrimp (Artemia franciscana Kellogg) and brine fly (Ephydridae sp.) have major ecological relevance as important food sources for large populations of waterfowl, breeding, and migratory shore birds. This aquatic ecosystem was an ideal model for study because it mimics trophic interactions in a Se polluted wetland. Inorganic selenate in drainage water was metabolized differently in microalgae, bacteria, and diatoms where it was accumulated and reduced into various inorganic forms (selenite, selenide, or elemental Se) or partially incorporated into organic Se mainly as selenomethionine. Brine shrimp and brine fly larva then bioaccumulated Se from ingesting aquatic microorganisms and further metabolized Se predominately into organic Se forms. Importantly, adult brine flies, which hatched from aquatic larva, bioaccumulated the highest Se concentrations of all organisms tested