Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control

When can a quantum system of finite dimension be used to simulate another quantum system of finite dimension? What restricts the capacity of one system to simulate another? In this paper we complete the program of studying what simulations can be done with entangling many-qudit Hamiltonians and local unitary control. By entangling we mean that every qudit is coupled to every other qudit, at least indirectly. We demonstrate that the only class of finite-dimensional entangling Hamiltonians that aren't universal for simulation is the class of entangling Hamiltonians on qubits whose Pauli operator expansion contains only terms coupling an odd number of systems, as identified by Bremner et. al. [Phys. Rev. A, 69, 012313 (2004)]. We show that in all other cases entangling many-qudit Hamiltonians are universal for simulation

Coherence-Preserving Quantum Bits

Real quantum systems couple to their environment and lose their intrinsic quantum nature through the process known as decoherence. Here we present a method for minimizing decoherence by making it energetically unfavorable. We present a Hamiltonian made up solely of two-body interactions between four two-level systems (qubits) which has a two-fold degenerate ground state. This degenerate ground state has the property that any decoherence process acting on an individual physical qubit must supply energy from the bath to the system. Quantum information can be encoded into the degeneracy of the ground state and such coherence-preserving qubits will then be robust to local decoherence at low bath temperatures. We show how this quantum information can be universally manipulated and indicate how this approach may be applied to a quantum dot quantum computer.Comment: 5 pages, 1 figur

Contamination

Soil contamination occurs when substances are added to soil, resulting in increases in concentrations above background or reference levels. Pollution may follow from contamination when contaminants are present in amounts that are detrimental to soil quality and become harmful to the environment or human health. Contamination can occur via a range of pathways including direct application to land and indirect application from atmospheric deposition. Contamination was identified by SEPA (2001) as a significant threat to soil quality in many parts of Scotland. Towers et al. (2006) identified four principal contamination threats to Scottish soils: acidification; eutrophication; metals; and pesticides. The Scottish Soil Framework (Scottish Government, 2009) set out the potential impact of these threats on the principal soil functions. Severe contamination can lead to “contaminated land” [as defined under Part IIA of the Environmental Protection Act (1990)]. This report does not consider the state and impacts of contaminated land on the wider environment in detail. For further information on contaminated land, see ‘Dealing with Land Contamination in Scotland’ (SEPA, 2009). This chapter considers the causes of soil contamination and their environmental and socio-economic impacts before going on to discuss the status of, and trends in, levels of contaminants in Scotland’s soils

Formation of Short-Period Binary Pulsars in Globular Clusters

We present a new dynamical scenario for the formation of short-period binary millisecond pulsars in globular clusters. Our work is motivated by the recent observations of 20 radio pulsars in 47 Tuc. In a dense cluster such as 47 Tuc, most neutron stars acquire binary companions through exchange interactions with primordial binaries. The resulting systems have semimajor axes in the range \~0.1-1 AU and neutron star companion masses ~1-3 Msun. For many of these systems we find that, when the companion evolves off the main sequence and fills its Roche lobe, the subsequent mass transfer is dynamically unstable. This leads to a common envelope phase and the formation of short-period neutron star - white dwarf binaries. For a significant fraction of these binaries, the decay of the orbit due to gravitational radiation will be followed by a period of stable mass transfer driven by a combination of gravitational radiation and tidal heating of the companion. The properties of the resulting short-period binaries match well those of observed binary pulsars in 47 Tuc.Comment: To appear in ApJ Letters, slightly abbreviated version with only minor change

Molecular basis of gap junctional communication in the CNS of the leech Hirudo medicinalis

Gap junctions are intercellular channels that allow the passage of ions and small molecules between cells. In the nervous system, gap junctions mediate electrical coupling between neurons. Despite sharing a common topology and similar physiology, two unrelated gap junction protein families exist in the animal kingdom. Vertebrate gap junctions are formed by members of the connexin family, whereas invertebrate gap junctions are composed of innexin proteins. Here we report the cloning of two innexins from the leech Hirudo medicinalis. These innexins show a differential expression in the leech CNS: Hm-inx1 is expressed by every neuron in the CNS but not in glia, whereas Hm-inx2 is expressed in glia but not neurons. Heterologous expression in the paired Xenopus oocyte system demonstrated that both innexins are able to form functional homotypic gap junctions. Hm-inx1 forms channels that are not strongly gated. In contrast, Hm-inx2 forms channels that are highly voltage-dependent; these channels demonstrate properties resembling those of a double rectifier. In addition, Hm-inx1 and Hm-inx2 are able to cooperate to form heterotypic gap junctions in Xenopus oocytes. The behavior of these channels is primarily that predicted from the properties of the constituent hemichannels but also demonstrates evidence of an interaction between the two. This work represents the first demonstration of a functional gap junction protein from a Lophotrochozoan animal and supports the hypothesis that connexin-based communication is restricted to the deuterostome clade

ANALYSIS OF TRENDS AND FORECASTS IN COFFEE PRICES AND CONSUMER CONSUMPTION IN THE NORTHEAST AND UNITED STATES

Demand and Price Analysis, Food Consumption/Nutrition/Food Safety,

Weak Gravitational Flexion

Flexion is the significant third-order weak gravitational lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. Here we demonstrate how flexion measurements can be used to measure galaxy halo density profiles and large-scale structure on non-linear scales, via galaxy-galaxy lensing, dark matter mapping and cosmic flexion correlation functions. We describe the origin of gravitational flexion, and discuss its four components, two of which are first described here. We also introduce an efficient complex formalism for all orders of lensing distortion. We proceed to examine the flexion predictions for galaxy-galaxy lensing, examining isothermal sphere and Navarro, Frenk & White (NFW) profiles and both circularly symmetric and elliptical cases. We show that in combination with shear we can precisely measure galaxy masses and NFW halo concentrations. We also show how flexion measurements can be used to reconstruct mass maps in 2-D projection on the sky, and in 3-D in combination with redshift data. Finally, we examine the predictions for cosmic flexion, including convergence-flexion cross-correlations, and find that the signal is an effective probe of structure on non-linear scales.Comment: 17 pages, including 12 figures, submitted to MNRA

Few-body spin couplings and their implications for universal quantum computation

Electron spins in semiconductor quantum dots are promising candidates for the experimental realization of solid-state qubits. We analyze the dynamics of a system of three qubits arranged in a linear geometry and a system of four qubits arranged in a square geometry. Calculations are performed for several quantum dot confining potentials. In the three-qubit case, three-body effects are identified that have an important quantitative influence upon quantum computation. In the four-qubit case, the full Hamiltonian is found to include both three-body and four-body interactions that significantly influence the dynamics in physically relevant parameter regimes. We consider the implications of these results for the encoded universality paradigm applied to the four-electron qubit code; in particular, we consider what is required to circumvent the four-body effects in an encoded system (four spins per encoded qubit) by the appropriate tuning of experimental parameters.Comment: 1st version: 33 pages, 25 figures. Described at APS March Meeting in 2004 (P36.010) and 2005 (B17.00009). Most figures made uglier here to reduce file size. 2nd version: 19 pages, 9 figures. Much mathematical detail chopped away after hearing from journal referee; a few typos correcte