Two Particle States and the SS-matrix Elements in Multi-channel Scattering

Using a quantum mechanical model, the exact energy eigenstates for two-particle two-channel scattering are studied in a cubic box with periodic boundary conditions in all three directions. A relation between the exact energy eigenvalue in the box and the two-channel $S$-matrix elements in the continuum is obtained. This result can be viewed as a generalization of the well-known L\"uscher's formula which establishes a similar relation in elastic scattering.Comment: 18 pages, no figures. minor changes compared with previous versio

An Arbitrary Two-qubit Computation In 23 Elementary Gates

Quantum circuits currently constitute a dominant model for quantum computation. Our work addresses the problem of constructing quantum circuits to implement an arbitrary given quantum computation, in the special case of two qubits. We pursue circuits without ancilla qubits and as small a number of elementary quantum gates as possible. Our lower bound for worst-case optimal two-qubit circuits calls for at least 17 gates: 15 one-qubit rotations and 2 CNOTs. To this end, we constructively prove a worst-case upper bound of 23 elementary gates, of which at most 4 (CNOT) entail multi-qubit interactions. Our analysis shows that synthesis algorithms suggested in previous work, although more general, entail much larger quantum circuits than ours in the special case of two qubits. One such algorithm has a worst case of 61 gates of which 18 may be CNOTs. Our techniques rely on the KAK decomposition from Lie theory as well as the polar and spectral (symmetric Shur) matrix decompositions from numerical analysis and operator theory. They are related to the canonical decomposition of a two-qubit gate with respect to the ``magic basis'' of phase-shifted Bell states, published previously. We further extend this decomposition in terms of elementary gates for quantum computation.Comment: 18 pages, 7 figures. Version 2 gives correct credits for the GQC "quantum compiler". Version 3 adds justification for our choice of elementary gates and adds a comparison with classical library-less logic synthesis. It adds acknowledgements and a new reference, adds full details about the 8-gate decomposition of topC-V and stealthily fixes several minor inaccuracies. NOTE: Using a new technique, we recently improved the lower bound to 18 gates and (tada!) found a circuit decomposition that requires 18 gates or less. This work will appear as a separate manuscrip

The Quantum Interest Conjecture

Although quantum field theory allows local negative energy densities and fluxes, it also places severe restrictions upon the magnitude and extent of the negative energy. The restrictions take the form of quantum inequalities. These inequalities imply that a pulse of negative energy must not only be followed by a compensating pulse of positive energy, but that the temporal separation between the pulses is inversely proportional to their amplitude. In an earlier paper we conjectured that there is a further constraint upon a negative and positive energy delta-function pulse pair. This conjecture (the quantum interest conjecture) states that a positive energy pulse must overcompensate the negative energy pulse by an amount which is a monotonically increasing function of the pulse separation. In the present paper we prove the conjecture for massless quantized scalar fields in two and four-dimensional flat spacetime, and show that it is implied by the quantum inequalities.Comment: 17 pages, Latex, 3 figures, uses eps

Ophiolites in the Xing’an-Inner Mongolia accretionary belt of the CAOB: Implications for two cycles of seafloor spreading and accretionary orogenic events

The Xing'an-Inner Mongolia accretionary belt in the southeastern segment of the Central Asian Orogenic Belt (CAOB) was produced by the long-lived subduction and eventual closure of the Paleo-Asian Ocean and by the convergence between the North China Craton and the Mongolian microcontinent. Two ophiolite belts have been recognized: the northern Erenhot-Hegenshan-Xi-Ujimqin ophiolite belt and the southern Solonker-Linxi ophiolite belt. Most basalts in the northern ophiolite belt exhibit characteristics of normal-type to enriched-type mid-ocean ridge basalt affinities with depleted Nd isotopic composition (εNd(t) > +5), comparable to modern Eastern Pacific mid-ocean ridge basalts. Most basaltic rocks in the southern belt show clear geochemical features of suprasubduction zone-type oceanic crust, probably formed in an arc/back-arc environment. The inferred back-arc extension along the Solonker-Linxi belt started at circa 280 Ma. Statistics of all the available age data for the ophiolites indicates two cycles of seafloor spreading/subduction, which gave rise to two main epochs of magmatic activity at 500–410 Ma and 360–220 Ma, respectively, with a gap of ~50 million years (Myr). The spatial and temporal distribution of the ophiolites and concurrent igneous rocks favor bilateral subduction toward the two continental margins in the convergence history, with final collision at ~230–220 Ma. In the whole belt, signals of continental collision and Himalayan-style mountain building are lacking. We thus conclude that the Xing'an-Inner Mongolia segment of the CAOB experienced two cycles of seafloor subduction, back-arc extension, and final “Appalachian-type” soft collision

Proteorhodopsin overproduction enhances the long-term viability of Escherichia coli

Genes encoding the photoreactive protein proteorhodopsin (PR) have been found in a wide range of marine bacterial species, reflecting the significant contribution that PR makes to energy flux and carbon cycling in ocean ecosystems. PR can also confer advantages to enhance the ability of marine bacteria to survive periods of starvation. Here, we investigate the effect of heterologously produced PR on the viability of Escherichia coli. Quantitative mass spectrometry shows that E. coli, exogenously supplied with the retinal cofactor, assembles as many as 187,000 holo-PR molecules per cell, accounting for approximately 47% of the membrane area; even cells with no retinal synthesize ∼148,000 apo-PR molecules per cell. We show that populations of E. coli cells containing PR exhibit significantly extended viability over many weeks, and we use single-cell Raman spectroscopy (SCRS) to detect holo-PR in 9-month-old cells. SCRS shows that such cells, even incubated in the dark and therefore with inactive PR, maintain cellular levels of DNA and RNA and avoid deterioration of the cytoplasmic membrane, a likely basis for extended viability. The substantial proportion of the E. coli membrane required to accommodate high levels of PR likely fosters extensive intermolecular contacts, suggested to physically stabilize the cell membrane and impart a long-term benefit manifested as extended viability in the dark. We propose that marine bacteria could benefit similarly from a high PR content, with a stabilized cell membrane extending survival when those bacteria experience periods of severe nutrient or light limitation in the oceans

The particle-in-cell model for ab initio thermodynamics: implications for the elastic anisotropy of the Earth's inner core

We assess the quantitative accuracy of the particle-in-cell (PIC) approximation used in recent ab initio predictions of the thermodynamic properties of hexagonal-close-packed iron at the conditions of the Earth's inner core. The assessment is made by comparing PIC predictions for a range of thermodynamic properties with the results of more exact calculations that avoid the PIC approximation. It is shown that PIC gives very accurate results for some properties, but that it gives an incorrect treatment of anharmonic lattice vibrations. In addition, our assessment does not support recent PIC-based predictions that the hexagonal c/a ratio increases strongly with increasing temperature, and we point out that this casts doubt on a proposed re-interpretation of the elastic anisotropy of the inner core.Comment: 25 pages, 9 figures, submitted to Physics of the Earth and Planetary Interior

Expression‐level support for gene dosage sensitivity in three Glycine subgenus Glycine polyploids and their diploid progenitors

Retention or loss of paralogs following duplication correlates strongly with the function of the gene and whether the gene was duplicated by whole\u2010genome duplication (WGD) or by small\u2010scale duplication. Selection on relative gene dosage (to maintain proper stoichiometry among interacting proteins) has been invoked to explain these patterns of duplicate gene retention and loss. In order for gene dosage to be visible to natural selection, there must necessarily be a correlation between gene copy number and gene expression level (transcript abundance), but this has rarely been examined. We used RNA\u2010Seq data from seven Glycine subgenus Glycine species (three recently formed allotetraploids and their four diploid progenitors) to determine if expression patterns and gene dosage responses at the level of transcription are consistent with selection on relative gene dosage. As predicted, metabolic pathways and gene ontologies that are putatively dosage\u2010sensitive based on duplication history exhibited reduced expression variance across species, and more coordinated expression responses to recent WGD, relative to putatively dosage\u2010insensitive networks. We conclude that selection on relative dosage has played an important role in shaping gene networks in Glycine

Quantum Inequalities for the Electromagnetic Field

A quantum inequality for the quantized electromagnetic field is developed for observers in static curved spacetimes. The quantum inequality derived is a generalized expression given by a mode function expansion of the four-vector potential, and the sampling function used to weight the energy integrals is left arbitrary up to the constraints that it be a positive, continuous function of unit area and that it decays at infinity. Examples of the quantum inequality are developed for Minkowski spacetime, Rindler spacetime and the Einstein closed universe.Comment: 19 pages, 1 table and 1 figure. RevTex styl

Enhanced production of tropane alkaloids in transgenic Scopolia parviflora hairy root cultures over-expressing putrescine N-methyl transferase (PMT) and hyoscyamine-6β-hydroxylase (H6H)

Scopolia parviflora adventitious roots were metabolically engineered by co-expression of the two gene putrescine N-methyl transferase (PMT) and hyoscyamine-6β-hydroxylase (H6H) cDNAs with the aid of Agrobacterium rhizogenes. The transformed roots developed into morphologically distinct S. parviflora PMT1 (SpPMT1), S. parviflora PMT1 (SpPMT2), and S. parviflora H6H (SpH6H) transgenic hairy root lines. Consequent to the introduction of these key enzyme genes, the production of the alkaloids hyoscyamine and scopolamine was enhanced. Among the transgenic hairy root lines, SpPMT2 line possessed the highest growth index. The treatment of transgenic hairy roots with growth regulators further enhanced the production of scopolamine. Thus, the results suggest that PMT1, PMT2, and H6H genes may not only be involved in the metabolic regulation of alkaloid production but also that these genes may play a role in the root development

Cryopreservation of specialised Chicken Lines using cultured primordial germ cells

Biosecurity and sustainability in poultry production requires reliable germplasm conservation. Germplasm conservation in poultry is more challenging in comparison to other livestock species. Embryo cryopreservation is not feasible for egg-laying animals, and chicken semen conservation has variable success for different chicken breeds. A potential solution is the cryopreservation of the committed diploid stem cell precursors to the gametes, the primordial germ cells (PGCs). Primordial germ cells are the lineage-restricted cells found at early embryonic stages in birds and form the sperm and eggs. We demonstrate here, using flocks of partially inbred, lower-fertility, major histocompatibility complex- (MHC-) restricted lines of chicken, that we can easily derive and cryopreserve a sufficient number of independent lines of male and female PGCs that would be sufficient to reconstitute a poultry breed. We demonstrate that germ-line transmission can be attained from these PGCs using a commercial layer line of chickens as a surrogate host. This research is a major step in developing and demonstrating that cryopreserved PGCs could be used for the biobanking of specialized flocks of birds used in research settings. The prospective application of this technology to poultry production will further increase sustainability to meet current and future production needs