Time Reversal and n-qubit Canonical Decompositions

For n an even number of qubits and v a unitary evolution, a matrix decomposition v=k1 a k2 of the unitary group is explicitly computable and allows for study of the dynamics of the concurrence entanglement monotone. The side factors k1 and k2 of this Concurrence Canonical Decomposition (CCD) are concurrence symmetries, so the dynamics reduce to consideration of the a factor. In this work, we provide an explicit numerical algorithm computing v=k1 a k2 for n odd. Further, in the odd case we lift the monotone to a two-argument function, allowing for a theory of concurrence dynamics in odd qubits. The generalization may also be studied using the CCD, leading again to maximal concurrence capacity for most unitaries. The key technique is to consider the spin-flip as a time reversal symmetry operator in Wigner's axiomatization; the original CCD derivation may be restated entirely in terms of this time reversal. En route, we observe a Kramers' nondegeneracy: the existence of a nondegenerate eigenstate of any time reversal symmetric n-qubit Hamiltonian demands (i) n even and (ii) maximal concurrence of said eigenstate. We provide examples of how to apply this work to study the kinematics and dynamics of entanglement in spin chain Hamiltonians.Comment: 20 pages, 3 figures; v2 (17pp.): major revision, new abstract, introduction, expanded bibliograph

Low-Temperature Properties of Two-Dimensional Ideal Ferromagnets

The manifestation of the spin-wave interaction in the low-temperature series of the partition function has been investigated extensively over more than seven decades in the case of the three-dimensional ferromagnet. Surprisingly, the same problem regarding ferromagnets in two spatial dimensions, to the best of our knowledge, has never been addressed in a systematic way so far. In the present paper the low-temperature properties of two-dimensional ideal ferromagnets are analyzed within the model-independent method of effective Lagrangians. The low-temperature expansion of the partition function is evaluated up to two-loop order and the general structure of this series is discussed, including the effect of a weak external magnetic field. Our results apply to two-dimensional ideal ferromagnets which exhibit a spontaneously broken spin rotation symmetry O(3) $\to$ O(2) and are defined on a square, honeycomb, triangular or Kagom\'e lattice. Remarkably, the spin-wave interaction only sets in at three-loop order. In particular, there is no interaction term of order $T^3$ in the low-temperature series for the free energy density. This is the analog of the statement that, in the case of three-dimensional ferromagnets, there is no interaction term of order $T^4$ in the free energy density. We also provide a careful discussion of the implications of the Mermin-Wagner theorem in the present context and thereby put our low-temperature expansions on safe grounds.Comment: 24 pages, 3 figure

Rayleigh-Ritz Calculation of Effective Potential Far From Equilibrium

We demonstrate the utility of a Rayleigh-Ritz scheme recently proposed to compute the nonequilibrium effective potential nonperturbatively in a strong noise regime far from equilibrium. A simple Kramers model of an ionic conductor is used to illustrate the efficiency of the method.Comment: 4 pages, Latex (Version 2.09), 2 figures (Postscript), tar+gzip+uuencoded. Submitted to Phys. Rev. Let

Quantum phase interference and spin parity in Mn12 single-molecule magnets

Magnetization measurements of Mn12 molecular nanomagnets with spin ground states of S = 10 and S = 19/2 showresonance tunneling at avoided energy level crossings. The observed oscillations of the tunnel probability as a function of the magnetic field applied along the hard anisotropy axis are due to topological quantum phase interference of two tunnel paths of opposite windings. Spin-parity dependent tunneling is established by comparing the quantum phase interference of integer and half-integer spin systems.Comment: 5 pages, 5 figure

The WKB Approximation without Divergences

In this paper, the WKB approximation to the scattering problem is developed without the divergences which usually appear at the classical turning points. A detailed procedure of complexification is shown to generate results identical to the usual WKB prescription but without the cumbersome connection formulas.Comment: 13 pages, TeX file, to appear in Int. J. Theor. Phy

Test of Quantum Action for Inverse Square Potential

We present a numerical study of the quantum action previously introduced as a parametrisation of Q.M. transition amplitudes. We address the questions: Is the quantum action possibly an exact parametrisation in the whole range of transition times ($0 < T < \infty$)? Is the presence of potential terms beyond those occuring in the classical potential required? What is the error of the parametrisation estimated from the numerical fit? How about convergence and stability of the fitting method (dependence on grid points, resolution, initial conditions, internal precision etc.)? Further we compare two methods of numerical determination of the quantum action: (i) global fit of the Q.M. transition amplitudes and (ii) flow equation. As model we consider the inverse square potential, for which the Q.M. transition amplitudes are analytically known. We find that the relative error of the parametrisation starts from zero at T=0 increases to about $10^{-3}$ at $T=1/E_{gr}$ and then decreases to zero when $T \to \infty$. Second, we observe stability of the quantum action under variation of the control parameters. Finally, the flow equation method works well in the regime of large $T$ giving stable results under variation of initial data and consistent with the global fit method.Comment: Text (LaTeX), Figures(ps

Unusual manganese enrichment in the Mesoarchean Mozaan Group, Pongola Supergroup, South Africa

An unusual sediment-hosted manganese deposit is described from the Mesoarchean Mozaan Group, Pongola Supergroup, South Africa. MnO contents up to 15 wt.% were observed in marine clastic and chemical sedimentary rocks. Mn enrichment is interpreted to have resulted from the hydrothermal alteration of manganiferous shale and BIF parent rocks, the primary MnO contents of which are as high as 8.5 wt.%. A detailed mineralogical and petrographic study shows that these parent rocks are characterized by manganoan siderite, ferroan rhodochrosite and other Mn-Fe-rich mineral phases, such as kutnohorite and Fe-Mn-chlorite. Their hypogene alteration gave rise to a diversification of mineral assemblages where ferroan tephroite, calcian rhodochrosite, rhodochrosite, pyrochroite, pyrophanite, cronstedtite, manganoan Fe-rich chlorite and manganoan phlogopite partially or totally replaced the previous mineral assemblage. Thermodynamic modeling performed on chlorite phases associated with the described mineral assemblages illustrates a decrease of average crystallization temperatures from ca. 310 °C during early metamorphic stages to ca. 250 °C during a hydrothermal stage. Mineral transformation processes were thus related to retrograde metamorphism and/or hydrothermal alteration post-dating metamorphism and gave rise to progressive Mn enrichment from unaltered parent to altered rocks. The timing of hypogene alteration was constrained by 40Ar/39Ar dating to between about 1500 and 1100 Ma ago, reflecting tectonic processes associated with the Namaqua-Natal orogeny along the southern Kaapvaal Craton margin. Manganiferous shale and BIF of the Mozaan Group may represent the oldest known examples of primary sedimentary Mn deposition, related to oxidation of dissolved Mn(II) by free oxygen in a shallow marine environment. Oxygenic photosynthesis would have acted as a first-order control during Mn precipitation. This hypothesis opens a new perspective for better constraining secular evolution of sediment-hosted mineral deposits linked to oxygen levels in the atmosphere-hydrosphere system during the Archean Eon

The association of glucagon with disease severity and progression in patients with autosomal dominant polycystic kidney disease:an observational cohort study

BACKGROUND: Mammalian target of rapamycin (mTOR) inhibitors and ketogenesis have been shown to ameliorate disease progression in experimental autosomal dominant polycystic kidney disease (ADPKD). Glucagon is known to lower mTOR activity and stimulate ketogenesis. We hypothesized that in ADPKD patients, higher endogenous glucagon is associated with less disease severity and progression. METHODS: Data were analysed from 664 Dutch ADPKD patients participating in the Developing Intervention Strategies to Halt Progression of ADPKD observational cohort, including patients >18 years of age with an estimated glomerular filtration rate (eGFR) ≥15 mL/min/1.73 m(2) and excluding patients with concomitant diseases or medication use that may impact the natural course of ADPKD. The association between glucagon and disease severity and progression was tested using multivariate linear regression and mixed modelling, respectively. RESULTS: The median glucagon concentration was 5.0 pmol/L [interquartile range (IQR) 3.4–7.2) and differed significantly between females and males [4.3 pmol/L (IQR 2.9–6.0) and 6.6 (4.5–9.5), P < 0.001, respectively]. Intrasubject stability of glucagon in 30 patients showed a strong correlation (Pearson’s correlation coefficient 0.893; P < 0.001). Moreover, glucagon showed significant associations with known determinants (sex, body mass index and copeptin; all P < 0.01) and known downstream effects (glucose, haemoglobin A1c and cholesterol; all P < 0.05), suggesting that glucagon was measured reliably. Cross-sectionally, glucagon was associated with eGFR and height-adjusted total kidney volume, but in the opposite direction of our hypothesis, and these lost significance after adjustment for confounders. Glucagon was not associated with an annual decline in kidney function or growth in kidney volume. CONCLUSIONS: These data do not provide evidence for a role of endogenous glucagon as a protective hormone in ADPKD. Intervention studies are needed to determine the relation between glucagon and ADPKD

Resonant soft X-ray Raman scattering of NiO

Resonant soft X-ray Raman scattering measurements on NiO have been made at photon energies across the Ni 2p absorption edges. The details of the spectral features are identified as Raman scattering due to d-d and charge-transfer excitations. The spectra are interpreted within the single impurity Anderson model, including multiplets, crystal-field and charge-transfer effects. At threshold excitation, the spectral features consists of triplet-triplet and triplet-singlet transitions of the 3d8 configuration. For excitation energies corresponding to the charge-transfer region in the Ni 2p X-ray absorption spectrum of NiO, the emission spectra are instead dominated by charge-transfer transitions to the 3d9L-1 final state. Comparisons of the final states with other spectroscopical techniques are also made.Comment: 9 pages, 2 figures, 2 tables, http://iopscience.iop.org/0953-8984/14/13/32

Cluster variation method and disorder varieties of two-dimensional Ising-like models

I show that the cluster variation method, long used as a powerful hierarchy of approximations for discrete (Ising-like) two-dimensional lattice models, yields exact results on the disorder varieties which appear when competitive interactions are put into these models. I consider, as an example, the plaquette approximation of the cluster variation method for the square lattice Ising model with nearest-neighbor, next-nearest-neighbor and plaquette interactions, and, after rederiving known results, report simple closed-form expressions for the pair and plaquette correlation functions.Comment: 10 revtex pages, 1 postscript figur