Entangled subspaces and quantum symmetries

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize its entanglement, so that a first subspace is more entangled than a second, if the Schmidt string of the second majorizes the Schmidt string of the first. The idea is applied to the antisymmetric and symmetric tensor products of a finite-dimensional Hilbert space with itself, and also to the tensor product of an angular momentum j with a spin 1/2. When adapted to the subspaces of states of the nonrelativistic hydrogen atom with definite total angular momentum (orbital plus spin), within the space of bound states with a given total energy, this leads to a complete ordering of those subspaces by their Schmidt strings.

Anomalous magnetic susceptibility values and traces of subsurface microbial activity in carbonate banks on San Salvador Island, Bahamas

Pure limestones beneath the paleosols on San Salvador Island, Bahamas, contain strong positive magnetic susceptibility anomalies, although the iron content is generally very low. These magnetic phenomena differ from those associated with disconformities, which are marked by accumulation of paramagnetic airborne dust deposits with relatively high iron content. The strength and characters of the magnetic response in these subsurface zones correspond to the presence of magnetite, particularly small single-domain magnetite crystals of microbial origin. These crystals are not present elsewhere in the intergranular rock pores or microvugs. They are preferentially concentrated in capillary microborings, which developed concurrently with formation of calcite cements that have soil-related C and O isotope compositions. These magnetic zones occur several meters below the overlying soil horizons. Very thin and long linear microborings may be attributable to cyanobacterial microborers. The single-domain magnetites in these micrometer-size tunnels plugged by calcite appear to result from later occupation of these tiny holes by magnetotactic bacteria. Inorganic origin of the magnetite seems unlikely. Numerous traces that suggest subsurface microbial activity provide evidence that may be used to develop possible scenarios for subsequent biological studies of the precise bacteria involved.

Anomalous Excitation Spectra of Frustrated Quantum Antiferromagnets

We use series expansions to study the excitation spectra of spin-1/2 antiferromagnets on anisotropic triangular lattices. For the isotropic triangular lattice model (TLM), the high-energy spectra show several anomalous features that differ strongly from linear spin-wave theory (LSWT). Even in the Neel phase, the deviations from LSWT increase sharply with frustration, leading to rotonlike minima at special wave vectors. We argue that these results can be interpreted naturally in a spinon language and provide an explanation for the previously observed anomalous finite-temperature properties of the TLM. In the coupled-chains limit, quantum renormalizations strongly enhance the one-dimensionality of the spectra, in agreement with experiments on Cs2CuCl4.

Anomalous scattering analysis of Agrobacterium radiobacter phosphotriesterase: the prominent role of iron in the heterobinuclear active site

Bacterial phosphotriesterases are binuclear metalloproteins for which the catalytic mechanism has been studied with a variety of techniques, principally using active sites reconstituted in vitro from apoenzymes. Here, atomic absorption spectroscopy and anomalous X-ray scattering have been used to determine the identity of the metals incorporated into the active site in vivo. We have recombinantly expressed the phosphotriesterase from Agrobacterium radiobacter (OpdA) in Escherichia coli grown in medium supplemented with 1 mM CoCl2 and in unsupplemented medium. Anomalous scattering data, collected from a single crystal at the Fe-K, Co-K and Zn-K edges, indicate that iron and cobalt are the primary constituents of the two metal-binding sites in the catalytic centre (alpha and P) in the protein expressed in E. coli grown in supplemented medium. Comparison with OpdA expressed in unsupplemented medium demonstrates that the cobalt present in the supplemented medium replaced zinc at the beta-position of the active site, which results in an increase in the catalytic efficiency of the enzyme. These results suggest an essential role for iron in the catalytic mechanism of bacterial phosphotriesterases, and that these phosphotriesterases are natively heterobinuclear iron-zinc enzymes.

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

Anisotropic scattering and anomalous normal-state transport in a high-temperature superconductor

The metallic state of high-temperature copper-oxide superconductors, characterized by unusual and distinct temperature dependences in the transport properties(1-4), is markedly different from that of textbook metals. Despite intense theoretical efforts(5-11), our limited understanding is impaired by our inability to determine experimentally the temperature and momentum dependence of the transport scattering rate. Here, we use a powerful magnetotransport probe to show that the resistivity and the Hall coefficient in highly doped Tl2Ba2CuO6+delta originate from two distinct inelastic scattering channels. One channel is due to conventional electron electron scattering; the other is highly anisotropic, has the same symmetry as the superconducting gap and a magnitude that grows approximately linearly with temperature. The observed form and anisotropy place tight constraints on theories of the metallic state. Moreover, in heavily doped non-superconducting La2-xSrxCuO4, this anisotropic scattering term is absent(12), suggesting an intimate connection between the origin of this scattering and superconductivity itself.