Factorization and Dilation Problems for Completely Positive Maps on von Neumann Algebras

We study factorization and dilation properties of Markov maps between von Neumann algebras equipped with normal faithful states, i.e., completely positive unital maps which preserve the given states and also intertwine their automorphism groups. The starting point for our investigation has been the question of existence of non-factorizable Markov maps, as formulated by C. Anantharaman-Delaroche. We provide simple examples of non-factorizable Markov maps on M_n(\mathbbC){M_n(\mathbb{C})} for all n ≥ 3, as well as an example of a one-parameter semigroup (T(t)) _t≥0 of Markov maps on M₄(\mathbbC){M_4(\mathbb{C})} such that T(t) fails to be factorizable for all small values of t > 0. As applications, we solve in the negative an open problem in quantum information theory concerning an asymptotic version of the quantum Birkhoff conjecture, as well as we sharpen the existing lower bound estimate for the best constant in the noncommutative little Grothendieck inequality.     

Splitting Quantum Information with Five-Atom Cluster State in Cavity QED

A realizable scheme is proposed for implementing quantum information splitting with five-atom cluster state in cavity QED, where we explicitly illustrate the procedure. The scheme does not involve Bell-state measurement and is insensitive to the cavity and the thermal field.     

The More the Merrier?

The trade-off between traits in life-history strategies has been widely studied for sexual and parthenogenetic organisms, but relatively little is known about the reproduction strategies of asexual animals. Here, we investigate clonal reproduction in the freshwater planarian Schmidtea mediterranea, an important model organism for regeneration and stem cell research. We find that these flatworms adopt a randomized reproduction strategy that comprises both asymmetric binary fission and fragmentation (generation of multiple offspring during a reproduction cycle). Fragmentation in planarians has primarily been regarded as an abnormal behavior in the past; using a large-scale experimental approach, we now show that about one third of the reproduction events in S. mediterranea are fragmentations, implying that fragmentation is part of their normal reproductive behavior. Our analysis further suggests that certain characteristic aspects of the reproduction statistics can be explained in terms of a maximum relative entropy principle.     

Slicing and Dicing the Genome: A Statistical Physics Approach to Population Genetics

The inference of past demographic parameters from current genetic polymorphism is a fundamental problem in population genetics. The standard techniques utilize a reconstruction of the gene-genealogy, a cumbersome process that may be applied only to small numbers of sequences. We present a method that compares the total number of haplotypes (distinct sequences) with the model prediction. By chopping the DNA sequence into pieces we condense the immense information hidden in sequence space into a function for the number of haplotypes versus subsequence size. The details of this curve are robust to statistical fluctuations and are seen to reflect the process parameters. This procedure allows for a clear visualization of the quality of the fit and, crucially, the numerical complexity grows only linearly with the number of sequences. Our procedure is tested against both simulated data as well as empirical mtDNA data from China and provides excellent fits in both cases.     

Observables in 3d spinfoam quantum gravity with fermions

We study expectation values of observables in three-dimensional spinfoam quantum gravity coupled to Dirac fermions. We revisit the model introduced by one of the authors and extend it to the case of massless fermionic fields. We introduce observables, analyse their symmetries and the corresponding proper gauge fixing. The Berezin integral over the fermionic fields is performed and the fermionic observables are expanded in open paths and closed loops associated to pure quantum gravity observables. We obtain the vertex amplitudes for gauge-invariant observables, while the expectation values of gauge-variant observables, such as the fermion propagator, are given by the evaluation of particular spin networks.     

The Entanglement Properties Induced by Atoms in Two Separate Cavities Connected by an Optical Fiber

We study the entanglement evolution between two atoms, which are initially entangled with a third atom and trapped in two separated cavities coupled by an optical fiber. We also investigate the temporal evolution in the entanglement between the atom and the local cavity mode. The influence of the state-selective measurement on the atom outside the cavities and the influence of cavity-fiber coupling coefficient on the entanglement are discussed. The results show that the entanglement can be strengthened through the state-selective measurement on the atom outside the cavities. We also find that, by increasing the cavity-fiber coupling coefficient, the atom-atom entanglement is strengthened, but the atom-cavity entanglement is weakened.     

Pseudo-Hyperkähler Geometry and Generalized Kähler Geometry

We discuss the conditions for additional supersymmetry and twisted super-symmetry in N = (2, 2) supersymmetric nonlinear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex structures. Focus is on linear non-manifest transformations of these fields that have an algebra that closes off-shell. We find that additional linear supersymmetry has no interesting solution, whereas additional linear twisted supersymmetry has solutions with interesting geometrical properties. We solve the conditions for invariance of the action and show that these solutions correspond to a bi-hermitian metric of signature (2, 2) and a pseudo-hyperkähler geometry of the target space.     

Synthesis of dimension-tunable ZnO nanostructures via the design of zinc hydroxide precursors

A facile synthesis route is presented to achieve dimension-tunable ZnO nanostructures by the design of zinc hydroxide precursors under the surfactant-free condition. From three types of zinc hydroxide precursors, namely, crystalline Zn(OH)(NO₃)(H₂O) nanobelts, amorphous zinc hydroxides microparticles and soluble Zn(OH)^2-₄\mathrm{Zn}(\mathrm{OH})^{2-}_{4} species, the porous ZnO nanosheets, ZnO nanoparticles and ZnO nanowires can be achieved, respectively. The porous ZnO nanosheets exhibit large polar surface area. Thermal analysis indicates that the crystalline Zn(OH)(NO₃)(H₂O) nanobelts were converted to the porous ZnO nanosheets by in situ lattice reconstruction, which was attributed to the unique fibrous structure of Zn(OH)(NO₃)(H₂O) nanobelts. The as-prepared dimension-tunable ZnO nanostructures have potential applications in solar cells, photocatalysis, novel chemical and biological sensors, etc.     

Burstein–Moss shift and room temperature near-band-edge luminescence in lithium-doped zinc oxide

Nanopowders of pure and lithium-doped semiconducting ZnO (Zn_1−x Li _x O, where x= 0, 0.01, 0.03, 0.06, 0.09 and 0.15 in atomic percent (at.%)) are prepared by PEG-assisted low-temperature hydrothermal method. The average crystallite size is calculated using Debye–Scherrer formula and corrected for strain-induced broadening by Williamson–Hall (W–H) plot. The peak shift in XRD and the lattice constant of ZnO as a function of unit cell composition are predicted by Vegard’s law. The evolution of ZnO nanostructures from rod-shaped to particle nature is observed from TEM images and the influence of dopant on the morphology is investigated. The optical absorption measurement marks an indication that the incorporation of lithium ion into the lattice of ZnO widens the optical band gap energy from ∼2.60 to ∼3.20 eV. The near band edge (NBE) emission peak centered at ∼3.10 eV is considered to be the dominant emission peak in the PL spectra. Blue emission peak is not observed in doped ZnO, thus promoting defect-free nanoparticles. The Burstein–Moss shift serves as a qualitative tool to analyze the widening of the optical band gap and to study the shape of the NBE luminescence in doped ZnO nanopowders. FT-IR spectra are used to identify the strong metal–oxide (Zn–O) interaction.