Correlation Energy and Entanglement Gap in Continuous Models

Our goal is to clarify the relation between entanglement and correlation energy in a bipartite system with infinite dimensional Hilbert space. To this aim we consider the completely solvable Moshinsky's model of two linearly coupled harmonic oscillators. Also for small values of the couplings the entanglement of the ground state is nonlinearly related to the correlation energy, involving logarithmic or algebraic corrections. Then, looking for witness observables of the entanglement, we show how to give a physical interpretation of the correlation energy. In particular, we have proven that there exists a set of separable states, continuously connected with the Hartree-Fock state, which may have a larger overlap with the exact ground state, but also a larger energy expectation value. In this sense, the correlation energy provides an entanglement gap, i.e. an energy scale, under which measurements performed on the 1-particle harmonic sub-system can discriminate the ground state from any other separated state of the system. However, in order to verify the generality of the procedure, we have compared the energy distribution cumulants for the 1-particle harmonic sub-system of the Moshinsky's model with the case of a coupling with a damping Ohmic bath at 0 temperature.Comment: 26 pages, 6 figure

Chern-Simons Field Theory and Completely Integrable Systems

We show that the classical non-abelian pure Chern-Simons action is related in a natural way to completely integrable systems of the Davey-Stewartson hyerarchy, via reductions of the gauge connection in Hermitian spaces and by performing certain gauge choices. The B\"acklund Transformations are interpreted in terms of Chern-Simons equations of motion or, on the other hand, as a consistency condition on the gauge. A mapping with a nonlinear $\sigma$-model is discussed.Comment: 11 pages, Late

Topological Field Theory and Nonlinear σ\sigma-Models on Symmetric Spaces

We show that the classical non-abelian pure Chern-Simons action is related to nonrelativistic models in (2+1)-dimensions, via reductions of the gauge connection in Hermitian symmetric spaces. In such models the matter fields are coupled to gauge Chern-Simons fields, which are associated with the isotropy subgroup of the considered symmetric space. Moreover, they can be related to certain (integrable and non-integrable) evolution systems, as the Ishimori and the Heisenberg model. The main classical and quantum properties of these systems are discussed in connection with the topological field theory and the condensed matter physics.Comment: LaTeX format, 31 page

Boundary-induced violation of the Dirac fermion parity and its signatures in local and global tunneling spectra of graphene

Extended defects in graphene, such as linear edges, break the translational invariance and can also have an impact on the symmetries specific to massless Dirac-like quasiparticles in this material. The paper examines the consequences of a broken Dirac fermion parity in the framework of the effective boundary conditions varying from the Berry-Mondragon mass confinement to a zigzag edge. The parity breaking reflects the structural sublattice asymmetry of zigzag-type edges and is closely related to the previously predicted time-reversal symmetric edge states. We calculate the local and global densities of the edge states and show that they carry a specific polarization, resembling, to some extent, that of spin-polarized materials. The lack of the parity leads to a nonanalytical particle-hole asymmetry in the edge-state properties. We use our findings to interpret recently observed tunneling spectra in zigzag-terminated graphene. We also propose a graphene-based tunneling device where the particle-hole asymmetric edge states result in a strongly nonlinear conductance-voltage characteristics, which could be used to manipulate the tunneling transport.Comment: 8 pages, 5 figures, to be published in Phys. Rev.

Light Scattering by Cholesteric Skyrmions

We study the light scattering by localized quasi planar excitations of a Cholesteric Liquid Crystal known as spherulites. Due to the anisotropic optical properties of the medium and the peculiar shape of the excitations, we quantitatively evaluate the cross section of the axis-rotation of polarized light. Because of the complexity of the system under consideration, first we give a simplified, but analytical, description of the spherulite and we compare the Born approximation results in this setting with those obtained by resorting to a numerical exact solution. The effects of changing values of the driving external static electric (or magnetic) field is considered. Possible applications of the phenomenon are envisaged.Comment: 18 pages, 14 figure

Deformation surfaces, integrable systems and Chern - Simons theory

A few years ago, some of us devised a method to obtain integrable systems in (2+1)-dimensions from the classical non-Abelian pure Chern-Simons action via reduction of the gauge connection in Hermitian symmetric spaces. In this paper we show that the methods developed in studying classical non-Abelian pure Chern-Simons actions, can be naturally implemented by means of a geometrical interpretation of such systems. The Chern-Simons equation of motion turns out to be related to time evolving 2-dimensional surfaces in such a way that these deformations are both locally compatible with the Gauss-Mainardi-Codazzi equations and completely integrable. The properties of these relationships are investigated together with the most relevant consequences. Explicit examples of integrable surface deformations are displayed and discussed.Comment: 24 pages, 1 figure, submitted to J. Math. Phy

Alternative final steps in berberine biosynthesis in Coptis japonica cell cultures

In Coptis japonica cell cultures an alternative pathway has been discovered which leads from (S)-tetrahydrocolumbamine via (S)-canadine to berberine. The two enzymes involved have been partially purified. (S)-Tetrahydrocolumbamine is stereospecifically transformed into (S)-canadine under formation of the methylenedioxy bridge in ring A. This new enzyme was named (S)-canadine synthase. (S)-Canadine in turn is stereospecifically dehydrogenated to berberine by an oxidase, (S)-canadine oxidase (COX), which was partially purified (25-fold). This enzyme has many physical properties in common with the already known (S)-tetrahydroprotoberberine oxidase from Berberis but grossly differs from the latter enzyme in its cofactor requirement (Fe) and its substrate specificity. Neither (S)-norreticuline nor (S)-scoulerine serves as substrate for the Coptis enzyme, while both substrates are readily oxidized by the Berberis enzyme. The four terminal enzymes catalyzing the pathway from (S)-reticuline to berberine are housed in Berberis as well as in Coptis in smooth vesicles with a density of =1.14 g/ml. These vesicles have been enriched and characterized by electron microscopy