Entropy and Correlation Functions of a Driven Quantum Spin Chain

We present an exact solution for a quantum spin chain driven through its critical points. Our approach is based on a many-body generalization of the Landau-Zener transition theory, applied to fermionized spin Hamiltonian. The resulting nonequilibrium state of the system, while being a pure quantum state, has local properties of a mixed state characterized by finite entropy density associated with Kibble-Zurek defects. The entropy, as well as the finite spin correlation length, are functions of the rate of sweep through the critical point. We analyze the anisotropic XY spin 1/2 model evolved with a full many-body evolution operator. With the help of Toeplitz determinants calculus, we obtain an exact form of correlation functions. The properties of the evolved system undergo an abrupt change at a certain critical sweep rate, signaling formation of ordered domains. We link this phenomenon to the behavior of complex singularities of the Toeplitz generating function.Comment: 16 pgs, 7 fg

Relativistic Green functions in a plane wave gravitational background

We consider a massive relativistic particle in the background of a gravitational plane wave. The corresponding Green functions for both spinless and spin 1/2 cases, previously computed by A. Barducci and R. Giachetti \cite{Barducci3}, are reobtained here by alternative methods, as for example, the Fock-Schwinger proper-time method and the algebraic method. In analogy to the electromagnetic case, we show that for a gravitational plane wave background a semiclassical approach is also sufficient to provide the exact result, though the lagrangian involved is far from being a quadratic one.Comment: Last paper by Professor Arvind Narayan Vaidya, 18 pages, no figure

Associations of body composition measures and C2, a marker for small artery elasticity: The MESA.

ObjectiveLower C2, a continuous blood pressure waveform characteristic asserted to represent small artery elasticity, predicts future cardiovascular disease events. It is hypothesized that the paradoxical positive association between body mass index (BMI) and C2 may reflect muscle instead of excess fat.MethodsIn a multi-ethnic, community-living cohort of 1,960 participants, computed tomography scans of the abdomen were used to measure visceral adipose tissue (VAT) and total abdominal muscle tissue (TAMT), and applanation tonometry of the radial arteries was used to assess C2. The period cross-sectional associations between BMI, TAMT, and VAT with C2 were ascertained.ResultsThe mean age was 62 ± 9 years and 51% were male. After adjustments for age, gender, ethnicity, pack years smoking cigarettes, diabetes, hypertension, and total and HDL cholesterol, higher BMI (standardized beta = 0.09, P-value < 0.01) and more TAMT (standardized beta = 0.12, P-value < 0.01) were significantly associated with higher C2. In contrast, more VAT (standardized beta = -0.09, P-value < 0.01) was associated with lower C2.ConclusionsIn multivariable analysis, VAT, in contrast to TAMT and BMI, was associated with less compliant small arteries. Visceral fat may be a better marker for detrimental excess body fat than BMI

Noncommutative Chiral Anomaly and the Dirac-Ginsparg-Wilson Operator

It is shown that the local axial anomaly in $2-$dimensions emerges naturally if one postulates an underlying noncommutative fuzzy structure of spacetime . In particular the Dirac-Ginsparg-Wilson relation on ${\bf S}^2_F$ is shown to contain an edge effect which corresponds precisely to the ``fuzzy'' $U(1)_A$ axial anomaly on the fuzzy sphere . We also derive a novel gauge-covariant expansion of the quark propagator in the form $\frac{1}{{\cal D}_{AF}}=\frac{a\hat{\Gamma}^L}{2}+\frac{1}{{\cal D}_{Aa}}$ where $a=\frac{2}{2l+1}$ is the lattice spacing on ${\bf S}^2_F$, $\hat{\Gamma}^L$ is the covariant noncommutative chirality and ${\cal D}_{Aa}$ is an effective Dirac operator which has essentially the same IR spectrum as ${\cal D}_{AF}$ but differes from it on the UV modes. Most remarkably is the fact that both operators share the same limit and thus the above covariant expansion is not available in the continuum theory . The first bit in this expansion $\frac{a\hat{\Gamma}^L}{2}$ although it vanishes as it stands in the continuum limit, its contribution to the anomaly is exactly the canonical theta term. The contribution of the propagator $\frac{1}{{\cal D}_{Aa}}$ is on the other hand equal to the toplogical Chern-Simons action which in two dimensions vanishes identically .Comment: 26 pages, latex fil

Spin Chains as Perfect Quantum State Mirrors

Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions which display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.Comment: Abstract extended, introduction shortened, some clarifications in the text, one new reference. Accepted by Phys. Rev. A (Rapid Communications

How to make a traversable wormhole from a Schwarzschild black hole

The theoretical construction of a traversable wormhole from a Schwarzschild black hole is described, using analytic solutions in Einstein gravity. The matter model is pure phantom radiation (pure radiation with negative energy density) and the idealization of impulsive radiation is employed.Comment: 4 pages, 4 figure

Kerr-Schild Symmetries

We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixed. The properties of these Lie algebras are briefly analyzed and we show that they are generically finite-dimensional but that they may have infinite dimension in some relevant situations. The most general vector fields of the above type are explicitly constructed for the following cases: any two-dimensional metric, the general spherically symmetric metric and deformation direction, and the flat metric with parallel or cylindrical deformation directions.Comment: 15 pages, no figures, LaTe

PRELIMINARY STUDIES ON BRAIN TARGETING OF INTRANASAL ATOMOXETINE LIPOSOMES

Objective: The objective of the present study was to evaluate the enhancement in brain uptake of liposomes containing atomoxetine (ATX-Lipo) for intranasal delivery in the management of Attention Deficit Hyperactivity Disorder (ADHD).Methods: ATX-Lipo and ATX mucoadhesive liposomes (ATX-Muco Lipo) with and without a vasoconstrictor phenylephrine (PHE) were prepared by lipid film hydration method and characterized for physicochemical parameters. Biodistribution and pharmacokinetic evaluation of ATX-Lipo in the brain and blood of Sprague Dawley rats following intranasal (i. n.) and intravenous (i. v.) administrations were examined using optimized technetium-labeled ([99]m Tc-labeled) atomoxetine formulations. Gamma scintigraphy imaging was performed in Sprague Dawley rats.Results: ATX-Lipo and ATX-Muco Lipo were found to be stable with average particle size of 404.35±1.86 nm and 510.50±1.22 nm respectively.[99]mTc tagged ATX-Lipo, ATX-Muco Lipo, ATX+PHE-Muco Lipo and ATX solution were found to be stable and suitable for in vivo studies. On comparing ATX concentrations after i. n. administrations of ATX-Lipo, ATX-Muco Lipo and ATX+PHE-Muco Lipo and i. v. administration of ATX-Lipo, brain/blood uptake ratios (BBR) at 30 min were found to be 0.161, 1.255, 0.331, and 0.003 respectively. These results revealed effective brain targeting following i. n. administration of mucoadhesive ATX liposomes. Higher drug targeting efficiency (% DTE) and direct transport percentage (%DTP) for mucoadhesive liposomes indicated considerable brain targeting from ATX-Muco liposomes. Gamma scintigraphy imaging of the rat brain conclusively demonstrated the greater extent of transport of atomoxetine by ATX+PHE-Muco Lipo (i. n.), when compared with ATX solution (i. n.) into the rat brain.Conclusion: This preliminary investigation demonstrates a considerable extent of transport of ATX into the brain through i. n. ATX+PHE-Muco Lipo, which may prove to be a new platform for better management of ADHD.Keywords: Intranasal delivery, Brain targeting, Mucoadhesive liposomes, Vasoconstrictor, Radiolabeling, Drug targeting efficiency, Direct transport percentage, Gamma scintigraphy

Gravitating magnetic monopole in Vaidya geometry

A magnetic-monopole solution of a non-Abelian gauge theory as proposed by 't Hooft and Polyakov is studied in the Vaidya spacetime. We find that the solutions of Einstein equations generates a geometry of the Bonnor-Vaidya corresponding to magnetically charged null fluid with Higgs field contributing a cosmological term. In the absence of the scalar fields the corresponding Wu-Yang solution of the gauge theory still generates the Bonnor-Vaidya geometry, but with no cosmological term.Comment: 5 RevTeX pages, no figures, minor changes, to appear in Physical Review