Twisted K-theory and finite-dimensional approximation

We provide a finite-dimensional model of the twisted K-group twisted by any degree three integral cohomology class of a CW complex. One key to the model is Furuta's generalized vector bundle, and the other is a finite-dimensional approximation of Fredholm operators.Comment: 26 pages, LaTeX 2e, Xypic; main theorem improve

Entanglement Cost of Three-Level Antisymmetric States

We show that the entanglement cost of the three-dimensional antisymmetric states is one ebit.Comment: 8page

Electro-spinon in one-dimensional Mott insulator

The low-energy dynamical optical response of dimerized and undimerized spin liquid states in a one-dimensional charge transfer Mott insulator is theoretically studied. An exact analysis is given for the low-energy asymptotic behavior using conformal field theory for the undimerized state. In the dimerized state, the infrared absorption due to the bound state of two solitons, i.e, the breather mode, is predicted with an accurate estimate for its oscillator strength, offering a way to detect experimentally the excited singlet state. Effects of external magnetic fields are also discussed.Comment: 5 pages, 2 figures, some typos are correcte

Non-local Matching Condition and Scale-invariant Spectrum in Bouncing Cosmology

In cosmological scenarios such as the pre-big bang scenario or the ekpyrotic scenario, a matching condition between the metric perturbations in the pre-big bang phase and those in the post big-bang phase is often assumed. Various matching conditions have been considered in the literature. Nevertheless obtaining a scale invariant CMB spectrum via a concrete mechanism remains impossible. In this paper, we examine this problem from the point of view of local causality. We begin with introducing the notion of local causality and explain how it constrains the form of the matching condition. We then prove a no-go theorem: independent of the details of the matching condition, a scale invariant spectrum is impossible as long as the local causality condition is satisfied. In our framework, it is easy to show that a violation of local causality around the bounce is needed in order to give a scale invariant spectrum. We study a specific scenario of this possibility by considering a nonlocal effective theory inspired by noncommutative geometry around the bounce and show that a scale invariant spectrum is possible. Moreover we demonstrate that the magnitude of the spectrum is compatible with observations if the bounce is assumed to occur at an energy scale which is a few orders of magnitude below the Planckian energy scale.Comment: 15 pages, 2 figures; v3: clarifications added, changes in references, version to appear in PR

Projection neurons in lamina III of the rat spinal cord are selectively innervated by local dynorphin-containing excitatory neurons

Large projection neurons in lamina III of the rat spinal cord that express the neurokinin 1 receptor are densely innervated by peptidergic primary afferent nociceptors and more sparsely by low-threshold myelinated afferents. However, we know little about their input from other glutamatergic neurons. Here we show that these cells receive numerous contacts from nonprimary boutons that express the vesicular glutamate transporter 2 (VGLUT2), and form asymmetrical synapses on their dendrites and cell bodies. These synapses are significantly smaller than those formed by peptidergic afferents, but provide a substantial proportion of the glutamatergic synapses that the cells receive (over a third of those in laminae I–II and half of those in deeper laminae). Surprisingly, although the dynorphin precursor preprodynorphin (PPD) was only present in 4–7% of VGLUT2 boutons in laminae I–IV, it was found in 58% of the VGLUT2 boutons that contacted these cells. This indicates a highly selective targeting of the lamina III projection cells by glutamatergic neurons that express PPD, and these are likely to correspond to local neurons (interneurons and possibly projection cells). Since many PPD-expressing dorsal horn neurons respond to noxious stimulation, this suggests that the lamina III projection cells receive powerful monosynaptic and polysynaptic nociceptive input. Excitatory interneurons in the dorsal horn have been shown to possess IA currents, which limit their excitability and can underlie a form of activity-dependent intrinsic plasticity. It is therefore likely that polysynaptic inputs to the lamina III projection neurons are recruited during the development of chronic pain states

On non commutative sinh-Gordon Equation

We give a noncommutative extension of sinh-Gordon equation. We generalize a linear system and Lax representation of the sinh-Gordon equation in noncommutative space. This generalization gives a noncommutative version of the sinh-Gordon equation with extra constraints, which can be expressed as global conserved currents.Comment: 7 Page

A quantitative study of neurochemically-defined populations of inhibitory interneurons in the superficial dorsal horn of the mouse spinal cord

Around a quarter of neurons in laminae I-II of the dorsal horn are inhibitory interneurons. These play an important role in modulating somatosensory information, including that perceived as pain or itch. Previous studies in rat identified four largely non-overlapping neurochemical populations among these cells, defined by expression of galanin, neuropeptide Y (NPY), neuronal nitric oxide synthase (nNOS) or parvalbumin. The galanin cells were subsequently shown to coexpress dynorphin. Several recent studies have used genetically-modified mice to investigate the function of different interneuron populations, and it is therefore important to determine whether the same pattern applies in mouse, and to estimate the relative sizes of these populations. We show that the neurochemical organisation of inhibitory interneurons in mouse superficial dorsal horn is similar to that in the rat, although a larger proportion of these neurons (33%) express NPY. Between them, these four populations account for ∼75% of inhibitory cells in laminae I-II. Since ∼25% of inhibitory interneurons in this region belong to a novel calretinin-expressing type, our results suggest that virtually all inhibitory interneurons in superficial dorsal horn can be assigned to one of these five neurochemical populations. Although our main focus was inhibitory neurons, we also identified a population of excitatory dynorphin-expressing cells in laminae I-II that are largely restricted to the medial part of the mid-lumbar dorsal horn, corresponding to glabrous skin territory. These findings are important for interpretation of studies using molecular-genetic techniques to manipulate the functions of interneuron populations to investigate their roles in somatosensory processing

Spin wave dispersion softening in the ferromagnetic Kondo lattice model for manganites

Spin dynamics is calculated in the ferromagnetic (FM) state of the generalized Kondo lattice model taking into account strong on-site correlations between e_g electrons and antiferromagnetic (AFM) exchange among t_{2g} spins. Our study suggests that competing FM double-exchange and AFM super-exchange interaction lead to a rather nontrivial spin-wave spectrum. While spin excitations have a conventional Dq^2 spectrum in the long-wavelength limit, there is a strong deviation from the spin-wave spectrum of the isotropic Heisenberg model close to the zone boundary. The relevance of our results to the experimental data are discussed.Comment: 6 RevTex pages, 3 embedded PostScript figure

Incoherent Noise and Quantum Information Processing

Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modelled as a distribution of unitary processes arising from slowly varying experimental parameters. We show how it introduces artifacts in quantum process tomography and we explain how the resulting estimate of the superoperator may not be completely positive. We then go on to attack the inverse problem of extracting an effective distribution of unitaries that characterizes the incoherence via a perturbation theory analysis of the superoperator eigenvalue spectra.Comment: 15 pages, 5 figures, replaced with future JCP published versio