Quantum Topological Excitations: from the Sawtooth Lattice to the Heisenberg Chain

The recently elucidated structure of the delafossite YCuO$_{2.5}$ reveals a Cu-O network with nearly independent $\Delta$ chains having different interactions between the $s=1/2$ spins. Motivated by this result, we study the $\Delta$ chain for various ratios $J_{\rm bb}/J_{\rm bv}$ of the base-base and base-vertex interactions. By exact diagonalization and extrapolation, we show that the elementary excitation spectrum, which (within numerical error) is the same for total spins $S_{\rm tot}=0$ and 1, has a gap only in the interval $0.4874(1) \leq J_{\rm bb}/J_{\rm bv} \leq 1.53(1)$. The gap is dispersionless for $J_{\rm bb}/J_{\rm bv}=1$, but has increasing $k$-dependence as $J_{\rm bb}/J_{\rm bv}$ moves away from unity, related to the instability of dimers in the ground state.Comment: 4 pages, 6 figures (revtex twocolumn

Explicit computations of low lying eigenfunctions for the quantum trigonometric Calogero-Sutherland model related to the exceptional algebra E7

In the previous paper math-ph/0507015 we have studied the characters and Clebsch-Gordan series for the exceptional Lie algebra E7 by relating them to the quantum trigonometric Calogero-Sutherland Hamiltonian with coupling constant K=1. Now we extend that approach to the case of general K

Electrical resistivity of the Ti4O7 Magneli phase under high pressure

We have measured resistivity as a function of temperature and pressure of Ti4O7 twinned crystals using different contact configurations. Pressures over 4kbar depress the localization of bipolarons and allow the study of the electrical conduction of the bipolaronic phase down to low temperatures. For pressures P > 40 kbar the bipolaron formation transition is suppressed and a nearly pressure independent behavior is obtained for the resistivity. We observed an anisotropic conduction. When current is injected parallel to the principal axis, a metallic conduction with interacting carrier effects is predominant. A superconducting state was not obtained down to 1.2 K, although evidences of the proximity of a quantum critical point were noticed. While when current is injected non-parallel to the crystal's principal axis, we obtained a logarithmic divergence of the resistivity at low temperatures. For this case, our results for the high pressure regime can be interpreted in the framework of interacting carriers (polarons or bipolarons) scattered by Two Level Systems.Comment: 9 Revtex pages, 12 EPS figures included, submitted to The European Physical Journal B. Contact author: C. Acha (e-mail address: [email protected]

Absence of a structural transition up to 40 Gpa in MgB2 and the relevance of magnesium non-stoichiometry

We report measurements on MgB2 up to ~40GPa. Increasing pressure yields a monotonous decrease of the lattice parameters and of the c/a ratio, but no structural transition down to parameters smaller than those of AlB2. The transition superconducting temperature also decreases with temperature in a sample dependent way. The results are explained by an increase of the filling of the 2D pxy bands with pressure, the Mg stoichiometry determining the starting position of the Fermi level. Our measurements indicate that these hole bands are the relevant ones for superconductivity.Comment: submitted March 9th 2001, PRB accepte

Condition-Measure Bounds on the Behavior of the Central Trajectory of a Semi-Definete Program

We present bounds on various quantities of interest regarding the central trajectory of a semi-definite program (SDP), where the bounds are functions of Renegar's condition number C(d) and other naturally-occurring quantities such as the dimensions n and m. The condition number C(d) is defined in terms of the data instance d = (A, b, C) for SDP; it is the inverse of a relative measure of the distance of the data instance to the set of ill-posed data instances, that is, data instances for which arbitrary perturbations would make the corresponding SDP either feasible or infeasible. We provide upper and lower bounds on the solutions along the central trajectory, and upper bounds on changes in solutions and objective function values along the central trajectory when the data instance is perturbed and/or when the path parameter defining the central trajectory is changed. Based on these bounds, we prove that the solutions along the central trajectory grow at most linearly and at a rate proportional to the inverse of the distance to ill-posedness, and grow at least linearly and at a rate proportional to the inverse of C(d)2 , as the trajectory approaches an optimal solution to the SDP. Furthermore, the change in solutions and in objective function values along the central trajectory is at most linear in the size of the changes in the data. All such bounds involve polynomial functions of C(d), the size of the data, the distance to ill-posedness of the data, and the dimensions n and m of the SDP

An Interneuron Circuit Reproducing Essential Spectral Features of Field Potentials

This document is the Accepted Manuscript version of the following article: Reinoud Maex, ‘An Interneuron Circuit Reproducing Essential Spectral Features of Field Potentials’, Neural Computation, March 2018. Under embargo until 22 June 2018. The final, definitive version of this paper is available online at doi: https://doi.org/10.1162/NECO_a_01068. © 2018 Massachusetts Institute of Technology. Content in the UH Research Archive is made available for personal research, educational, and non-commercial purposes only. Unless otherwise stated, all content is protected by copyright, and in the absence of an open license, permissions for further re-use should be sought from the publisher, the author, or other copyright holder.Recent advances in engineering and signal processing have renewed the interest in invasive and surface brain recordings, yet many features of cortical field potentials remain incompletely understood. In the present computational study, we show that a model circuit of interneurons, coupled via both GABA(A) receptor synapses and electrical synapses, reproduces many essential features of the power spectrum of local field potential (LFP) recordings, such as 1/f power scaling at low frequency (< 10 Hz) , power accumulation in the γ-frequency band (30–100 Hz), and a robust α rhythm in the absence of stimulation. The low-frequency 1/f power scaling depends on strong reciprocal inhibition, whereas the α rhythm is generated by electrical coupling of intrinsically active neurons. As in previous studies, the γ power arises through the amplifica- tion of single-neuron spectral properties, owing to the refractory period, by parameters that favour neuronal synchrony, such as delayed inhibition. The present study also confirms that both synaptic and voltage-gated membrane currents substantially contribute to the LFP, and that high-frequency signals such as action potentials quickly taper off with distance. Given the ubiquity of electrically coupled interneuron circuits in the mammalian brain, they may be major determinants of the recorded potentials.Peer reviewe

Meson mass and confinement force driven by dilaton

Meson spectra given as fluctuations of a D7 brane are studied under the background driven by the dilaton. This leads to a dual gauge theory with quark confinement due to the gauge condensate. We find that the effect of the gauge condensate on the meson spectrum is essential in order to make a realistic hadron spectrum in the non-supersymmetric case. In the supersymmetric case, however, only the spectra of the scalars are affected, but they are changed in an opposite way compared to the non-supersymmetric case.Comment: 11 pages, 2 figure