Uses of a small field value which falls from a metastable maximum over cosmological times

We consider a small, metastable maximum vacuum expectation value $b_0$ of order of a few eV, for a pseudoscalar Goldstone-like field, which is related to the scalar inflaton field $\phi$ in an idealized model of a cosmological, spontaneously-broken chiral symmetry. The b field allows for relating semi-quantitatively three distinct quantities in a cosmological context. (1) A very small, residual vacuum energy density or effective cosmological constant of ~ lambda b_0^4 ~ 2.7 x 10^{-47}GeV^4, for lambda ~ 3 x 10^{-14}, the same as an empirical inflaton self-coupling. (2) A tiny neutrino mass, less then b_0. (3) A possible small variation downward of the proton to electron mass ratio over cosmological time. The latter arises from the motion downward of the $b$ field over cosmological time, toward a nonzero limiting value as $t \to \infty$. Such behavior is consistent with an equation of motion. We argue that hypothetical b quanta, potentially inducing new long-range forces, are absent, because of negative, effective squared mass in an equation of motion for $b$-field fluctuations.Comment: version accepted for publication in Mod.Phys.Lett.

The anomalous chiral perturbation theory meson Lagrangian to order p6p^6 revisited

We present a revised and extended construction of the mesonic Lagrangian density in chiral perturbation theory (ChPT) at order $p^6$ in the anomalous (or epsilon) sector, ${\cal{L}}_{6,\epsilon}$. After improving several aspects of the strategy we used originally, i.e., a more efficient application of partial integration, the implementation of so-called Bianchi identities, and additional trace relations, we find the new monomial sets to include 24 $SU(N_f)$, 23 SU(3), and 5 SU(2) elements. Furthermore, we introduce 8 supplementary terms due to the extension of the chiral group to $SU(N_f)_L \times SU(N_f)_R \times U(1)_V$.Comment: 21 pages, Latex, using RevTe

Improved Error-Scaling for Adiabatic Quantum State Transfer

We present a technique that dramatically improves the accuracy of adiabatic state transfer for a broad class of realistic Hamiltonians. For some systems, the total error scaling can be quadratically reduced at a fixed maximum transfer rate. These improvements rely only on the judicious choice of the total evolution time. Our technique is error-robust, and hence applicable to existing experiments utilizing adiabatic passage. We give two examples as proofs-of-principle, showing quadratic error reductions for an adiabatic search algorithm and a tunable two-qubit quantum logic gate.Comment: 10 Pages, 4 figures. Comments are welcome. Version substantially revised to generalize results to cases where several derivatives of the Hamiltonian are zero on the boundar

Anomaly Cancellation in 2+1 dimensions in the presence of a domainwall mass

A Fermion in 2+1 dimensions, with a mass function which depends on one spatial coordinate and passes through a zero ( a domain wall mass), is considered. In this model, originally proposed by Callan and Harvey, the gauge variation of the effective gauge action mainly consists of two terms. One comes from the induced Chern-Simons term and the other from the chiral fermions, bound to the 1+1 dimensional wall, and they are expected to cancel each other. Though there exist arguments in favour of this, based on the possible forms of the effective action valid far from the wall and some facts about theories of chiral fermions in 1+1 dimensions, a complete calculation is lacking. In this paper we present an explicit calculation of this cancellation at one loop valid even close to the wall. We show that, integrating out the ``massive'' modes of the theory does produce the Chern-Simons term, as appreciated previously. In addition we show that it generates a term that softens the high energy behaviour of the 1+1 dimensional effective chiral theory thereby resolving an ambiguity present in a general 1+1 dimensional theory.Comment: 17 pages, LaTex file, CU-TP-61

Cardiovascular gene expression profiles of dioxin exposure in zebrafish embryos

Author Posting. © The Authors, 2005. This is the author's version of the work. It is posted here by permission of Society of Toxicology for personal use, not for redistribution. The definitive version was published in Toxicological Sciences 85 (2005): 683-693, doi:10.1093/toxsci/kfi116.2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD) is a widespread environmental contaminant that causes altered heart morphology, circulatory impairment, edema, hemorrhage, and early life stage mortality in fish. TCDD toxicity is largely dependent upon the aryl hydrocarbon receptor, but understanding of the molecular mechanism of cardiovascular embryotoxicity remains incomplete. In order to identify genes potentially involved in cardiovascular impacts, we constructed custom cDNA microarrays consisting of 4,896 zebrafish adult heart cDNA clones and over 200 genes with known developmental, toxicological, and housekeeping roles. Gene expression profiles were obtained for 3-day old zebrafish following early embryonic exposure to either 0.5 or 5.0 nM TCDD. 516 clones were significantly differentially expressed (p-value < 0.005) under at least one treatment condition; 123 high-priority clones were selected for further investigation. CYP1A, CYP1B1, and other members of the AHR gene battery, were strongly and dose-dependently induced by TCDD. Importantly, altered expression of cardiac sarcomere components, including cardiac troponin T2 and multiple myosin isoforms, was consistent with the hypothesis that TCDD causes dilated cardiomyopathy. Observed increases in expression levels of mitochondrial energy transfer genes also may be related to cardiomyopathy. Other TCDD-responsive genes included fatty acid and steroid metabolism enzymes, ribosomal and signal transduction proteins, and 18 ESTs with no known protein homologs. As the first broadscale study of TCDD-modulated gene expression in a non-mammalian system, this work provides an important perspective on mechanisms of TCDD toxicity.This work was supported by funding from the National Institutes of Health

A Hardy inequality in twisted waveguides

We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page

Spatial search by quantum walk

Grover's quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial dimensions can be searched in time of order sqrt(N) for d>2, and in time of order sqrt(N) poly(log N) for d=2. We consider an alternative search algorithm based on a continuous time quantum walk on a graph. The case of the complete graph gives the continuous time search algorithm of Farhi and Gutmann, and other previously known results can be used to show that sqrt(N) speedup can also be achieved on the hypercube. We show that full sqrt(N) speedup can be achieved on a d-dimensional periodic lattice for d>4. In d=4, the quantum walk search algorithm takes time of order sqrt(N) poly(log N), and in d<4, the algorithm does not provide substantial speedup.Comment: v2: 12 pages, 4 figures; published version, with improved arguments for the cases where the algorithm fail

The Continuum Limit and Integral Vacuum Charge

We investigate a commonly used formula which seems to give non-integral vacuum charge in the continuum limit. We show that the limit is subtle and care must be taken to get correct results.Comment: 5 pages. Submitted to JETP Letter

Gravitation Interaction and Electromagnetic Interaction in the Relativistic Universe with Total Zero and Local Non-Zero Energy

In the model of flat expansive homogeneous and isotropic relativistic universe with total zero and local non-zero energy the gravitation energy of bodies and the elecromagnetic energy of charged bodies can be localised.Comment: LaTeX, 10 pages, 1 figur

Unfrustrated Qudit Chains and their Ground States

We investigate chains of 'd' dimensional quantum spins (qudits) on a line with generic nearest neighbor interactions without translational invariance. We find the conditions under which these systems are not frustrated, i.e. when the ground states are also the common ground states of all the local terms in the Hamiltonians. The states of a quantum spin chain are naturally represented in the Matrix Product States (MPS) framework. Using imaginary time evolution in the MPS ansatz, we numerically investigate the range of parameters in which we expect the ground states to be highly entangled and find them hard to approximate using our MPS method.Comment: 5 pages, 5 figures. Typos correcte