An entropy based proof of the Moore bound for irregular graphs

We provide proofs of the following theorems by considering the entropy of random walks: Theorem 1.(Alon, Hoory and Linial) Let G be an undirected simple graph with n vertices, girth g, minimum degree at least 2 and average degree d: Odd girth: If g=2r+1,then n \geq 1 + d*(\Sum_{i=0}^{r-1}(d-1)^i) Even girth: If g=2r,then n \geq 2*(\Sum_{i=0}^{r-1} (d-1)^i) Theorem 2.(Hoory) Let G = (V_L,V_R,E) be a bipartite graph of girth g = 2r, with n_L = |V_L| and n_R = |V_R|, minimum degree at least 2 and the left and right average degrees d_L and d_R. Then, n_L \geq \Sum_{i=0}^{r-1}(d_R-1)^{i/2}(d_L-1)^{i/2} n_R \geq \Sum_{i=0}^{r-1}(d_L-1)^{i/2}(d_R-1)^{i/2}Comment: 6 page

The Quantum Complexity of Set Membership

We study the quantum complexity of the static set membership problem: given a subset S (|S| \leq n) of a universe of size m (m \gg n), store it as a table of bits so that queries of the form `Is x \in S?' can be answered. The goal is to use a small table and yet answer queries using few bitprobes. This problem was considered recently by Buhrman, Miltersen, Radhakrishnan and Venkatesh, where lower and upper bounds were shown for this problem in the classical deterministic and randomized models. In this paper, we formulate this problem in the "quantum bitprobe model" and show tradeoff results between space and time.In this model, the storage scheme is classical but the query scheme is quantum.We show, roughly speaking, that similar lower bounds hold in the quantum model as in the classical model, which imply that the classical upper bounds are more or less tight even in the quantum case. Our lower bounds are proved using linear algebraic techniques.Comment: 19 pages, a preliminary version appeared in FOCS 2000. This is the journal version, which will appear in Algorithmica (Special issue on Quantum Computation and Quantum Cryptography). This version corrects some bugs in the parameters of some theorem

Surface structure of Quark stars with magnetic fields

We investigate the impact of magnetic fields on the electron distribution in the electrosphere of quark stars. For moderately strong magnetic fields $B\sim 10^{13}$G, quantization effects are generally weak due to the large number density of electrons at surface, but can nevertheless affect the spectral features of quark stars. We outline the main observational characteristics of quark stars as determined by their surface emission, and briefly discuss their formation in explosive events termed Quark-Novae, which may be connected to the $r$-process.Comment: 9 pages, 3 figures. Contribution to the proceedings of the IXth Workshop on High Energy Physics Phenomenology (WHEPP-9), Bhubaneswar, India, 3-14 Jan. 200

Quark Matter in Neutron Stars: An apercu

The existence of deconfined quark matter in the superdense interior of neutron stars is a key question that has drawn considerable attention over the past few decades. Quark matter can comprise an arbitrary fraction of the star, from 0 for a pure neutron star to 1 for a pure quark star, depending on the equation of state of matter at high density. From an astrophysical viewpoint, these two extreme cases are generally expected to manifest different observational signatures. An intermediate fraction implies a hybrid star, where the interior consists of mixed or homogeneous phases of quark and nuclear matter, depending on surface and Coulomb energy costs, as well as other finite size and screening effects. In this brief review article, we discuss what we can deduce about quark matter in neutron stars in light of recent exciting developments in neutron star observations. We state the theoretical ideas underlying the equation of state of dense quark matter, including color superconducting quark matter. We also highlight recent advances stemming from re-examination of an old paradigm for the surface structure of quark stars and discuss possible evolutionary scenarios from neutron stars to quark stars, with emphasis on astrophysical observations.Comment: 15 pages, 1 figure. Invited review for Modern Physics Letters

Constraining phases of quark matter with studies of r-mode damping in neutron stars

The r-mode instability in rotating compact stars is used to constrain the phase of matter at high density. The color-flavor-locked phase with kaon condensation (CFL-K0) and without (CFL) is considered in the temperature range 10^8K < T <10^{11} K. While the bulk viscosity in either phase is only effective at damping the r-mode at temperatures T > 10^{11} K, the shear viscosity in the CFL-K0 phase is the only effective damping agent all the way down to temperatures T > 10^8 K characteristic of cooling neutron stars. However, it cannot keep the star from becoming unstable to gravitational wave emission for rotation frequencies f ~ 56-11 Hz at T ~ 10^8-10^9 K. Stars composed almost entirely of CFL or CFL-K0 matter are ruled out by observation of rapidly rotating neutron stars, indicating that dissipation at the quark-hadron interface or nuclear crust interface must play a key role in damping the instability.Comment: 8 pages, 2 figure

Scalar-isoscalar excitation in dense quark matter

We study the spectrum of scalar-isoscalar excitations in the color-flavor locked phase of dense quark matter. The sigma meson in this phase appears as a four-quark state (of diquark and anti-diquark) with a well-defined mass and extremely small width, as a consequence of it's small coupling to two pions. The quark particle/hole degrees of freedom also contribute significantly to the correlator just above the threshold 2\Delta where \Delta is the superconducting gap.Comment: RevTeX, 11 pages, 4 fig

Neutrino emission in neutron matter from magnetic moment interactions

Neutrino emission drives neutron star cooling for the first several hundreds of years after its birth. Given the low energy ($\sim$ keV) nature of this process, one expects very few nonstandard particle physics contributions which could affect this rate. Requiring that any new physics contributions involve light degrees of freedom, one of the likely candidates which can affect the cooling process would be a nonzero magnetic moment for the neutrino. To illustrate, we compute the emission rate for neutrino pair bremsstrahlung in neutron-neutron scattering through photon-neutrino magnetic moment coupling. We also present analogous differential rates for neutrino scattering off nucleons and electrons that determine neutrino opacities in supernovae. Employing current upper bounds from collider experiments on the tau magnetic moment, we find that the neutrino emission rate can exceed the rate through neutral current electroweak interaction by a factor two, signalling the importance of new particle physics input to a standard calculation of relevance to neutron star cooling. However, astrophysical bounds on the neutrino magnetic moment imply smaller effects.Comment: 9 pages, 1 figur

Angiotensin-Converting Enzyme Gene Polymorphism in Patients with Coronary Artery Disease

Several genetic investigations have been attempted to elucidate the association of gene polymorphism of angiotensin-converting enzyme (ACE) in coronary artery disease. This study was conducted to investigate the role of gene polymorphism of ACE in patients with coronary artery disease. The study included fifty-six numbers of patients with atherosclerotic coronary artery disease where proven angiographically and fifty-six numbers of healthy individuals of sex matched as a control group. The patients and control group were subjected to routine investigations, assays like, serum cholesterol, triglycerides, high-density Lipoprotein-cholesterol (HDL-C), low-density lipoprotein-cholesterol (LDL-C). Genomic DNA was extracted and analyzed for angiotensin-converting enzyme insertion/deletion polymorphism using polymerase chain reaction (PCR). When we compared the genotypes of patients with coronary artery disease and controls, it was observed that all three genotypes were not statistically different also no significant difference of alleles in ACE gene genotypes was found. Inpatient serum cholesterol, triglyceride and HDL-C (P &lt;0.001, P &lt;0.001 and P &lt;0.001: respectively) showed a significant increase than the control group. In patients, LDL-C level was not more significant than controls. In the evaluated population, we conclude that the gene I/D polymorphism for ACE are not risk associated and may not be a useful marker for coronary artery disease

Thermal Photons in Strong Interactions

A brief survey is given on the current status of evaluating thermal production of photons from a strongly interacting medium. Emphasis is put on recent progress in assessing equilibrium emission rates in both hadronic and quark-gluon matter. We also give an update on the status of comparing theoretical calculations with experimental data from heavy-ion collisions at the SPS, as well as prospects for RHIC. Finally, applications of photon rate calculations to colorsuperconducting quark matter are discussed.Comment: Brief Review for Mod. Phys. Lett A, 15 pages latex incl. 12 ps/eps figs and style file ws-mpla.cl