Quantum Entanglement in Second-quantized Condensed Matter Systems

The entanglement between occupation-numbers of different single particle basis states depends on coupling between different single particle basis states in the second-quantized Hamiltonian. Thus in principle, interaction is not necessary for occupation-number entanglement to appear. However, in order to characterize quantum correlation caused by interaction, we use the eigenstates of the single-particle Hamiltonian as the single particle basis upon which the occupation-number entanglement is defined. Using the proper single particle basis, we discuss occupation-number entanglement in important eigenstates, especially ground states, of systems of many identical particles. The discussions on Fermi systems start with Fermi gas, Hatree-Fock approximation, and the electron-hole entanglement in excitations. The entanglement in a quantum Hall state is quantified as -fln f-(1-f)ln(1-f), where f is the proper fractional part of the filling factor. For BCS superconductivity, the entanglement is a function of the relative momentum wavefunction of the Cooper pair, and is thus directly related to the superconducting energy gap. For a spinless Bose system, entanglement does not appear in the Hatree-Gross-Pitaevskii approximation, but becomes important in the Bogoliubov theory.Comment: 11 pages. Journal versio

Istraživanja 3,4-diaril-1,2,5-oksadiazola i njihovih N-oksida: Potraga za boljim COX-2 inhibitorima

A series of 3,4-diaryl-1,2,5-oxadiazoles and 3,4-diaryl-1,2,5-oxadiazole N-oxides were prepared and evaluated for COX-2 and COX-1 binding affinity in vitro and for anti-inflammatory activity by the rat paw edema method. p-Methoxy (p-OMe) substituted compounds 9, 21, 34, 41, 42 showed COX-2 enzyme inhibition higher than that showed by compounds with other substituents. 3,4-Di(4-methoxyphenyl)-1,2,5-oxadiazole N-oxide (42) showed COX-2 enzyme inhibition of 54% at 22 µmol L-1 and COX-1 enzyme inhibition of 44% at 88 µmol L-1 concentrations, but showed very low in vivo anti-inflammatory activity. Its deoxygenated derivative (21) showed lower COX-2 enzyme inhibition (26% at 22 µmol L-1) and higher COX-1 enzyme inhibition (53% at 88 µmol L-1) but marked in vivo anti-inflammatory activity (71% at 25 mg kg-1) vs. celecoxib (48% at 12.5 mg kg-1). Molecular modeling (docking) studies showed that the methoxy group is positioned in the vicinity of the COX-2 secondary pocket and it also participates in hydrogen bonding interactions in the COX-2 active site. These preliminary studies suggest that the p-methoxy (p-OMe) group in one of benzene rings may give potentially active leads in this series of oxadiazole/N-oxides.Sintetizirana je serija 3,4-diaril-1,2,5-oksadiazola i 3,4-diaril-1,2,5-oksadiazol N-oksida i ocijenjena njihova sposobnost vezivanja na COX-2 i COX-1 in vitro i protuupalno djelovanje na edem šape štakora. Spojevi sa p-metoksi (p-OMe) supstituentom 9, 21, 34, 41, 42 bolje su inhibirali COX-2 nego ostali spojevi. 3,4-Di(4-metoksifenil)-1,2,5-oksadiazol N-oksid (42) inhibirao je COX-2 za 54% u koncentraciji od 22 µmol L-1, a COX-1 za 44% u koncentraciji 88 µmol L-1, ali je in vivo slabo djelovao protuupalno. Njegov deoksigenirani derivat 21 pokazao je slabiju inhibiciju COX-2 enzima (26% u koncentraciji 22 µmol L-1) i jaču inhibiciju COX-1 (71% u koncentraciji 25 mg kg-1) što je bolje od standarda celekoksiba (48% u koncentraciji 12,5 mg kg-1). Molekularno je modeliranje pokazalo da je metoksi skupina smještena u blizini sekundarnog džepa na enzimu COX-2 i da utječe na vodikove veze interakcija na aktivnom mjestu COX-2. Ova preliminarna istraživanja sugeriraju da bi se u seriji oksadiazol/N-oksida mogao naći predvodni spoj s p-metoksi skupinom na benzenskom prstenu

New varying speed of light theories

We review recent work on the possibility of a varying speed of light (VSL). We start by discussing the physical meaning of a varying $c$, dispelling the myth that the constancy of $c$ is a matter of logical consistency. We then summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz invariance; bimetric theories (where the speeds of gravity and light are not the same); locally Lorentz invariant VSL theories; theories exhibiting a color dependent speed of light; varying $c$ induced by extra dimensions (e.g. in the brane-world scenario); and field theories where VSL results from vacuum polarization or CPT violation. We show how VSL scenarios may solve the cosmological problems usually tackled by inflation, and also how they may produce a scale-invariant spectrum of Gaussian fluctuations, capable of explaining the WMAP data. We then review the connection between VSL and theories of quantum gravity, showing how ``doubly special'' relativity has emerged as a VSL effective model of quantum space-time, with observational implications for ultra high energy cosmic rays and gamma ray bursts. Some recent work on the physics of ``black'' holes and other compact objects in VSL theories is also described, highlighting phenomena associated with spatial (as opposed to temporal) variations in $c$. Finally we describe the observational status of the theory. The evidence is currently slim -- redshift dependence in the atomic fine structure, anomalies with ultra high energy cosmic rays, and (to a much lesser extent) the acceleration of the universe and the WMAP data. The constraints (e.g. those arising from nucleosynthesis or geological bounds) are tight, but not insurmountable. We conclude with the observational predictions of the theory, and the prospects for its refutation or vindication.Comment: Final versio