On Chern-Simons theory with an inhomogeneous gauge group and BF theory knot invariants

We study the Chern-Simons topological quantum field theory with an inhomogeneous gauge group, a non-semi-simple group obtained from a semi-simple one by taking its semi-direct product with its Lie algebra. We find that the standard knot observables (i.e. traces of holonomies along knots) essentially vanish, but yet, the non-semi-simplicity of our gauge group allows us to consider a class of un-orthodox observables which breaks gauge invariance at one point and which lead to a non-trivial theory on long knots in $\mathbb{R}^3$. We have two main morals : 1. In the non-semi-simple case, there is more to observe in Chern-Simons theory! There might be other interesting non semi-simple gauge groups to study in this context beyond our example. 2. In our case of an inhomogeneous gauge group, we find that Chern-Simons theory with the un-orthodox observable is actually the same as 3D BF theory with the Cattaneo-Cotta-Ramusino-Martellini knot observable. This leads to a simplification of their results and enables us to generalize and solve a problem they posed regarding the relation between BF theory and the Alexander-Conway polynomial. Our result is that the most general knot invariant coming from pure BF topological quantum field theory is in the algebra generated by the coefficients of the Alexander-Conway polynomial.Comment: To appear in Journal of Mathematical Physics vol.46 issue 12. Available on http://link.aip.org/link/jmapaq/v46/i1

Cavity optomechanics with stoichiometric SiN films

We study high-stress SiN films for reaching the quantum regime with mesoscopic oscillators connected to a room-temperature thermal bath, for which there are stringent requirements on the oscillators' quality factors and frequencies. Our SiN films support mechanical modes with unprecedented products of mechanical quality factor $Q_m$ and frequency $\nu_m$ reaching $Q_{m} \nu_m \simeq2 \times 10^{13}$ Hz. The SiN membranes exhibit a low optical absorption characterized by Im$(n) \lesssim 10^{-5}$ at 935 nm, representing a 15 times reduction for SiN membranes. We have developed an apparatus to simultaneously cool the motion of multiple mechanical modes based on a short, high-finesse Fabry-Perot cavity and present initial cooling results along with future possibilities.Comment: 4 pages, 5 figure

Energy and Momentum densities of cosmological models, with equation of state ρ=μ\rho=\mu, in general relativity and teleparallel gravity

We calculated the energy and momentum densities of stiff fluid solutions, using Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum complexes, in both general relativity and teleparallel gravity. In our analysis we get different results comparing the aforementioned complexes with each other when calculated in the same gravitational theory, either this is in general relativity and teleparallel gravity. However, interestingly enough, each complex's value is the same either in general relativity or teleparallel gravity. Our results sustain that (i) general relativity or teleparallel gravity are equivalent theories (ii) different energy-momentum complexes do not provide the same energy and momentum densities neither in general relativity nor in teleparallel gravity. In the context of the theory of teleparallel gravity, the vector and axial-vector parts of the torsion are obtained. We show that the axial-vector torsion vanishes for the space-time under study.Comment: 15 pages, no figures, Minor typos corrected; version to appear in International Journal of Theoretical Physic

Energy and Momentum Distributions of Kantowski and Sachs Space-time

We use the Einstein, Bergmann-Thomson, Landau-Lifshitz and Papapetrou energy-momentum complexes to calculate the energy and momentum distributions of Kantowski and Sachs space-time. We show that the Einstein and Bergmann-Thomson definitions furnish a consistent result for the energy distribution, but the definition of Landau-Lifshitz do not agree with them. We show that a signature switch should affect about everything including energy distribution in the case of Einstein and Papapetrou prescriptions but not in Bergmann-Thomson and Landau-Lifshitz prescriptions.Comment: 12 page

CP violation and the 4th generation

Within the Standard model with the 4th generation quarks b' and t' we have analyzed CP-violating flavor changing neutral current processes t -> cX; b'-> sX, b'-> bX,t'-> cX, and t'-> tX, with X=Z,H,gamma,g, by constructing and employing global, unique fit for the 4th generation mass mixing matrix CKM4 at 300 < m_t' < 700 GeV. All quantities appearing in the CKM4 were subject to our fitting procedure. We have found that our fit produces the following CP partial rate asymmetry dominance: a_CP(b'-> s(Z,H,gamma,g))= (90,73,52,30)%, at m_t' ~ 300,300,380,400 GeV, respectively. From the experimental point of view the best decay mode, out of the above four, is certainly b'-> s gamma, because of the presence of a clean high energy single final state photon. We have also obtained relatively large a_CP(t -> c g) ~ 15 (10)% for t' running in the loops with the mass m_t'= 650(500) GeV. There are fair chances that the 4th generation quarks will be discovered at Tevatron or LHC and that some of their decay rates shall be measured. If b' and t' exist at energies we assumed, with well executed tagging, large a_CP could be found too.Comment: 19 pages, 12 figures, some of them new, references added, minor corrections in the text, version to appear in PR

Energy Distribution of a Stringy Charged Black Hole

The energy distribution associated with a stringy charged black hole is studied using M{\o}ller's energy-momentum complex. Our result is reasonable and it differs from that known in literature using Einstein's energy-momentum complex.Comment: Latex, no figure

An extension to the Navier-Stokes equations to incorporate gas molecular collisions with boundaries

We investigate a model for micro-gas-flows consisting of the Navier-Stokes equations extended to include a description of molecular collisions with solid boundaries, together with first and second order velocity slip boundary conditions. By considering molecular collisions affected by boundaries in gas flows we capture some of the near-wall affects that the conventional Navier-Stokes equations with a linear stress/strain-rate relationship are unable to describe. Our model is expressed through a geometry-dependent mean-free-path yielding a new viscosity expression, which makes the stress/strain-rate constitutive relationship non-linear. Test cases consisting of Couette and Poiseuille flows are solved using these extended Navier-Stokes equations, and we compare the resulting velocity profiles with conventional Navier-Stokes solutions and those from the BGK kinetic model. The Poiseuille mass flow-rate results are compared with results from the BGK-model and experimental data, for various degrees of rarefaction. We assess the range of applicability of our model and show that it can extend the applicability of conventional fluid dynamic techniques into the early continuum-transition regime. We also discuss the limitations of our model due to its various physical assumptions, and we outline ideas for further development

Self-consistent treatment of the self-energy in nuclear matter

The influence of hole-hole propagation in addition to the conventional particle-particle propagation, on the energy per nucleon and the momentum distribution is investigated. The results are compared to the Brueckner-Hartree-Fock (BHF) calculations with a continuous choice and conventional choice for the single-particle spectrum. The Bethe-Goldstone equation has been solved using realistic $NN$ interactions. Also, the structure of nucleon self-energy in nuclear matter is evaluated. All the self-energies are calculated self-consistently. Starting from the BHF approximation without the usual angle-average approximation, the effects of hole-hole contributions and a self-consistent treatment within the framework of the Green function approach are investigated. Using the self-consistent self-energy, the hole and particle self-consistent spectral functions including the particle-particle and hole-hole ladder contributions in nuclear matter are calculated using realistic $NN$ interactions. We found that, the difference in binding energy between both results, i.e. BHF and self-consistent Green function, is not large. This explains why is the BHF ignored the 2h1p contribution.Comment: Preprint 20 pages including 15 figures and one tabl

Enhancement of the superconducting transition temperature in La2-xSrxCuO4 bilayers: Role of pairing and phase stiffness

The superconducting transition temperature, Tc, of bilayers comprising underdoped La2-xSrxCuO4 films capped by a thin heavily overdoped metallic La1.65Sr0.35CuO4 layer, is found to increase with respect to Tc of the bare underdoped films. The highest Tc is achieved for x = 0.12, close to the 'anomalous' 1/8 doping level, and exceeds that of the optimally-doped bare film. Our data suggest that the enhanced superconductivity is confined to the interface between the layers. We attribute the effect to a combination of the high pairing scale in the underdoped layer with an enhanced phase stiffness induced by the overdoped film.Comment: Published versio