Thermalization, Viscosity and the Averaged Null Energy Condition

We explore the implications of the averaged null energy condition for thermal states of relativistic quantum field theories. A key property of such thermal states is the thermalization length. This lengthscale generalizes the notion of a mean free path beyond weak coupling, and allows finite size regions to independently thermalize. Using the eigenstate thermalization hypothesis, we show that thermal fluctuations in finite size `fireballs' can produce states that violate the averaged null energy condition if the thermalization length is too short or if the shear viscosity is too large. These bounds become very weak with a large number N of degrees of freedom but can constrain real-world systems, such as the quark-gluon plasma.Comment: 28 pages, 3 figure

Rational approximation and arithmetic progressions

A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a metrical and a non-metrical point of view and, on the other hand, from an asymptotic and also a uniform point of view. The principal novelty is a Khintchine type theorem for uniform approximation in this context. Some applications of this theory are also discussed

Evaluation of performance impairment by spacecraft contaminants

The environmental contaminants (isolated as off-gases in Skylab and Apollo missions) were evaluated. Specifically, six contaminants were evaluated for their effects on the behavior of juvenile baboons. The concentrations of contaminants were determined through preliminary range-finding studies with laboratory rats. The contaminants evaluated were acetone, methyl ethyl ketone (MEK), methyl isobutyl ketone (MIBK), trichloroethylene (TCE), heptane and Freon 21. When the studies of the individual gases were completed, the baboons were also exposed to a mixture of MEK and TCE. The data obtained revealed alterations in the behavior of baboons exposed to relatively low levels of the contaminants. These findings were presented at the First International Symposium on Voluntary Inhalation of Industrial Solvents in Mexico City, June 21-24, 1976. A preprint of the proceedings is included

Microscale application of column theory for high resolution force and displacement sensing

We present the design, fabrication and experimental validation of a novel device that exploits the amplification of displacement and attenuation of structural stiffness in the post-buckling deformation of slender columns to obtain pico-Newton force and nanometer displacement resolution even under an optical microscope. The extremely small size, purely mechanical sensing scheme and vacuum compatibility of the instrument makes it compatible with existing visualization tools of nanotechnology. The instrument has a wide variety of potential applications ranging from electro-mechanical characterization of one dimensional solids to single biological cells

Extending Romanovski polynomials in quantum mechanics

Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally-extended Scarf II and Rosen-Morse I potentials, are considered. For the former potentials, the generalized polynomials satisfy a finite orthogonality relation, while for the latter an infinite set of relations among polynomials with degree-dependent parameters is obtained. Both types of relations are counterparts of those known for conventional polynomials. In the absence of any direct information on the zeros of the Romanovski polynomials present in denominators, the regularity of the constructed potentials is checked by taking advantage of the disconjugacy properties of second-order differential equations of Schr\"odinger type. It is also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to Rosen-Morse I potentials, the variety of rational extensions is narrowed down from types I, II, and III to type III only.Comment: 25 pages, no figure, small changes, 3 additional references, published versio

On problem of polarization tomography, I

The polarization tomography problem consists of recovering a matrix function f from the fundamental matrix of the equation $D\eta/dt=\pi_{\dot\gamma}f\eta$ known for every geodesic $\gamma$ of a given Riemannian metric. Here $\pi_{\dot\gamma}$ is the orthogonal projection onto the hyperplan $\dot\gamma^{\perp}$. The problem arises in optical tomography of slightly anisotropic media. The local uniqueness theorem is proved: a $C^1$- small function f can be recovered from the data uniquely up to a natural obstruction. A partial global result is obtained in the case of the Euclidean metric on $R^3$

New derivation for the equations of motion for particles in electromagnetism

We present equations of motion for charged particles using balanced equations, and without introducing explicitly divergent quantities. This derivation contains as particular cases some well known equations of motion, as the Lorentz-Dirac equations. An study of our main equations in terms of order of the interaction with the external field conduces us to the Landau-Lifshitz equations. We find that the analysis in second order show a special behavior. We give an explicit presentation up to third order of our main equations, and expressions for the calculation of general orders.Comment: 11 pages, 2 figures. Minor changes. Closer to published versio

On the CFT duals for near-extremal black holes

We consider Kerr-Newman-AdS-dS black holes near extremality and work out the near-horizon geometry of these near-extremal black holes. We identify the exact U(1)_L x U(1)_R isometries of the near-horizon geometry and provide boundary conditions enhancing them to a pair of commuting Virasoro algebras. The conserved charges of the corresponding asymptotic symmetries are found to be well defined and non-vanishing and to yield central charges c_L\neq0 and c_R=0. The Cardy formula subsequently reproduces the Bekenstein-Hawking entropy of the black hole. This suggests that the near-extremal Kerr-Newman-AdS-dS black hole is holographically dual to a non-chiral two-dimensional conformal field theory.Comment: 11 page

Transition Probabilities Of Astrophysical Interest In The Niobium Ions Nb+ And Nb2+

Aims. We attempt to derive accurate transition probabilities for astrophysically interesting spectral lines of Nb II and Nb III and determine the niobium abundance in the Sun and metal-poor stars rich in neutron-capture elements. Methods. We used the time-resolved laser-induced fluorescence technique to measure radiative lifetimes in Nb II. Branching fractions were measured from spectra recorded using Fourier transform spectroscopy. The radiative lifetimes and the branching fractions were combined yielding transition probabilities. In addition, we calculated lifetimes and transition probablities in Nb II and Nb III using a relativistic Hartree-Fock method that includes core polarization. Abundances of the sun and five metal-poor stars were derived using synthetic spectra calculated with the MOOG code, including hyperfine broadening of the lines. Results. We present laboratory measurements of 17 radiative lifetimes in Nb II. By combining these lifetimes with branching fractions for lines depopulating the levels, we derive the transition probabilities of 107 Nb II lines from 4d(3)5p configuration in the wavelength region 2240-4700 angstrom. For the first time, we present theoretical transition probabilities of 76 Nb III transitions with wavelengths in the range 1430-3140 angstrom. The derived solar photospheric niobium abundance log epsilon(circle dot) = 1.44 +/- 0.06 is in agreement with the meteoritic value. The stellar Nb/Eu abundance ratio determined for five metal-poor stars confirms that the r-process is a dominant production method for the n-capture elements in these stars.Integrated Initiative of Infrastructure RII3-CT-2003-506350Swedish Research CouncilKnut and Alice Wallenberg FoundationBelgian FRS-FNRSFRIAUS National Science Foundation AST-0607708, AST-0908978Astronom