Active Mass Under Pressure

After a historical introduction to Poisson's equation for Newtonian gravity, its analog for static gravitational fields in Einstein's theory is reviewed. It appears that the pressure contribution to the active mass density in Einstein's theory might also be noticeable at the Newtonian level. A form of its surprising appearance, first noticed by Richard Chase Tolman, was discussed half a century ago in the Hamburg Relativity Seminar and is resolved here.Comment: 28 pages, 4 figure

Testing Hawking particle creation by black holes through correlation measurements

Hawking's prediction of thermal radiation by black holes has been shown by Unruh to be expected also in condensed matter systems. We show here that in a black hole-like configuration realised in a BEC this particle creation does indeed take place and can be unambiguously identified via a characteristic pattern in the density-density correlations. This opens the concrete possibility of the experimental verification of this effect.Comment: 13 pages, 2 figures. Honorable mention in the 2010 GRF Essay Competitio

Hierarchy of Conservation Laws of Diffusion--Convection Equations

We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such systems. We also revise the notion of linear dependence of conservation laws and define the notion of local dependence of potentials. To construct conservation laws, we develop and apply the most direct method which is effective to use in the case of two independent variables. Admitting possibility of dependence of conserved vectors on a number of potentials, we generalize the iteration procedure proposed by Bluman and Doran-Wu for finding nonlocal (potential) conservation laws. As an example, we completely classify potential conservation laws (including arbitrary order local ones) of diffusion--convection equations with respect to the equivalence group and construct an exhaustive list of locally inequivalent potential systems corresponding to these equations.Comment: 24 page

Mn local moments prevent superconductivity in iron-pnictides Ba(Fe 1-x Mn x)2As2

75As nuclear magnetic resonance (NMR) experiments were performed on Ba(Fe1-xMnx)2As2 (xMn = 2.5%, 5% and 12%) single crystals. The Fe layer magnetic susceptibility far from Mn atoms is probed by the75As NMR line shift and is found similar to that of BaFe2As2, implying that Mn does not induce charge doping. A satellite line associated with the Mn nearest neighbours (n.n.) of 75As displays a Curie-Weiss shift which demonstrates that Mn carries a local magnetic moment. This is confirmed by the main line broadening typical of a RKKY-like Mn-induced staggered spin polarization. The Mn moment is due to the localization of the additional Mn hole. These findings explain why Mn does not induce superconductivity in the pnictides contrary to other dopants such as Co, Ni, Ru or K.Comment: 6 pages, 7 figure

Two hard spheres in a pore: Exact Statistical Mechanics for different shaped cavities

The Partition function of two Hard Spheres in a Hard Wall Pore is studied appealing to a graph representation. The exact evaluation of the canonical partition function, and the one-body distribution function, in three different shaped pores are achieved. The analyzed simple geometries are the cuboidal, cylindrical and ellipsoidal cavities. Results have been compared with two previously studied geometries, the spherical pore and the spherical pore with a hard core. The search of common features in the analytic structure of the partition functions in terms of their length parameters and their volumes, surface area, edges length and curvatures is addressed too. A general framework for the exact thermodynamic analysis of systems with few and many particles in terms of a set of thermodynamic measures is discussed. We found that an exact thermodynamic description is feasible based in the adoption of an adequate set of measures and the search of the free energy dependence on the adopted measure set. A relation similar to the Laplace equation for the fluid-vapor interface is obtained which express the equilibrium between magnitudes that in extended systems are intensive variables. This exact description is applied to study the thermodynamic behavior of the two Hard Spheres in a Hard Wall Pore for the analyzed different geometries. We obtain analytically the external work, the pressure on the wall, the pressure in the homogeneous zone, the wall-fluid surface tension, the line tension and other similar properties

On the Geometry of Surface Stress

We present a fully general derivation of the Laplace--Young formula and discuss the interplay between the intrinsic surface geometry and the extrinsic one ensuing from the immersion of the surface in the ordinary euclidean three-dimensional space. We prove that the (reversible) work done in a general surface deformation can be expressed in terms of the surface stress tensor and the variation of the intrinsic surface metric

A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram

Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories

We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus system by considering a planar secular model, that can be regarded as a major refinement of the approach first introduced by Lagrange. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a solution that is invariant up to order two in the masses; therefore, we investigate the stability of the secular system for rather small values of the eccentricities. First, we explicitly construct a Kolmogorov normal form, so as to find an invariant KAM torus which approximates very well the secular orbits. Finally, we adapt the approach that is at basis of the analytic part of the Nekhoroshev's theorem, so as to show that there is a neighborhood of that torus for which the estimated stability time is larger than the lifetime of the Solar System. The size of such a neighborhood, compared with the uncertainties of the astronomical observations, is about ten times smaller.Comment: 31 pages, 2 figures. arXiv admin note: text overlap with arXiv:1010.260

The Measure Problem in Cosmology

The Hamiltonian structure of general relativity provides a natural canonical measure on the space of all classical universes, i.e., the multiverse. We review this construction and show how one can visualize the measure in terms of a "magnetic flux" of solutions through phase space. Previous studies identified a divergence in the measure, which we observe to be due to the dilatation invariance of flat FRW universes. We show that the divergence is removed if we identify universes which are so flat they cannot be observationally distinguished. The resulting measure is independent of time and of the choice of coordinates on the space of fields. We further show that, for some quantities of interest, the measure is very insensitive to the details of how the identification is made. One such quantity is the probability of inflation in simple scalar field models. We find that, according to our implementation of the canonical measure, the probability for N e-folds of inflation in single-field, slow-roll models is suppressed by of order exp(-3N) and we discuss the implications of this result.Comment: 22 pages, 6 figures. Revised version with clarifying remarks on meaning of adopted measure, extra references and minor typographical correction

Crossover from commensurate to incommensurate antiferromagnetism in stoichiometric NaFeAs revealed by single-crystal 23Na,75As-NMR experiments

We report results of 23Na and 75As nuclear magnetic resonance (NMR) experiments on a self-flux grown high-quality single crystal of stoichiometric NaFeAs. The NMR spectra revealed a tetragonal to twinned-orthorhombic structural phase transition at T_O = 57 K and an antiferromagnetic (AF) transition at T_AF = 45 K. The divergent behavior of nuclear relaxation rate near T_AF shows significant anisotropy, indicating that the critical slowing down of stripe-type AF fluctuations are strongly anisotropic in spin space. The NMR spectra at low enough temperatures consist of sharp peaks showing a commensurate stripe AF order with a small moment \sim 0.3 muB. However, the spectra just below T_AF exhibits highly asymmetric broadening pointing to an incommensurate modulation. The commensurate-incommensurate crossover in NaFeAs shows a certain similarity to the behavior of SrFe2As2 under high pressure.Comment: 5 pages, 5 figures, revised version to appear in J. Phys. Soc. Jp