Axiomatization of Inconsistency Indicators for Pairwise Comparisons

This study proposes revised axioms for defining inconsistency indicators in pairwise comparisons. It is based on the new findings that "PC submatrix cannot have a worse inconsistency indicator than the PC matrix containing it" and that there must be a PC submatrix with the same inconsistency as the given PC matrix. This study also provides better reasoning for the need of normalization. It is a revision of axiomatization by Koczkodaj and Szwarc, 2014 which proposed axioms expressed informally with some deficiencies addressed in this study.Comment: This paper should have been withdrawn by the first author a long time ago. The work has been finished with another researcher, I have been pushed out the projec

Microscopic observations of X-ray and gamma-ray induced decomposition of ammonium perchlorate crystals

The X-ray and gamma-ray induced decomposition of ammonium perchlorate was studied by optical, transmission, and scanning electron microscopy. This material is a commonly used oxidizer in solid propellents which could be employed in deep-space probes, and where they will be subjected to a variety of radiations for as long as ten years. In some respects the radiation-induced damage closely resembles the effects produced by thermal decomposition, but in other respects the results differ markedly. Similar radiation and thermal effects include the following: (1) irregular or ill-defined circular etch pits are formed in both cases; (2) approximately the same size pits are produced; (3) the pit density is similar; (4) the c face is considerably more reactive than the m face; and (5) most importantly, many of the etch pits are aligned in crystallographic directions which are the same for thermal or radiolytic decomposition. Thus, dislocations play an important role in the radiolytic decomposition process

Dimensional enhancement of kinetic energies

Simple thermodynamics considers kinetic energy to be an extensive variable which is proportional to the number, N, of particles. We present a quantum state of N non-interacting particles for which the kinetic energy increases quadratically with N. This enhancement effect is tied to the quantum centrifugal potential whose strength is quadratic in the number of dimensions of configuration space.Comment: 9 pages, accepted by Phys. Rev.

Probability of Reflection by a Random Laser

A theory is presented (and supported by numerical simulations) for phase-coherent reflection of light by a disordered medium which either absorbs or amplifies radiation. The distribution of reflection eigenvalues is shown to be the Laguerre ensemble of random-matrix theory. The statistical fluctuations of the albedo (the ratio of reflected and incident power) are computed for arbitrary ratio of sample thickness, mean free path, and absorption or amplification length. On approaching the laser threshold all moments of the distribution of the albedo diverge. Its modal value remains finite, however, and acquires an anomalous dependence on the illuminated surface area.Comment: 8 pages (revtex), 3 figures, to appear in Phys.Rev.Let

The origin of phase in the interference of Bose-Einstein condensates

We consider the interference of two overlapping ideal Bose-Einstein condensates. The usual description of this phenomenon involves the introduction of a so-called condensate wave functions having a definite phase. We investigate the origin of this phase and the theoretical basis of treating interference. It is possible to construct a phase state, for which the particle number is uncertain, but phase is known. However, how one would prepare such a state before an experiment is not obvious. We show that a phase can also arise from experiments using condensates in Fock states, that is, having known particle numbers. Analysis of measurements in such states also gives us a prescription for preparing phase states. The connection of this procedure to questions of ``spontaneously broken gauge symmetry'' and to ``hidden variables'' is mentioned.Comment: 22 pages 4 figure

Stochastic mean-field dynamics for fermions in the weak coupling limit

Assuming that the effect of the residual interaction beyond mean-field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of Markovian quantum jump are presented. A simplified scenario for the introduction of fluctuations beyond mean-field is first presented. In this theory, part of the quantum correlations between the residual interaction and the one-body density matrix are neglected and jumps occur between many-body densities formed of pairs of states $D=| \Phi_a > < \Phi_b |/$ where $| \Phi_a >$ and $| \Phi_b >$ are antisymmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical $^{40}$Ca nucleus under the influence of a statistical ensemble of two-body contact interaction. This framework is however too simplistic to account for both fluctuation and dissipation. In the second part of this work, an alternative quantum jump method is obtained without making the approximation on quantum correlations. Restricting to two particles-two holes residual interaction, the evolution of the one-body density matrix of a correlated system is transformed into a Lindblad equation. The associated dissipative dynamics can be simulated by quantum jumps between densities written as $D = | \Phi >$ is a normalized Slater determinant. The associated stochastic Schroedinger equation for single-particle wave-functions is given.Comment: Enlarged version, 10 pages, 2 figure

Magneto-Acoustic Spectroscopy in Superfluid 3He-B

We have used the recently discovered acoustic Faraday effect in superfluid 3He to perform high resolution spectroscopy of an excited state of the superfluid condensate. With acoustic cavity interferometry we measure the rotation of the plane of polarization of a transverse sound wave propagating in the direction of magnetic field from which we determine the Zeeman energy of the excited state. We interpret the Lande g-factor, combined with the zero-field energies of the state, using the theory of Sauls and Serene to calculate the strength of f -wave interactions in 3He.Comment: 4 pages, 5 figures, submitted to PRL, Aug 30th, 200

Disproportionation Transition at Critical Interaction Strength: Na1/2_{1/2}CoO2_2

Charge disproportionation (CD) and spin differentiation in Na$_{1/2}$CoO$_2$ are studied using the correlated band theory approach. The simultaneous CD and gap opening seen previously is followed through a first order charge disproportionation transition 2Co$^{3.5+} \to$ Co$^{3+}$+Co$^{4+}$, whose ionic identities are connected more closely to spin (S=0, S=1/2 respectively) than to real charge. Disproportionation in the Co $a_g$ orbital is compensated by opposing charge rearrangement in other 3d orbitals. At the transition large and opposing discontinuities in the (all-electron) kinetic and potential energies are slightly more than balanced by a gain in correlation energy. The CD state is compared to characteristics of the observed charge-ordered insulating phase in Na$_{1/2}$CoO$_2$, suggesting the Coulomb repulsion value $U$ is concentration-dependent, with $U(x=1/2)\simeq$3.5 eV.Comment: 4 pages and 4 embedded figure

Quantum-mechanical communication theory

Optimum signal reception using quantum-mechanical communication theor