A model for the condensation of a dusty plasma

A model for the condensation of a dusty plasma is constructed by considering the spherical shielding layers surrounding a dust grain test particle. The collisionless region less than a collision mean free path from the test particle is shown to separate into three concentric layers, each having distinct physics. The method of matched asymptotic expansions is invoked at the interfaces between these layers and provides equations which determine the radii of the interfaces. Despite being much smaller than the Wigner-Seitz radius, the dust Debye length is found to be physically significant because it gives the scale length of a precipitous cut-off of the shielded electrostatic potential at the interface between the second and third layers. Condensation is predicted to occur when the ratio of this cut-off radius to the Wigner-Seitz radius exceeds unity and this prediction is shown to be in good agreement with experiments.Comment: 29 pages, 4 figures, 1 table, to appear in Physics of Plasmas. Manuscript revised on May 1, 2004 to take into account accuracy of Mie scattering dust grain diameter measurement method used in Hayashi/Tachibana experiment. Model now compared to Hayashi/Tachibana experiment using measured rather than fitted dust grain diameter and using higher estimate for Te/Ti (two new references added; revisions made to two paragraphs in Sec. VII, to bottom plot of Fig. 3, and to right-most column of Table 1

On the failure of subadditivity of the Wigner-Yanase entropy

It was recently shown by Hansen that the Wigner-Yanase entropy is, for general states of quantum systems, not subadditive with respect to decomposition into two subsystems, although this property is known to hold for pure states. We investigate the question whether the weaker property of subadditivity for pure states with respect to decomposition into more than two subsystems holds. This property would have interesting applications in quantum chemistry. We show, however, that it does not hold in general, and provide a counterexample.Comment: LaTeX2e, 4 page

A Bargmann-Wightman-Wigner Type Quantum Field Theory

This version corrects an inportant typographical error in Eq. 17. COMMENTS, FOR THE RECORD: A referees reoprt from Phys. Rev. Lett. read in part ``The first named author has appreciated my exceptionally long report. He has read and well assimilated the literature I suggested. Congratulations! This very new version of the manuscript has now three authors and carries a very well chosen title. Indeed Bargmann, Wightman and Wigner had studied, this subject forty years ago, in an unpublished book (several chapters were distributed as preprints). The authors explain well the scope of their paper. They have made a thorough construction of a field theory of a non usual Wigner type; that is completely new and all references are relevant. {\it This paper should be published.}" Despite the fact that no other report was received, the editors of Phys. Rev. Lett. rejected this paper. D.V.A.Comment: 13 pages, RevTex, LA-UR-92-3726-RE

Metric adjusted skew information

We extend the concept of Wigner-Yanase-Dyson skew information to something we call ``metric adjusted skew information'' (of a state with respect to a conserved observable). This ``skew information'' is intended to be a non-negative quantity bounded by the variance (of an observable in a state) that vanishes for observables commuting with the state. We show that the skew information is a convex function on the manifold of states. It also satisfies other requirements, proposed by Wigner and Yanase, for an effective measure-of-information content of a state relative to a conserved observable. We establish a connection between the geometrical formulation of quantum statistics as proposed by Chentsov and Morozova and measures of quantum information as introduced by Wigner and Yanase and extended in this article. We show that the set of normalized Morozova-Chentsov functions describing the possible quantum statistics is a Bauer simplex and determine its extreme points. We determine a particularly simple skew information, the ``lambda-skew information,'' parametrized by a lambda in (0,1], and show that the convex cone this family generates coincides with the set of all metric adjusted skew informations. Key words: Skew information, convexity, monotone metric, Morozova-Chentsov function, lambda-skew information.Comment: Edited the abstract and the introductio

Back Reaction and Semiclassical Approximation of cosmological models coupled to matter

Bianchi -I, -III, and FRW type models minimally coupled to a massive spatially homogeneous scalar field (i.e. a particle) are studied in the framework of semiclassical quantum gravity. In a first step we discuss the solutions of the corresponding equation for a Schr\"odinger particle propagating on a classical background. The back reaction of the Schr\"odinger particle on the classical metric is calculated by means of the Wigner function and by means of the expectation value of the energy-momentum-tensor of the field as a source. Both methods in general lead to different results.Comment: 4 pages, Latex, to appear in: Proceedings of the Second Meeting on constrained Dynamics and Quantum Gravity (Santa Margherita Ligure 1996

A proof of the Kramers degeneracy of transmission eigenvalues from antisymmetry of the scattering matrix

In time reversal symmetric systems with half integral spins (or more concretely, systems with an antiunitary symmetry that squares to -1 and commutes with the Hamiltonian) the transmission eigenvalues of the scattering matrix come in pairs. We present a proof of this fact that is valid both for even and odd number of modes and relies solely on the antisymmetry of the scattering matrix imposed by time reversal symmetry.Comment: 2 page

Dark matter: A spin one half fermion field with mass dimension one?

We report an unexpected theoretical discovery of a spin one half matter field with mass dimension one. It is based on a complete set of eigenspinors of the charge conjugation operator. Due to its unusual properties with respect to charge conjugation and parity it belongs to a non standard Wigner class. Consequently, the theory exhibits non-locality with (CPT)^2 = - I. Its dominant interaction with known forms of matter is via Higgs, and with gravity. This aspect leads us to contemplate it as a first-principle candidate for dark matter.Comment: 5 pages, RevTex, v2: slightly extended discussion, new refs. and note adde

The ultimate tactics of self-referential systems

Mathematics is usually regarded as a kind of language. The essential behavior of physical phenomena can be expressed by mathematical laws, providing descriptions and predictions. In the present essay I argue that, although mathematics can be seen, in a first approach, as a language, it goes beyond this concept. I conjecture that mathematics presents two extreme features, denoted here by {\sl irreducibility} and {\sl insaturation}, representing delimiters for self-referentiality. These features are then related to physical laws by realizing that nature is a self-referential system obeying bounds similar to those respected by mathematics. Self-referential systems can only be autonomous entities by a kind of metabolism that provides and sustains such an autonomy. A rational mind, able of consciousness, is a manifestation of the self-referentiality of the Universe. Hence mathematics is here proposed to go beyond language by actually representing the most fundamental existence condition for self-referentiality. This idea is synthesized in the form of a principle, namely, that {\sl mathematics is the ultimate tactics of self-referential systems to mimic themselves}. That is, well beyond an effective language to express the physical world, mathematics uncovers a deep manifestation of the autonomous nature of the Universe, wherein the human brain is but an instance.Comment: 9 pages. This essay received the 4th. Prize in the 2015 FQXi essay contest: "Trick or Truth: the Mysterious Connection Between Physics and Mathematics

Wigner-Araki-Yanase theorem on Distinguishability

The presence of an additive conserved quantity imposes a limitation on the measurement process. According to the Wigner-Araki-Yanase theorem, the perfect repeatability and the distinguishability on the apparatus cannot be attained simultaneously. Instead of the repeatability, in this paper, the distinguishability on both systems is examined. We derive a trade-off inequality between the distinguishability of the final states on the system and the one on the apparatus. The inequality shows that the perfect distinguishability of both systems cannot be attained simultaneously.Comment: To be published in Phys.Rev.

Fingerprints for spin-selection rules in the interaction dynamics of O2 at Al(111)

We performed mixed quantum-classical molecular dynamics simulations based on first-principles potential-energy surfaces to demonstrate that the scattering of a beam of singlet O2 molecules at Al(111) will enable an unambiguous assessment of the role of spin-selection rules for the adsorption dynamics. At thermal energies we predict a sticking probability that is substantially less than unity, with the repelled molecules exhibiting characteristic kinetic, vibrational and rotational signatures arising from the non-adiabatic spin transition.Comment: 4 pages including 3 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm