Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach

We study the continuity of an abstract generalization of the maximum-entropy inference - a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function on the convex body. Using convex geometry we prove, amongst others, the existence of discontinuities of the maximizer at limits of extremal points not being extremal points themselves and apply the result to quantum correlations. Further, we use numerical range methods in the case of quantum inference which refers to two observables. One result is a complete characterization of points of discontinuity for $3\times 3$ matrices.Comment: 27 page

Entropy Distance: New Quantum Phenomena

We study a curve of Gibbsian families of complex 3x3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology and information geometry. This research is motivated by a theory of info-max principles, where we contribute by computing first order optimality conditions of the entropy distance.Comment: 34 pages, 5 figure

Critical behavior of the restricted primitive model revisited

Reassessment of the critical temperature and density of the restricted primitive model of an ionic fluid by Monte Carlo simulations performed for system sizes with linear dimension up to $L/\sigma=34$ and sampling of $\sim 10^9$ trial moves leads to $T^*_c=0.04917 \pm 0.00002$ and $\rho_c^* =0.080 \pm 0.005$. Finite size scaling analysis based in the Bruce-Wilding procedure gives critical exponents in agreement with those of the 3d Ising universality class. An analysis similar to that proposed by Orkoulas et al [Phys. Rev. E 63, 051507 (2001)], not relying on an a priori knowledge of the universality class, leads to an unaccurate estimate of $T_c^*$ and to unexpected behavior of the specific heat and value of the critical exponent ratio $\gamma/\nu$.Comment: 17 pages, 11 figure

Strongly birefringent cut-wire pair structure as negative index wave plates at THz frequencies

We report a new approach for the design and fabrication of thin wave plates with high transmission in the terahertz (THz) regime. The wave plates are based on strongly birefringent cut-wire pair metamaterials that exhibit refractive indices of opposite signs for two orthogonal polarization components of an incident wave. As specific examples, we fabricated and investigated a quarter- and a half-wave plate that revealed a peak intensity transmittance of 74% and 58% at 1.34 THz and 1.3 THz, respectively. Furthermore, the half wave plate displayed a maximum figure of merit (FOM) of 23 at 1.3 THz where the refractive index was -1.7. This corresponds to one of the highest FOMs reported at THz frequencies so far. The presented results evidence that negative index materials enter an application stage in terms of optical components for the THz technology.Comment: 4 pages, 3 figures, submitted to Appl. Phys. Let

On the Social Traits of Luminous Blue Variables

In a recent paper, Smith and Tombleson (2015) state that the Luminous Blue Variables (LBVs) in the Milky Way and the Magellanic Clouds are isolated; that they are not spatially associated with young O-type stars. They propose a novel explanation that would overturn the standard view of LBVs. In this paper we test their hypothesis for the LBVs in M31 and M33 as well as the LMC and SMC. In M31 and M33, the LBVs are associated with luminous young stars and supergiants appropriate to their luminosities and positions on the HR Diagram. Moreover, in the Smith and Tombleson scenario most of the LBVs should be runaway stars, but the stars' velocities are consistent with their positions in the respective galaxies. In the Magellanic Clouds, those authors' sample was a mixed population. We reassess their analysis, removing seven stars that have no clear relation to LBVs. When we separate the more massive classical and the less luminous LBVs, the classical LBVs have a distribution similar to the late O-type stars, while the less luminous LBVs have a distribution like the red supergiants. None of the confirmed LBVs have high velocities or are candidate runaway stars. These results support the accepted description of LBVs as evolved massive stars that have shed a lot of mass, and are now close to their Eddington limit.Comment: To appear in the Astrophysical Journal With an expanded discussion of statistical error

On the Connection Between 2d Topological Gravity and the Reduced Hermitian Matrix Model

We discuss how concepts such as geodesic length and the volume of space-time can appear in 2d topological gravity. We then construct a detailed mapping between the reduced Hermitian matrix model and 2d topological gravity at genus zero. This leads to a complete solution of the counting problem for planar graphs with vertices of even coordination number. The connection between multi-critical matrix models and multi-critical topological gravity at genus zero is studied in some detail.Comment: 29 pages, LaTe

Effective interactions and phase behaviour for a model clay suspension in an electrolyte

Since the early observation of nematic phases of disc-like clay colloids by Langmuir in 1938, the phase behaviour of such systems has resisted theoretical understanding. The main reason is that there is no satisfactory generalization for charged discs of the isotropic DLVO potential describing the effective interactions between a pair of spherical colloids in an electrolyte. In this contribution, we show how to construct such a pair potential, incorporating approximately both the non-linear effects of counter-ion condensation (charge renormalization) and the anisotropy of the charged platelets. The consequences on the phase behaviour of Laponite dispersions (thin discs of 30 nm diameter and 1 nm thickness) are discussed, and investigation into the mesostructure via Monte Carlo simulations are presented.Comment: LaTeX, 12 pages, 11 figure