Simulated Dark-Matter Halos as a Test of Nonextensive Statistical Mechanics

In the framework of nonextensive statistical mechanics, the equilibrium structures of astrophysical self-gravitating systems are stellar polytropes, parameterized by the polytropic index n. By careful comparison to the structures of simulated dark-matter halos we find that the density profiles, as well as other fundamental properties, of stellar polytropes are inconsistent with simulations for any value of n. This result suggests the need to reconsider the applicability of nonextensive statistical mechanics (in its simplest form) to equilibrium self-gravitating systems.Comment: Accepted for publication in Physical Review

Simple proof of gauge invariance for the S-matrix element of strong-field photoionization

The relationship between the length gauge (LG) and the velocity gauge (VG) exact forms of the photoionization probability amplitude is considered. Our motivation for this paper comes from applications of the Keldysh-Faisal-Reiss (KFR) theory, which describes atoms (or ions) in a strong laser field (in the nonrelativistic approach, in the dipole approximation). On the faith of a certain widely-accepted assumption, we present a simple proof that the well-known LG form of the exact photoionization (or photodetachment) probability amplitude is indeed the gauge-invariant result. In contrast, to obtain the VG form of this probability amplitude, one has to either (i) neglect the well-known Goeppert-Mayer exponential factor (which assures gauge invariance) during all the time evolution of the ionized electron or (ii) put some conditions on the vector potential of the laser field.Comment: The paper was initially submitted (in a previous version) on 16 October 2006 to J. Phys. A and rejected. This is the extended version (with 2 figures), which is identical to the paper published online on 12 December 2007 in Physica Script

Interplay of chiral and helical states in a Quantum Spin Hall Insulator lateral junction

We study the electronic transport across an electrostatically-gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without applied magnetic field. We control carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the 2D gap, magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus which reflect the equilibration between 1D chiral modes across the junction. As carrier density approaches zero in the central region and at moderate fields, we observe oscillations in resistance that we attribute to Fabry-Perot interference in the helical states, enabled by the broken time reversal symmetry. At higher fields, those oscillations disappear, in agreement with the expected absence of helical states when band inversion is lifted.Comment: 5 pages, 4 figures, supp. ma

Velocity quantization approach of the one-dimensional dissipative harmonic oscillator

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian.Comment: 10 pages, 2 figure

One-dimensional relativistic dissipative system with constant force and its quantization

For a relativistic particle under a constant force and a linear velocity dissipation force, a constant of motion is found. Problems are shown for getting the Hamiltoninan of this system. Thus, the quantization of this system is carried out through the constant of motion and using the quantization of the velocity variable. The dissipative relativistic quantum bouncer is outlined within this quantization approach.Comment: 11 pages, no figure

A nonextensive entropy approach to solar wind intermittency

The probability distributions (PDFs) of the differences of any physical variable in the intermittent, turbulent interplanetary medium are scale dependent. Strong non-Gaussianity of solar wind fluctuations applies for short time-lag spacecraft observations, corresponding to small-scale spatial separations, whereas for large scales the differences turn into a Gaussian normal distribution. These characteristics were hitherto described in the context of the log-normal, the Castaing distribution or the shell model. On the other hand, a possible explanation for nonlocality in turbulence is offered within the context of nonextensive entropy generalization by a recently introduced bi-kappa distribution, generating through a convolution of a negative-kappa core and positive-kappa halo pronounced non-Gaussian structures. The PDFs of solar wind scalar field differences are computed from WIND and ACE data for different time lags and compared with the characteristics of the theoretical bi-kappa functional, well representing the overall scale dependence of the spatial solar wind intermittency. The observed PDF characteristics for increased spatial scales are manifest in the theoretical distribution functional by enhancing the only tuning parameter $\kappa$, measuring the degree of nonextensivity where the large-scale Gaussian is approached for $\kappa \to \infty$. The nonextensive approach assures for experimental studies of solar wind intermittency independence from influence of a priori model assumptions. It is argued that the intermittency of the turbulent fluctuations should be related physically to the nonextensive character of the interplanetary medium counting for nonlocal interactions via the entropy generalization.Comment: 17 pages, 7 figures, accepted for publication in Astrophys.

Progress in Classical and Quantum Variational Principles

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis Principle is the classical limit of Schr\"{o}dinger's variational principle of wave mechanics, and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems

Tyrosine 23 Phosphorylation-Dependent Cell-Surface Localization of Annexin A2 Is Required for Invasion and Metastases of Pancreatic Cancer

The aggressiveness of pancreatic ductal adenocarcinoma (PDA) is characterized by its high metastatic potential and lack of effective therapies, which is the result of a lack of understanding of the mechanisms involved in promoting PDA metastases. We identified Annexin A2 (ANXA2), a member of the Annexin family of calcium-dependent phospholipid binding proteins, as a new molecule that promotes PDA invasion and metastases. We found ANXA2 to be a PDA-associated antigen recognized by post-treatment sera of patients who demonstrated prolonged survival following treatment with a PDA-specific vaccine. Cell surface ANXA2 increases with PDA development and progression. Knockdown of ANXA2 expression by RNA interference or blocking with anti-ANXA2 antibodies inhibits in vitro invasion of PDA cells. In addition, post-vaccination patient sera inhibits in vitro invasion of PDA cells, suggesting that therapeutic anti-ANXA2 antibodies are induced by the vaccine. Furthermore, cell-surface localization of ANXA2 is tyrosine 23 phosphorylation-dependent; and tyrosine 23 phosphorylation is required for PDA invasion. We demonstrated that tyrosine 23 phosphorylation resulting in surface expression of ANXA2 is required for TGFβ-induced, Rho-mediated epithelial-mesenchymal transition (EMT), linking the cellular function of ANXA2 which was previously shown to be associated with small GTPase-regulated cytoskeletal rearrangements, to the EMT process in PDA. Finally, using mouse PDA models, we showed that shRNA knock-down of ANXA2, a mutation at tyrosine 23, or anti-ANXA2 antibodies, inhibit PDA metastases and prolong mouse survival. Thus, ANXA2 is part of a novel molecular pathway underlying PDA metastases and a new target for development of PDA therapeutics