On the instabilities of the static, spherically symmetric SU(2) Einstein-Yang-Mills-Dilaton solitons and black holes

We prove that the number of odd parity instabilities of the n-th SU(2) Einstein-Yang-Mills-Dilaton soliton and black hole equals n.Comment: Added reference

Hudson's Theorem for finite-dimensional quantum systems

We show that, on a Hilbert space of odd dimension, the only pure states to possess a non-negative Wigner function are stabilizer states. The Clifford group is identified as the set of unitary operations which preserve positivity. The result can be seen as a discrete version of Hudson's Theorem. Hudson established that for continuous variable systems, the Wigner function of a pure state has no negative values if and only if the state is Gaussian. Turning to mixed states, it might be surmised that only convex combinations of stabilizer states give rise to non-negative Wigner distributions. We refute this conjecture by means of a counter-example. Further, we give an axiomatic characterization which completely fixes the definition of the Wigner function and compare two approaches to stabilizer states for Hilbert spaces of prime-power dimensions. In the course of the discussion, we derive explicit formulas for the number of stabilizer codes defined on such systems.Comment: 17 pages, 3 figures; References updated. Title changed to match published version. See also quant-ph/070200

A classification of primitive permutation groups with finite stabilizers

We classify all infinite primitive permutation groups possessing a finite point stabilizer, thus extending the seminal Aschbacher-O'Nan-Scott Theorem to all primitive permutation groups with finite point stabilizers.Comment: Accepted in J. Algebra. Various changes, some due to the author, some due to suggestions from readers and others due to the comments of anonymous referee

Gender Differences in the Consistency of Middle School Students’ Interest in Engineering and Science Careers

This longitudinal study analyzes survey responses in seventh, eighth, and ninth grade from diverse public school students (n = 482) to explore gender differences in engineering and science career preferences. Females were far more likely to express interest in a science career (31%) than an engineering career (13%), while the reverse was true for males (58% in engineering, 39% in science). After controlling for student and school demographic characteristics, females were as consistent as males in their science career interests during the three years of the study but less consistent in their engineering career interests. Knowing an engineer significantly predicted consistent career interest in engineering for males but not for females. Childhood interest in science and engineering was related to whether females and males expressed any interest in those subjects. Females and males both showed interest for careers where they can discover new things that help the environment or people’s health; females were less interested in designing and inventing, solving problems, and using technology. These findings suggest that increasing the number of diverse students who pursue engineering careers may require introducing students from early elementary to middle school to engineering as an array of careers that can improve health, happiness, and safety, and make the world a better place

Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms

In this paper we study the problem of uniqueness of solutions to the Hartree and Hartree-Fock equations of atoms. We show, for example, that the Hartree-Fock ground state of a closed shell atom is unique provided the atomic number $Z$ is sufficiently large compared to the number $N$ of electrons. More specifically, a two-electron atom with atomic number $Z\geq 35$ has a unique Hartree-Fock ground state given by two orbitals with opposite spins and identical spatial wave functions. This statement is wrong for some $Z>1$, which exhibits a phase segregation.Comment: 18 page

Non-zero entropy density in the XY chain out of equilibrium

The von Neumann entropy density of a block of n spins is proved to be non-zero for large n in the non-equilibrium steady state of the XY chain constructed by coupling a finite cutout of the chain to the two infinite parts to its left and right which act as thermal reservoirs at different temperatures. Moreover, the non-equilibrium density is shown to be strictly greater than the density in thermal equilibrium