What price the spin-statistics theorem?

We examine a number of recent proofs of the spin-statistics theorem. All, of course, get the target result of Bose-Einstein statistics for identical integral spin particles and Fermi-Dirac statistics for identical half-integral spin particles. It is pointed out that these proofs, distinguished by their purported simple and intuitive kinematic character, require assumptions that are outside the realm of standard quantum mechanics. We construct a counterexample to these non-dynamical kinematic 'proofs' to emphasize the necessity of a dynamical proof as distinct from a kinematic proof. Sudarshan's simple non-relativistic dynamical proof is briefly described. Finally, we make clear the price paid for any kinematic 'proof'

Weak Value in Wave Function of Detector

A simple formula to read out the weak value from the wave function of the measuring device after the postselection with the initial Gaussian profile is proposed. We apply this formula for the weak value to the classical experiment of the realization of the weak measurement by the optical polarization and obtain the weak value for any pre- and post-selections. This formula automatically includes the interference effect which is necessary to yields the weak value as an outcome of the weak measurement.Comment: 3 pages, no figures, Published in Journal of the Physical Society of Japa

Quantum statistics on graphs

Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph, concentrating on the simplest case of abelian statistics for two particles. In spite of the fact that graphs are locally one-dimensional, anyon statistics emerge in a generalized form. A given graph may support a family of independent anyon phases associated with topologically inequivalent exchange processes. In addition, for sufficiently complex graphs, there appear new discrete-valued phases. Our analysis is simplified by considering combinatorial rather than metric graphs -- equivalently, a many-particle tight-binding model. The results demonstrate that graphs provide an arena in which to study new manifestations of quantum statistics. Possible applications include topological quantum computing, topological insulators, the fractional quantum Hall effect, superconductivity and molecular physics.Comment: 21 pages, 6 figure

Quantum indistinguishability from general representations of SU(2n)

A treatment of the spin-statistics relation in nonrelativistic quantum mechanics due to Berry and Robbins [Proc. R. Soc. Lond. A (1997) 453, 1771-1790] is generalised within a group-theoretical framework. The construction of Berry and Robbins is re-formulated in terms of certain locally flat vector bundles over n-particle configuration space. It is shown how families of such bundles can be constructed from irreducible representations of the group SU(2n). The construction of Berry and Robbins, which leads to a definite connection between spin and statistics (the physically correct connection), is shown to correspond to the completely symmetric representations. The spin-statistics connection is typically broken for general SU(2n) representations, which may admit, for a given value of spin, both bose and fermi statistics, as well as parastatistics. The determination of the allowed values of the spin and statistics reduces to the decomposition of certain zero-weight representations of a (generalised) Weyl group of SU(2n). A formula for this decomposition is obtained using the Littlewood-Richardson theorem for the decomposition of representations of U(m+n) into representations of U(m)*U(n).Comment: 32 pages, added example section 4.

An examination of the factors correlating with course failure in a high school computer science course

Across the United States, enrollment in high school computer science (CS) courses is increasing. These increases, however, are not spread evenly across race and gender. CS remains largely an elective class, and fewer than three-fourths of the states allow it to count towards graduation. The Chicago Public Schools has sought to ensure access for all students by recently enacting computer science as a high school graduation requirement. The primary class that fulfills the graduation requirement is Exploring Computer Science (ECS), a high school introductory course and professional development program designed to foster deep engagement through equitable inquiry around CS concepts. The number of students taking CS in the district increased significantly and these increases are distributed equitably across demographic characteristics. With ECS serving as a core class, it becomes critical to ensure success for all students independent of demographic characteristics, as success in the course directly affects a student\u27s ability to graduate from high school. In this paper, we examine the factors that correlate with student failure in the course. At the student level, attendance and prior general academic performance correlate with passing the class. After controlling for student characteristics, whether or not teachers participated in the professional development program associated with ECS correlates with student success in passing the course. These results provide evidence for the importance of engaging teachers in professional development, in conjunction with requiring a course specifically designed to provide an equitable computer science experience, in order to broaden participation in computing

The sense in which a "weak measurement" of a spin-½ particle's spin component yields a value 100

We give a critical discussion of a recent Letter of Aharonov, Albert, and Vaidman. Although their work contains several flaws, their main point is valid: namely, that there is a sense in which a certain "weak measurement" procedure yields values outside the eigenvalue spectrum. Our analysis requires no approximations and helps to clarify the physics behind the effect. We describe an optical analog of the experiment and discuss the conditions necessary to realize the effect experimentally

Trans-Pacific dust events observed at Whistler, British Columbia during INTEX-B

International audienceThe meteorology and physico-chemical characteristics of aerosol associated with two new cases of long range dust transport affecting western Canada during spring 2006 are described. Each event showed enhancements of both sulfate aerosol and crustal material of Asian origin. However, the events were of quite different character and demonstrate the highly variable nature of such events. The April event was a significant dust event with moderate sulfate enhancement while the May event was a weak dust event with very significant sulfate enhancement. The latter event was interesting in the sense that it was of short duration and was quickly followed by significant enhancement of organic material likely of regional origin. Comparison of these two events with other documented cases extending back to 1993, suggests that all dust events show coincident enhancements of sulfate and crustal aerosol. However, events vary across a wide continuum based on the magnitude of aerosol enhancements and their sulfate to calcium ratios. At one extreme, events are dominated by highly significant crustal enhancements (e.g. the well-documented 1998 and 2001 "dust" events) while at the other are events with some dust transport, but where sulfate enhancements are of very high magnitude (e.g. the 1993 event at Crater Lake and the 15 May 2006 event at Whistler). Other events represent a "mix". It is likely that this variability is a function of the comparative strengths of the dust and anthropogenic SO2 sources, the transport pathway and in particular the extent to which dust is transported across industrial SO2 sources, and finally, meteorological and chemical processes

An Examination of the Correlation of Exploring Computer Science Course Performance and the Development of Programming Expertise

This study investigated patterns in the development of computational thinking and programming expertise in the context of the Exploring Computer Science (ECS) program, a high school introductory CS course and professional development program designed to foster deep engagement through equitable inquiry around CS concepts. Prior research on programming expertise has identified three general areas of development --- program comprehension, program planning, and program generation. The pedagogical practices in ECS are consistent with problem solving approaches that support the development of programming expertise. The study took place in a large urban district during the 2016--17 school year with 28 ECS teachers and 1,931 students. A validated external assessment was used to measure the development of programming expertise. The results indicate that there were medium-sized, statistically significant increases from pretest to posttest, and there were no statistically significant differences by gender or race/ethnicity. After controlling for prior academic achievement, performance in the ECS course correlated with performance on the posttest. With respect to specific programming concepts, the results also provide evidence on the progression of the development of programming expertise. Students seem to develop comprehension and planning expertise prior to expertise in program generation. In addition, students seem to develop expertise with concrete tasks prior to abstract tasks

Does a Computer Science Graduation Requirement Contribute to Increased Enrollment in Advanced Computer Science Coursework?

Prior research has shown that students pursuing Exploring Computer Science (ECS) as their first elective course were more likely to pursue another computer science course in high school, as compared to students who took a traditional course as the first course. This study investigated whether the results are consistent when students are pursuing ECS to fulfill the Chicago Public Schools\u27 graduation requirement. ECS is designed to foster deep engagement through equitable inquiry around computer science concepts. It is hypothesized that students who are fulfilling a graduation requirement will pursue additional computer science coursework at rates similar to students who were pursuing ECS as an elective course

On the geometry of quantum indistinguishability

An algebraic approach to the study of quantum mechanics on configuration spaces with a finite fundamental group is presented. It uses, in an essential way, the Gelfand-Naimark and Serre-Swan equivalences and thus allows one to represent geometric properties of such systems in algebraic terms. As an application, the problem of quantum indistinguishability is reformulated in the light of the proposed approach. Previous attempts aiming at a proof of the spin-statistics theorem in non-relativistic quantum mechanics are explicitly recast in the global language inherent to the presented techniques. This leads to a critical discussion of single-valuedness of wave functions for systems of indistinguishable particles. Potential applications of the methods presented in this paper to problems related to quantization, geometric phases and phase transitions in spin systems are proposed.Comment: 24 page