Entanglement of two delocalised electrons

Several convenient formulae for the entanglement of two indistinguishable delocalised spin-1/2 particles are introduced. This generalizes the standard formula for concurrence, valid only in the limit of localised or distinguishable particles. Several illustrative examples are given.Comment: 4 page

Chaotic Explosions

We investigate chaotic dynamical systems for which the intensity of trajectories might grow unlimited in time. We show that (i) the intensity grows exponentially in time and is distributed spatially according to a fractal measure with an information dimension smaller than that of the phase space,(ii) such exploding cases can be described by an operator formalism similar to the one applied to chaotic systems with absorption (decaying intensities), but (iii) the invariant quantities characterizing explosion and absorption are typically not directly related to each other, e.g., the decay rate and fractal dimensions of absorbing maps typically differ from the ones computed in the corresponding inverse (exploding) maps. We illustrate our general results through numerical simulation in the cardioid billiard mimicking a lasing optical cavity, and through analytical calculations in the baker map.Comment: 7 pages, 5 figure

Interacting electrons in polygonal quantum dots

The low-lying eigenstates of a system of two electrons confined within a two-dimensional quantum dot with a hard polygonal boundary are obtained by means of exact diagonalization. The transition from a weakly correlated charge distribution for small dots to a strongly correlated "Wigner molecule" for large dots is studied, and the behaviour at the crossover is determined. In sufficiently large dots, a recently proposed mapping to an effective charge-spin model is investigated, and is found to produce the correct ordering of the energy levels and to give a good first approximation to the size of the level spacings. We conclude that this approach is a valuable method to obtain the low energy spectrum of few-electron quantum dots

Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality

We have computed the surface energies, work functions, and interlayer surface relaxations of clean (111), (110), and (100) surfaces of Al, Cu, Ru, Rh, Pd, Ag, Pt, and Au. Many of these metallic surfaces have technological or catalytic applications. We compare experimental reference values to those of the local density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), the PBEsol (PBE for solids) GGA, the SCAN meta-GGA, and SCAN+rVV10 (SCAN with a long-range van der Waals or vdW correction). The closest agreement with uncertain experimental values is achieved by the simplest density functional (LDA) and by the most sophisticated general-purpose one (SCAN+rVV10). The long-range vdW interaction increases the surface energies by about 10%, and the work functions by about 1%. LDA works for metal surfaces through a stronger-than-usual error cancellation. PBE yields the most-underestimated and presumably least accurate surface energies and work functions. Surface energies within the random phase approximation (RPA) are also reported. Interlayer relaxations from different functionals are in reasonable agreement with one another, and usually with experiment

Arts Integration Experiences of Elementary Educators

The purpose of this study was to examine how elementary teachers applied their professional learning to integrate arts in the classroom. The research questions guiding the study included: (1) What content, skills, and understandings do teachers transfer from professional learning to practice? and (2) How do teachers navigate the implementation of arts integration? Knowles\u27 (1978) Adult Learning Theory was used to examine how meeting the needs of teachers as adult learners during professional learning influenced the implementation experience. A case study design employing qualitative data collection methods such as focus groups, individual interviews, and the sharing of artifacts from practice was used to better understand the knowledge transferred from professional learning to practice and the influences on these participants’ actions during implementation (Creswell & Poth, 2018). Four participants were purposefully selected to ensure they work with Prek-5 students, have attended professional learning for arts integration through the same organization, and planned to employ arts integration methods in the spring of 2022. Transcripts were analyzed through memoing, inductive hand-coding, and the development of themes, while shared artifacts informed the understanding of participant responses. The central finding of this study suggests that the use of an experience-based instructional approach during professional learning for arts integration supports the acquisition and transfer of new knowledge to practice. This finding is significant because it suggests implications for the field of arts integration and adult learning. Specifically, being in the role of a student while immersed in the arts helps teachers acquire and transfer specific arts concepts, skills, and understandings to practice, thus expanding their instructional capacity to provide meaningful learning for students. Other key points of significance in the findings show that the variation in the support these participants received and the obstacles they faced did not influence whether implementation occurred, only to what degree. Similarly, the participant\u27s district, building leadership, and subject/teaching responsibility appeared to influence the support received, and the obstacles faced. Recommendations for further research suggest a more extended timeframe without restrictions of the COVID-19 pandemic to allow the researcher to develop an increased understanding of implementation through classroom visits and observation of arts integration in practice

The occupational needs of Hawkins County, Tennessee

Purpose The purpose of the study was to determine the occupational needs of Hawkins County, Tennessee. Method A survey form was developed by the investigator and the information was secured by personal interview. Summary 1. Occupations other than farming exist in HawkinsCounty for approximately 4,788 males and 767 females,2. The annual turnover in occupations other than farming in the county is approximately 178 males and 94 females.3. The additional employees needed in occupations other than farming next year due to growth is estimated to be 281 males and 58 females.4. The total additional employees needed in occupations other than farming for the next five years due to turnover and growth is expected to be 1,645 males and 654 females.5. There is a shortage of trained personnel to fill the needs in occupations other than farming in the county.6. Vocational classes in high school to meet the county vocational needs were recommended by 83 percent of the employer in sales and office work, 81 percent in mechanical skilled trades and 21 percent in service skilled trades. 7. A need exists in the county for expanded high school vocational programs to meet the needs of the county occupational community