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

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

Letter, 1973 December 5, from Louise E. Jefferson to Eva Jessye

1 page, Jeffereson is a graphic designer. A list of books of African American artist is attached