Entropy of a Quantum Oscillator coupled to a Heat Bath and implications for Quantum Thermodynamics

The free energy of a quantum oscillator in an arbitrary heat bath at a temperature T is given by a "remarkable formula" which involves only a single integral. This leads to a corresponding simple result for the entropy. The low temperature limit is examined in detail and we obtain explicit results both for the case of an Ohmic heat bath and a radiation heat bath. More general heat bath models are also examined. This enables us to determine the entropy at zero temperature in order to check the third law of thermodynamics in the quantum regimeComment: International Conference on "Frontiers of Quantum and Mesoscopic Thermodynamics

Decoherence in Nanostructures and Quantum Systems

Decoherence phenomena are pervasive in the arena of nanostructures but perhaps even more so in the study of the fundamentals of quantum mechanics and quantum computation. Since there has been little overlap between the studies in both arenas, this is an attempt to bridge the gap. Topics stressed include (a) wave packet spreading in a dissipative environment, a key element in all arenas, (b) the definition of a quantitative measure of decoherence, (c) the near zero and zero temperature limit, and (d) the key role played by initial conditions: system and environment entangled at all times so that one must use the density matrix (or Wigner distribution) for the complete system or initially decoupled system and environment so that use of a reduced density matrix or reduced Wigner distribution is feasible. Our approach utilizes generalized quantum Langevin equations and Wigner distributions

Quantum states with negative energy density in the Dirac field and quantum inequalities

Energy densities of the quantum states that are superposition of two multi-electron-positron states are examined. It is shown that the energy densities can be negative only when two multi-particle states have the same number of electrons and positrons or when one state has one more electron-positron pair than the other. In the cases in which negative energy could arise, we find that the energy is that of a positive constant plus a propagating part which oscillates between positive and negative, and the energy can dip to negative at some places at for a certain period of time if the quantum states are properly manipulated. It is demonstrated that the negative energy densities satisfy the quantum inequality. Our results also reveal that for a given particle content, the detection of negative energy is an operation that depends on the frame where any measurement is to be performed. This suggests that the sign of energy density for a quantum state may be a coordinate-dependent quantity in quantum theory.Comment: Revtex,9 pages, no figures, a couple of typos correcte

Parallel Algorithm for Solving Kepler's Equation on Graphics Processing Units: Application to Analysis of Doppler Exoplanet Searches

[Abridged] We present the results of a highly parallel Kepler equation solver using the Graphics Processing Unit (GPU) on a commercial nVidia GeForce 280GTX and the "Compute Unified Device Architecture" programming environment. We apply this to evaluate a goodness-of-fit statistic (e.g., chi^2) for Doppler observations of stars potentially harboring multiple planetary companions (assuming negligible planet-planet interactions). We tested multiple implementations using single precision, double precision, pairs of single precision, and mixed precision arithmetic. We find that the vast majority of computations can be performed using single precision arithmetic, with selective use of compensated summation for increased precision. However, standard single precision is not adequate for calculating the mean anomaly from the time of observation and orbital period when evaluating the goodness-of-fit for real planetary systems and observational data sets. Using all double precision, our GPU code outperforms a similar code using a modern CPU by a factor of over 60. Using mixed-precision, our GPU code provides a speed-up factor of over 600, when evaluating N_sys > 1024 models planetary systems each containing N_pl = 4 planets and assuming N_obs = 256 observations of each system. We conclude that modern GPUs also offer a powerful tool for repeatedly evaluating Kepler's equation and a goodness-of-fit statistic for orbital models when presented with a large parameter space.Comment: 19 pages, to appear in New Astronom

Effect of an External Field on Decoherence

"Decoherence of quantum superpositions through coupling to engineered reservoirs" is the topic of a recent article by Myatt et al. [Nature {\underline{403}}, 269 (2000)] which has attracted much interest because of its relevance to current research in fundamental quantum theory, quantum computation, teleportation, entanglement and the quantum-classical interface. However, the preponderance of theoretical work on decoherence does not consider the effect of an {\underline{external field}}. Here, we present an analysis of such an effect in the case of the random delta-correlated force discussed by Myatt et al

An ergonomics analysis of manual versus chainsaw high ladder pruning of Pinus radiata in New Zealand : a thesis in partial fulfilment of the requirements for the degree of Master of Philosophy at Massey University

Two methods of ladder pruning Pinus radiata from 4.5 - 6.0 metres were compared using a cost-benefit approach within a framework provided by ergonomics. Chainsaw pruning is practiced in areas of New Zealand where large branches occur. The objectives of the research were to compare the costs and benefits of the two pruning techniques and provide recommendations as to whether or not the practice of chainsaw pruning should continue. These objectives were achieved by comparing the risk of injury, the physiological costs, the musculoskeletal costs, the productivity and the quality associated with the use of the two techniques. The general methods used to assess the relative costs and benefits of the two techniques were: l. Numeric descriptions of the 'risk' involved with each method of pruning 2. The use of a relative heart rate index to compare the physiological cost of the two techniques 3. Using questionnaires focusing on musculoskeletal pain and discomfort to assess any relative differences between the two techniques 4. Using continuous time study to quantify any difference in labour productivity between the two techniques 5. Sampling pruned trees to assess differences in the quality of work between manual and chainsaw pruning The research concludes that although both methods of pruning are hazardous, chainsaw pruning is more hazardous than manual pruning. Chainsaw and manual pruning were found to have the same physiological costs. Findings of the research indicate that manual pruning is not associated with a higher prevalence of musculoskeletal discomfort than chainsaw pruning on a yearly basis, although it is associated with a greater relative increase in BPD on a day to day basis and that this may lead to the development of musculoskeletal disease. Chainsaw pruning was found to be significantly more productive than manual pruning, although this was at the cost of quality. The research concludes by recommending that the use of chainsaw pruning should be limited to areas where the branches are demonstrably large. Further research is called for to compare the physiological and musculoskeletal costs of manual pruning in plantation areas of both large and small branch sizes. Further research is called for to compare the safety of two methods of chainsaw pruning with the use of the technique of wrapping one leg around the tree as opposed to not wrapping the leg around the tree. Research to investigate new ladder designs which are safer to use in the New Zealand forest environment is also called for

THE NORMAL BEHAVIOR OF THE SMARANDACHE FUNCTION

Let S(n) be the smallest integer k so that nlk!. This is known as the Smarandache function and has been studied by many authors

Decoherence at zero temperature

Most discussions of decoherence in the literature consider the high-temperature regime but it is also known that, in the presence of dissipation, decoherence can occur even at zero temperature. Whereas most previous investigations all assumed initial decoupling of the quantum system and bath, we consider that the system and environment are entangled at all times. Here, we discuss decoherence for a free particle in an initial Schr\"{o}dinger cat state. Memory effects are incorporated by use of the single relaxation time model (since the oft-used Ohmic model does not give physically correct results)