Measurement as Absorption of Feynman Trajectories: Collapse of the Wave Function Can be Avoided

We define a measuring device (detector) of the coordinate of quantum particle as an absorbing wall that cuts off the particle's wave function. The wave function in the presence of such detector vanishes on the detector. The trace the absorbed particles leave on the detector is identifies as the absorption current density on the detector. This density is calculated from the solution of Schr\"odinger's equation with a reflecting boundary at the detector. This current density is not the usual Schr\"odinger current density. We define the probability distribution of the time of arrival to a detector in terms of the absorption current density. We define coordinate measurement by an absorbing wall in terms of 4 postulates. We postulate, among others, that a quantum particle has a trajectory. In the resulting theory the quantum mechanical collapse of the wave function is replaced with the usual collapse of the probability distribution after observation. Two examples are presented, that of the slit experiment and the slit experiment with absorbing boundaries to measure time of arrival. A calculation is given of the two dimensional probability density function of a free particle from the measurement of the absorption current on two planes.Comment: 20 pages, latex, no figure

A Path Intergal Approach to Current

Discontinuous initial wave functions or wave functions with discontintuous derivative and with bounded support arise in a natural way in various situations in physics, in particular in measurement theory. The propagation of such initial wave functions is not well described by the Schr\"odinger current which vanishes on the boundary of the support of the wave function. This propagation gives rise to a uni-directional current at the boundary of the support. We use path integrals to define current and uni-directional current and give a direct derivation of the expression for current from the path integral formulation for both diffusion and quantum mechanics. Furthermore, we give an explicit asymptotic expression for the short time propagation of initial wave function with compact support for both the cases of discontinuous derivative and discontinuous wave function. We show that in the former case the probability propagated across the boundary of the support in time $\Delta t$ is $O(\Delta t^{3/2})$ and the initial uni-directional current is $O(\Delta t^{1/2})$. This recovers the Zeno effect for continuous detection of a particle in a given domain. For the latter case the probability propagated across the boundary of the support in time $\Delta t$ is $O(\Delta t^{1/2})$ and the initial uni-directional current is $O(\Delta t^{-1/2})$. This is an anti-Zeno effect. However, the probability propagated across a point located at a finite distance from the boundary of the support is $O(\Delta t)$. This gives a decay law.Comment: 17 pages, Late

Oscillator Damped by a Constant-Magnitude Friction Force

Although a simple spring/mass system damped by a friction force of constant magnitude shares many of the characteristics of the simple and damped harmonic oscillators, its solution is not presented in most texts. Closed form solutions for the turning and stopping points can be found using an energy-based approach. A dynamical approach leads to a closed form solution for the position of the mass as a function of time. The main result is that the amplitude of the oscillator damped by a constant magnitude friction force decreases by a constant amount each swing and the motion dies out after a finite time. We present these two solutions and suggest ways that the system can be used in the classroom

review of the social and environmental factors affecting the behavior and welfare of turkeys meleagris gallopavo

ABSTRACT In modern rearing systems, turkey producers often face economic losses due to increased aggression, feather pecking, cannibalism, leg disorders, or injuries among birds, which are also significant welfare issues. The main underlying causes appear to relate to rapid growth, flock size, density, poor environmental complexity, or lighting, which may be deficient in providing the birds with an adequate physical or social environment. To date, there is little information regarding the effect of these factors on turkey welfare. This knowledge is, however, essential to ensure the welfare of turkeys and to improve their quality of life, but may also be beneficial to industry, allowing better bird performance, improved carcass quality, and reduced mortality and condemnations. This paper reviews the available scientific literature related to the behavior of turkeys as influenced by the physical and social environment that may be relevant to advances toward turkey production systems that take welfare into consideration. We addressed the effects that factors such as density, group size, space availability, maturation, lightning, feeding, and transport may have over parameters that may be relevant to ensure welfare of turkeys. Available scientific studies were based in experimental environments and identified individual factors corresponding to particular welfare problems. Most of the studies aimed at finding optimal levels of rearing conditions that allow avoiding or decreasing most severe welfare issues. This paper discusses the importance of these factors for development of production environments that would be better suited from a welfare and economic point of view

Quantum particle displacement by a moving localized potential trap

We describe the dynamics of a bound state of an attractive $\delta$-well under displacement of the potential. Exact analytical results are presented for the suddenly moved potential. Since this is a quantum system, only a fraction of the initially confined wavefunction remains confined to the moving potential. However, it is shown that besides the probability to remain confined to the moving barrier and the probability to remain in the initial position, there is also a certain probability for the particle to move at double speed. A quasi-classical interpretation for this effect is suggested. The temporal and spectral dynamics of each one of the scenarios is investigated.Comment: 5 pages, 6 figure

Trapping of quantum particles and light beams by switchable potential wells

We consider basic dynamical effects in settings based on a pair of local potential traps that may be effectively switched on and off, or suddenly displaced, by means of appropriate control mechanisms, such as the scanning tunneling microscopy (STM) or photo-switchable quantum dots. The same models, based on the linear Schrodinger equation with time-dependent trapping potentials, apply to the description of optical planar systems designed for the switching of trapped light beams. The analysis is carried out in the analytical form, using exact solutions of the Schrodinger equation. The first dynamical problem considered in this work is the retention of a particle released from a trap which was suddenly turned off, while another local trap was switched on at a distance - immediately or with a delay. In this case, we demonstrate that the maximum of the retention rate is achieved at a specific finite value of the strength of the new trap, and at a finite value of the temporal delay, depending on the distance between the two traps. Another ptoblem is retrapping of the bound particle when the addition of the second trap transforms the single-well setting into a double-well potential (DWP). In that case, we find probabilities for the retrapping into the ground or first excited state of the DWP. We also analyze effects entailed by the application of a kick to a bound particle, the most interesting one being a kick-induced transition between the DWP's ground and excited states. In the latter case, the largest transition probability is achieved at particular strength of the kick.Comment: 20 pages, 10 figure

Private animal health and welfare standards in quality assurance programmes: a review and proposed framework for critical evaluation

peer-reviewedIn recent years, ‘private standards’ in animal health and welfare have become increasingly common, and are often incorporated into quality assurance (QA) programmes. Here, we present an overview of the use of private animal health and welfare standards in QA programmes, and propose a generic framework to facilitate critical programme review. Private standards are being developed in direct response to consumer demand for QA, and offer an opportunity for product differentiation and a means to drive consumer choice. Nonetheless, a range of concerns have been raised, relating to the credibility of these standards, their potential as a discriminatory barrier to trade, the multiplicity of private standards that have been developed, the lack of consumer input and compliance costs. There is a need for greater scrutiny of private standards and of associated QA programmes. We propose a framework to clarify the primary programme goal(s) and measureable outputs relevant to animal health and welfare, the primary programme beneficiaries and to determine whether the programme is effective, efficient and transparent. This paper provides a theoretical overview, noting that this framework could be used as a tool directly for programme evaluation, or as a tool to assist with programme development and review

Experimental results for a 1.5 MW, 110 GHz gyrotron oscillator with reduced mode competition

A new result from a 110 GHz gyrotron at MIT is reported with an output power of 1.67 MW and an efficiency of 42% when operated at 97 kV and 41 A for 3 mu s pulses in the TE22,6 mode. These results are a major improvement over results obtained with an earlier cavity design, which produced 1.43 MW of power at 37% efficiency. These new results were obtained using a cavity with a reduced output taper angle and a lower ohmic loss when compared with the earlier cavity. The improved operation is shown experimentally to be the result of reduced mode competition from the nearby TE19,7 mode. The reduced mode competition agrees well with an analysis of the startup scenario based on starting current simulations. The present results should prove useful in planning long pulse and CW versions of the 110 GHz gyrotron.open141

Behaviour of tail-docked lambs tested in isolation

peer-reviewedThe aims of the current study were to detect behavioural indicators of pain of tail-docked sheep tested in isolation and to determine the relationship between behaviour and the pain levels to which they were exposed. Twenty-four female lambs, randomly assigned to four pens, had their tail docked with a rubber ring (TD; n = 6) without pain control procedures, TD with anaesthesia (TDA; n = 6) or TD with anaesthesia and analgesia (TDAA; n = 6). Additionally, six lambs handled but without tail docking or application of pain relief measures were used as the control (C). On the day prior (Day –1) to the TD and on days 1, 3 and 5 post-procedure, each lamb was individually removed from its group and underwent a 2.5 min open field test in a separate pen. Frequencies of behaviours such as rest, running, standing, walking and exploring were directly observed. Frequencies of exploratory climbs (ECs) and abrupt climbs (ACs) over the testing pen’s walls were video-recorded. Data were analysed using generalised linear mixed models with repeated measurements, including treatment and day as fixed effects and behaviour on Day –1 as a linear covariate. Control and TDAA lambs stood more frequently than TD lambs. TD lambs performed significantly more ACs compared to all other treatment groups. No other treatment effects were detected. A day effect was detected for all behaviours, while the EC frequency was highest for all tail-docked lambs on Day 5. Findings suggest that standing, ACs and ECs could be used as potential indicators of pain in isolated tail-docked lambs. However, differences in ECs between treatments only appeared 3 d after tail docking