Transmission and Reflection in a Double Potential Well: Doing it the Bohmian Way

The Bohm interpretation of quantum mechanics is applied to a transmission and reflection process in a double potential well. We consider a time dependent periodic wave function and study the particle trajectories. The average time, eventally transmitted particles stay inside the barrier is the average transmission time, which can be defined using the causal interpretation. The question remains whether these transmission times can be experimentally measured.Comment: 19 page

Object-oriented Programming Laws for Annotated Java Programs

Object-oriented programming laws have been proposed in the context of languages that are not combined with a behavioral interface specification language (BISL). The strong dependence between source-code and interface specifications may cause a number of difficulties when transforming programs. In this paper we introduce a set of programming laws for object-oriented languages like Java combined with the Java Modeling Language (JML). The set of laws deals with object-oriented features taking into account their specifications. Some laws deal only with features of the specification language. These laws constitute a set of small transformations for the development of more elaborate ones like refactorings

Are chimpanzees really so poor at understanding imperative pointing? Some new data and an alternative view of canine and ape social cognition

There is considerable interest in comparative research on different species’ abilities to respond to human communicative cues such as gaze and pointing. It has been reported that some canines perform significantly better than monkeys and apes on tasks requiring the comprehension of either declarative or imperative pointing and these differences have been attributed to domestication in dogs. Here we tested a sample of chimpanzees on a task requiring comprehension of an imperative request and show that, though there are considerable individual differences, the performance by the apes rival those reported in pet dogs. We suggest that small differences in methodology can have a pronounced influence on performance on these types of tasks. We further suggest that basic differences in subject sampling, subject recruitment and rearing experiences have resulted in a skewed representation of canine abilities compared to those of monkeys and apes

Probability distribution of arrival times in quantum mechanics

In a previous paper [V. Delgado and J. G. Muga, Phys. Rev. A 56, 3425 (1997)] we introduced a self-adjoint operator $\hat {{\cal T}}(X)$ whose eigenstates can be used to define consistently a probability distribution of the time of arrival at a given spatial point. In the present work we show that the probability distribution previously proposed can be well understood on classical grounds in the sense that it is given by the expectation value of a certain positive definite operator $\hat J^{(+)}(X)$ which is nothing but a straightforward quantum version of the modulus of the classical current. For quantum states highly localized in momentum space about a certain momentum $p_0 \neq 0$, the expectation value of $\hat J^{(+)}(X)$ becomes indistinguishable from the quantum probability current. This fact may provide a justification for the common practice of using the latter quantity as a probability distribution of arrival times.Comment: 21 pages, LaTeX, no figures; A Note added; To be published in Phys. Rev.

The plight of the sense-making ape

This is a selective review of the published literature on object-choice tasks, where participants use directional cues to find hidden objects. This literature comprises the efforts of researchers to make sense of the sense-making capacities of our nearest living relatives. This chapter is written to highlight some nonsensical conclusions that frequently emerge from this research. The data suggest that when apes are given approximately the same sense-making opportunities as we provide our children, then they will easily make sense of our social signals. The ubiquity of nonsensical contemporary scientific claims to the effect that humans are essentially--or inherently--more capable than other great apes in the understanding of simple directional cues is, itself, a testament to the power of preconceived ideas on human perception

Strong quantum violation of the gravitational weak equivalence principle by a non-Gaussian wave-packet

The weak equivalence principle of gravity is examined at the quantum level in two ways. First, the position detection probabilities of particles described by a non-Gaussian wave-packet projected upwards against gravity around the classical turning point and also around the point of initial projection are calculated. These probabilities exhibit mass-dependence at both these points, thereby reflecting the quantum violation of the weak equivalence principle. Secondly, the mean arrival time of freely falling particles is calculated using the quantum probability current, which also turns out to be mass dependent. Such a mass-dependence is shown to be enhanced by increasing the non-Gaussianity parameter of the wave packet, thus signifying a stronger violation of the weak equivalence principle through a greater departure from Gaussianity of the initial wave packet. The mass-dependence of both the position detection probabilities and the mean arrival time vanish in the limit of large mass. Thus, compatibility between the weak equivalence principle and quantum mechanics is recovered in the macroscopic limit of the latter. A selection of Bohm trajectories is exhibited to illustrate these features in the free fall case.Comment: 11 pages, 7 figure

Correcting the quantum clock: conditional sojourn times

Can the quantum-mechanical sojourn time be clocked without the clock affecting the sojourn time? Here we re-examine the previously proposed non-unitary clock, involving absorption/amplification by an added infinitesimal imaginary potential($iV_{i}$), and find it {\it not} to preserve, in general, the positivity of the sojourn time, conditional on eventual reflection or transmission. The sojourn time is found to be affected by the scattering concomitant with the mismatch, however small, due to the very clock potential($iV_{i}$) introduced for the purpose, as also by any prompt scattering involving partial waves that have not traversed the region of interest. We propose a formal procedure whereby the sojourn time so clocked can be corrected for these spurious scattering effects. The resulting conditional sojourn times are then positive definite for an arbitrary potential, and have the proper high- and low-energy limits.Comment: Corrected and rewritten, RevTeX, 4 pages, 2 figures (ps files) include

Possibility of the tunneling time determination

We show that it is impossible to determine the time a tunneling particle spends under the barrier. However, it is possible to determine the asymptotic time, i.e., the time the particle spends in a large area including the barrier. We propose a model of time measurements. The model provides a procedure for calculation of the asymptotic tunneling and reflection times. The model also demonstrates the impossibility of determination of the time the tunneling particle spends under the barrier. Examples for delta-form and rectangular barrier illustrate the obtained results.Comment: 8 figure

Diffraction in time of a confined particle and its Bohmian paths

Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial wavefunctions. In each case Bohmian trajectories of the particles are computed and also the mean arrival time at a given location is studied as a function of the initial state.Comment: 8 pages, 6 figure

Renormalization group approach to anisotropic superconductivity

The superconducting instability of the Fermi liquid state is investigated by considering anisotropic electron-boson couplings. Both electron-electron interactions and anisotropic electron-boson couplings are treated with a renormalization-group method that takes into account retardation effects. Considering a non-interacting circular Fermi surface, we find analytical solutions for the flow equations and derive a set of generalized Eliashberg equations. Electron-boson couplings with different momentum dependences are studied, and we find superconducting instabilities of the metallic state with competition between order parameters of different symmetries. Numerical solutions for some couplings are given to illustrate the frequency dependence of the vertices at different coupling regimes.Comment: 9 pages, 7 figures. Final version as published in Phys. Rev.