The measure and significance of Bateman's principles

Bateman's principles explain sex roles and sexual dimorphism through sex-specific variance in mating success, reproductive success and their relationships within sexes (Bateman gradients). Empirical tests of these principles, however, have come under intense scrutiny. Here, we experimentally show that in replicate groups of red junglefowl, Gallus gallus, mating and reproductive successes were more variable in males than in females, resulting in a steeper male Bateman gradient, consistent with Bateman's principles. However, we use novel quantitative techniques to reveal that current methods typically overestimate Bateman's principles because they (i) infer mating success indirectly from offspring parentage, and thus miss matings that fail to result in fertilization, and (ii) measure Bateman gradients through the univariate regression of reproductive over mating success, without considering the substantial influence of other components of male reproductive success, namely female fecundity and paternity share. We also find a significant female Bateman gradient but show that this likely emerges as spurious consequences of male preference for fecund females, emphasizing the need for experimental approaches to establish the causal relationship between reproductive and mating success. While providing qualitative support for Bateman's principles, our study demonstrates how current approaches can generate a misleading view of sex differences and roles

Then again, how often does the Unruh-DeWitt detector click if we switch it carefully?

The transition probability in first-order perturbation theory for an Unruh-DeWitt detector coupled to a massless scalar field in Minkowski space is calculated. It has been shown recently that the conventional $i\epsilon$ regularisation prescription for the correlation function leads to non-Lorentz invariant results for the transition rate, and a different regularisation, involving spatial smearing of the field, has been advocated to replace it. We show that the non-Lorentz invariance arises solely from the assumption of sudden switch-on and switch-off of the detector, and that when the model includes a smooth switching function the results from the conventional regularisation are both finite and Lorentz invariant. The sharp switching limit of the model is also discussed, as well as the falloff properties of the spectrum for large frequencies.Comment: 16 pages, v3. Final published version with section 5 expande

Excited by a quantum field: Does shape matter?

The instantaneous transition rate of an arbitrarily accelerated Unruh-DeWitt particle detector on four-dimensional Minkowski space is ill defined without regularisation. We show that Schlicht's regularisation as the zero-size limit of a Lorentz-function spatial profile yields a manifestly well-defined transition rate with physically reasonable asymptotic properties. In the special case of stationary trajectories, including uniform acceleration, we recover the results that have been previously obtained by a regularisation that relies on the stationarity. Finally, we discuss evidence for the conjecture that the zero-size limit of the transition rate is independent of the detector profile.Comment: 7 pages, uses jpconf. Talk given at NEB XII (Nafplio, Greece, 29 June - 2 July 2006

Considerations on the Unruh Effect: Causality and Regularization

This article is motivated by the observation, that calculations of the Unruh effect based on idealized particle detectors are usually made in a way that involves integrations along the {\em entire} detector trajectory up to the infinitely remote {\em future}. We derive an expression which allows time-dependence of the detector response in the case of a non-stationary trajectory and conforms more explicitely to the principle of causality, namely that the response at a given instant of time depends only on the detectors {\em past} movements. On trying to reproduce the thermal Unruh spectrum we are led to an unphysical result, which we trace down to the use of the standard regularization t\to t-i\eps of the correlation function. By consistently employing a rigid detector of finite extension, we are led to a different regularization which works fine with our causal response function.Comment: 19 pages, 2 figures, v2: some minor change

How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile

We analyse within first-order perturbation theory the instantaneous transition rate of an accelerated Unruh-DeWitt particle detector whose coupling to a massless scalar field on four-dimensional Minkowski space is regularised by a spatial profile. For the Lorentzian profile introduced by Schlicht, the zero size limit is computed explicitly and expressed as a manifestly finite integral formula that no longer involves regulators or limits. The same transition rate is obtained for an arbitrary profile of compact support under a modified definition of spatial smearing. Consequences for the asymptotic behaviour of the transition rate are discussed. A number of stationary and nonstationary trajectories are analysed, recovering in particular the Planckian spectrum for uniform acceleration.Comment: 30 pages, 1 figure. v3: Added references and minor clarification

Selection Wages and Discrimination

Applicants for any given job are more or less suited to fill it, and the firm will select the best among them. Increasing the wage offer attracts more applicants and makes it possible to raise the hiring standard and improve the productivity of the staff. Wages that optimize on the trade-off between the wage level and the productivity of the workforce are known as selection wages. As men react more strongly to wage differentials than females, the trade-off is more pronounced for men and a profit-maximizing firm will offer a higher wage for men than for women in equilibrium

Is life a thermal horizon ?

This talk aims at questioning the vanishing of Unruh temperature for an inertial observer in Minkovski spacetime with finite lifetime, arguing that in the non eternal case the existence of a causal horizon is not linked to the non-vanishing of the acceleration. This is illustrated by a previous result, the diamonds temperature, that adapts the algebraic approach of Unruh effect to the finite case.Comment: Proceedings of the conference DICE 2006, Piombino september 200

Accelerated detectors in Dirac vacuum: the effects of horizon fluctuations

We consider an Unruh-DeWitt detector interacting with a massless Dirac field. Assuming that the detector is moving along an hyperbolic trajectory, we modeled the effects of fluctuations in the event horizon using a Dirac equation with random coefficients. First, we develop the perturbation theory for the fermionic field in a random media. Further we evaluate corrections due to the randomness in the response function associated to different model detectors.Comment: 19 pages, 1 figur

Transition rate of the Unruh-DeWitt detector in curved spacetime

We examine the Unruh-DeWitt particle detector coupled to a scalar field in an arbitrary Hadamard state in four-dimensional curved spacetime. Using smooth switching functions to turn on and off the interaction, we obtain a regulator-free integral formula for the total excitation probability, and we show that an instantaneous transition rate can be recovered in a suitable limit. Previous results in Minkowski space are recovered as a special case. As applications, we consider an inertial detector in the Rindler vacuum and a detector at rest in a static Newtonian gravitational field. Gravitational corrections to decay rates in atomic physics laboratory experiments on the surface of the Earth are estimated to be suppressed by 42 orders of magnitude.Comment: 27 pages, 1 figure. v3: Typos corrected. Published versio

Relativistic Quantum Information in Detectors-Field Interactions

We review Unruh-DeWitt detectors and other models of detector-field interaction in a relativistic quantum field theory setting as a tool for extracting detector-detector, field-field and detector-field correlation functions of interest in quantum information science, from entanglement dynamics to quantum teleportation. We in particular highlight the contrast between the results obtained from linear perturbation theory which can be justified provided switching effects are properly accounted for, and the nonperturbative effects from available analytic expressions which incorporate the backreaction effects of the quantum field on the detector behaviour.Comment: 21 pages, 3 figures. Prepared for the special focus issue on RQ