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

Localised projective measurement of a relativistic quantum field in non-inertial frames

We propose a scheme to study the effect of motion on measurements of a quantum field carried out by a finite-size detector. We introduce a model of projective detection of a localised field mode in an arbitrary reference frame. We apply it to extract vacuum entanglement by a pair of counter-accelerating detectors and to estimate the Unruh temperature of a single accelerated detector. The introduced method allows us to directly relate the observed effects with the instantaneous proper acceleration of the detector.Comment: 5 pages, 2 figures. v2 Significant increase in the detail level regarding the motivation of the detector mode

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

In Vitro Characterisation of Physiological and Maximum Elastic Modulus of Ascending Thoracic Aortic Aneurysms Using Uniaxial Tensile Testing

AbstractObjectiveAscending thoracic aortic aneurysms (ATAA) are a life-threatening condition due to the risk of rupture or dissection. This risk is increased in the presence of a bicuspid aortic valve (BAV). The purpose of this study was to provide data on the elastic modulus of aortic wall of ATAA using uniaxial tensile testing in two different areas of the stress–strain relationship: physiological and maximum range of stresses. The influence of tissue location, tissue orientation and valve type on these parameters was investigated.Materials and methodsTissues freshly excised from ATAA with bicuspid or tricuspid aortic valve were obtained from greater and lesser curvature (GC and LC) and the specimens were tested uniaxially in circumferential (CIRC) and longitudinal (LONG) orientation. Maximum elastic modulus (MEM) was given by the maximum slope of the stress–strain curve before failure. Physiological modulus (PM) was derived from the Laplace law and from ranges of pressure of 80–120 mmHg. Means of each group of specimen were compared using Student's t-test to assess the influence of location, orientation and valve type on each mechanical parameter.ResultsPM was found to be significantly lower than the MEM (p < 0.001). The MEM and PM were significantly higher (p < 0.01) in the CIRC (n = 66) than in the LONG orientation (n = 42). The MEM was higher in the circumferential orientation in the BAV group (p < 0.001 in GC and p < 0.05 in LC). MEM and PM in GC specimens were higher in the longitudinal orientation than the LC specimens (p < 0.05).ConclusionThis study demonstrates the anisotropy of the aortic wall in ATAA and provides data on the mechanical behaviour in the physiological range of pressure

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

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

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