A perturbative approach to the spectral zeta functions of strings, drums and quantum billiards

We have obtained an explicit expression for the spectral zeta functions and for the heat kernel of strings, drums and quantum billiards working to third order in perturbation theory, using a generalization of the binomial theorem to operators. The perturbative parameter used in the expansion is either the small deformation of a reference domain (for instance a square), or a small variation of the density around a constant value (in two dimensions both cases can apply). This expansion is well defined even in presence of degenerations of the unperturbed spectrum. We have discussed several examples in one, two and three dimensions, obtaining in some cases the analytic continuation of the series, which we have then used to evaluate the corresponding Casimir energy. For the case of a string with piecewise constant density, subject to different boundary conditions, and of two concentric cylinders of very close radii, we have reproduced results previously published, thus obtaining a useful check of our method.Comment: 23 pages, 5 figures, 2 tables; version accepted on Journal of Mathematical Physic

Different behaviour of the N-terminal and C-terminal fragment of proatrial natriuretic factor in plasma of healthy subjects as well as of patients with cirrhosis

N-terminal (atrial natriuretic factor (ANF) 1-98) and C-terminal (ANF 99-126) fragments of proatrial natriuretic factor (NTA and CTA, respectively) were determined in plasma of healthy subjects adopting different postures and in patients with cirrhosis. Seven healthy subjects were investigated while seated and 30 min after assuming a horizontal position. NTA plasma concentrations increased in subjects in the horizontal position (from 734±250 (SE) fmol/ml to 9021227 fmol/ml; p<0.05). In contrast, CTA plasma concentrations remained unchanged (9.2+1.3 fmol/ml vs 8.9±1.6 fmol/ml). In 10 patients with cirrhosis of the liver, NTA concentrations were markedly (p<0.001) elevated compared to 11 healthy subjects (2334±291 fmol/ml vs 743±155 fmol/ml). However, there was no difference of CTA plasma levels between cirrhotic patients and healthy subjects (8.7±1.3 fmol/ml vs 8.2±0.9 fmol/ml). These data demonstrate changes of the plasma concentration of the N-terminal fragment of proatrial natriuretic factor by posture and in liver disease, in contrast to unchanged levels of the C-terminal fragment

Within the heart's darkness:The role of emotions in Arendt's political thought

Interest in the political relevance of the emotions is growing rapidly. In light of this, Hannah Arendt’s claim that the emotions are apolitical has come under renewed fire. But many critics have misunderstood her views on the relationship between individuals, emotions and the political. This paper addresses this issue by reconstructing the conceptual framework through which Arendt understands the emotions. Arendt often describes the heart – where the emotions reside – as a place of darkness. I begin by tracing this metaphor through her work to demonstrate that it is meant to convey the inherently uncertain nature of emotions rather than a devaluation of them. I proceed to challenge the notion that Arendt adopts the Enlightenment dichotomy between reason and emotion. In fact, she rejects both as a basis for politics. However, she does identify some constructive roles for the emotions. I argue that fear is intrinsically connected to courage – the principal political virtue – in Arendt’s philosophy. In light of my discussion, I then reinterpret the role of compassion and pity in On Revolution, concluding that Arendt’s insights can help us avoid the potential pitfalls of the contemporary project to recuperate the emotions in politics