The Bose-Einstein condensation of free relativistic particles [ε=(M 2 c 4 +c 2 p 2 ) 1/2 −Mc 2 ] is studied rigorously. For massless bosons (ε=cp), the condensation transition of third (second) order occurs in2 (3) dimensions (D). The molar heat capacity follows the T 2 (T 3 ) law below the condensation temperature Tc [k B Tc=(2πħ 2 c 2 n/1.645) 1/2 [(π 2 ħ 3 c 3 n/1.202) 1/3 ], reaches4.38 (10.8) R at T=Tc, and approaches the (...) high-temperature-limit value2 (3) R with no jump (a jump equal to6.75R) in2 (3)D. For finite-mass (M) bosons, the phase transition occurs only in3D with the condensation temperature Tc always smaller than that of the corresponding nonrelativistic bosons [ε=(2M) −1 p 2 ]. If the mass M is reduced to zero, the condensation temperature Tc grows monotonically and reaches eventually that of massless relativistic bosons. This mass-dependence of Tc is therefore distinct from the case of nonrelativistic bosons, where Tc grows to infinity as M →0. A brief discussion is given for a possible connection with the normal-to-super transition of the independently moving Cooper pairs (bosons). (shrink)

A molecular dynamics (MD) approach which determines automatically the complex magnetic structures in itinerant electron systems is applied to Fe-Cr alloys with use of 250 atoms in a MD unit cell (5×5×5 bcc lattice). It is demonstrated that the Fe-Cr alloys show various complex magnetic structures due to competing interactions: the collinear ferromagnetism (F) of matrix Fe with antiparallel Cr moments beyond 80 at.% Fe, the coexistence of non-collinear structure of Cr and collinear F of Fe between 50 and 75 (...) at.% Fe, the coexistence of broken antiferromagnetism (AF) of Cr and the F of Fe between 25 and 45 at.% Fe, the coexistence of F of Fe and antiferromagnetic long-range order of Cr around 20 at.% Fe, the AF of Cr matrix with non-collinear Fe moments (spin-glass like structure) between 5 and 15 at.% Fe, and the AF below 5 at.% Fe. In the concentration region between 5 and 20 at.% Fe, ferromagnetic Fe pairs which are stabilized with different amplitudes of local moments are found. The magnetic phase diagram and calculated magnetic moments are shown to be consistent with the neutron, Mössbauer, and photoemission experiments. (shrink)

Subliminal perception (SP) is today considered a well-supported theory stating that perception can occur without conscious awareness and have a significant impact on later behaviour and thought. In this article, we first present and discuss different approaches to the study of SP. In doing this, we claim that most approaches are based on a dichotomic measure of awareness. Drawing upon recent advances and discussions in the study of introspection and phenomenological psychology, we argue for both the possibility and necessity of (...) using an elaborated measure of subjective states. In the second part of the article, we present findings where these considerations are implemented in an empirical study. The results and implications are discussed in detail, both with reference to SP, and in relation to the more general problem of using elaborate introspective reports as data in relation to studies of cognition. (shrink)

Two thought experiments are discussed which suggest, first, a geometric interpretation of the concept of a (say, vector) potential (i.e., as a kinematic quantity associated with a transformation between moving frames of reference suitably related to the problem) and, second, that, in a quantum treatment one should extend the notion of the equivalence principle to include not only the equivalence of inertial forces with suitable “real” forces, but also the equivalence of potentials of such inertial forces and the potentials of (...) suitable real forces. The two types of cancellation are physically independent of each other, because of the Aharonov-Bohm effect. Finally, we show that the latter effect itself can be understood “geometrically” as a kinematic effect arising upon the transformation between the two reference frames. (shrink)

1. Escritos doctrinales -- 2. Escritos histórico-filosóficos.

Ben-Israel and Vaidman have raised objections to my arguments that there are cases where a quantum mechanical weak value can be said not to represent the system to which it pertains. They are correct in pointing out that some of my conclusions were too general. However, for weak values of projection operators my conclusions still stand.

Criticism of authority was a prominent feature of medieval philosophical writing. In this study the critiques of two contemporaneous scholars, Moses Maimonides and Fakhr al-Dīn al-Rāzī, are compared. Maimonides criticized Hellenistic authorities, mainly Aristotle. However, the starting point for his critique was Aristotle's admission of the limitations of his own inquiries. Maimonides admired Aristotle's questioning of his own conclusions; indeed, his own thought was characterized by constant self-doubt. Al-Rāzī criticized an earlier Muslim scholar, Ibn Sīnā , an intellectual giant whose (...) imprint was strongly felt in philosophy and medicine. Al Rāzī used his commentaries on a number of Ibn Sīnā's books as a stage for criticizing the master and for arguing for his own, alternative viewpoints. (shrink)

Rabbi HaCohen Kook’s essay on vegetarianism and peace, first published in instalments in 1903–4, and reissued 60 years later, is the only treatise in rabbinic Judaism on the relationship between humans and animals. It is here examined as central to his ethical beliefs. His writings, shaped by his background as rabbi and mystic, illuminate the history of environmental and applied ethics. A century ago, he perceived the main challenge that confronts reform movements: multiculturalism.

In the present paper, we consider a bio-economic equilibrium model which describes the dynamics of a fish population fished by several fishermen seeking to maximize their profits. Each fisherman tries to find the fishing effort which maximizes his profit at biological equilibrium without any consultation with others, but all of them have to respect two constraints: (1) the sustainable management of the resources ; and (2) the preservation of the biodiversity. With all these considerations, our problem leads to a generalized (...) Nash equilibrium problem. The objective is to show that even when a fisherman i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i$$\end{document} provides a fishing effort equal to twice the fishing effort of a fisherman j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$j$$\end{document}, then the profit of fisherman i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i$$\end{document} is not necessarily double that of fisherman j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$j$$\end{document}. (shrink)