Thermal bound entanglement in macroscopic systems and area law

Does bound entanglement naturally appear in quantum many-body systems? We address this question by showing the existence of bound-entangled thermal states for harmonic oscillator systems consisting of an arbitrary number of particles. By explicit calculations of the negativity for different partitions, we find a range of temperatures for which no entanglement can be distilled by means of local operations, despite the system being globally entangled. We offer an interpretation of this result in terms of entanglement-area laws, typical of these systems. Finally, we discuss generalizations of this result to other systems, including spin chains.

ARTICLE: Anarchy and International Law: The Approaches of Hedley Bull and Noam Chomsky

Are anarchy and the law antithetical? Not so, as for more than 350 years international law has governed a legal order based on anarchy; wherein no central authority exists and law functions not on the basis of coercion but on cooperation whereby States must agree to each specific laws before it is bound by its obligations. This article contemplates two manners in which an anarchist might consider international law interesting: first, as a legal system which governs an anarchical society as described by Hedley Bull in line with the English School of International Relations; and second, as a manifestation of a State system which, though illegitimate can be utilized, as Noam Chomsky does, for tactical reasons to demonstrate its inconsistencies and thus weakening the system with the ultimate aim being its implosion

Testing of a Market Fraction Model and Power-law Behaviour in the DAX 30

This paper tests a simple market fraction asset pricing model with heterogeneous
agents. By selecting a set of structural parameters of the model through a systematic procedure, we show that the autocorrelations (of returns, absolute returns and squared returns) of the market fraction model share the same pattern as those of the DAX 30. By conducting econometric analysis via Monte Carlo simulations, we characterize these power-law behaviours and find that estimates of the power-law decay indices, the (FI)GARCH parameters, and the tail index of the selected market fraction model closely match those of the DAX 30. The results strongly support the explanatory power of the heterogeneous agent models.