Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem

The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann's 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the "quantum H-theorem", is actually a much weaker statement than Boltzmann's classical H-theorem, the other theorem, which he calls the "quantum ergodic theorem", is a beautiful and very non-trivial result. It expresses a fact we call "normal typicality" and can be summarized as follows: For a "typical" finite family of commuting macroscopic observables, every initial wave function $\psi_0$ from a micro-canonical energy shell so evolves that for most times $t$ in the long run, the joint probability distribution of these observables obtained from $\psi_t$ is close to their micro-canonical distribution.Comment: 34 pages LaTeX, no figures; v2: minor improvements and additions. The English translation of von Neumann's article is available as arXiv:1003.213

Low-Energy Universality in Atomic and Nuclear Physics

An effective field theory developed for systems interacting through short-range interactions can be applied to systems of cold atoms with a large scattering length and to nucleons at low energies. It is therefore the ideal tool to analyze the universal properties associated with the Efimov effect in three- and four-body systems. In this "progress report", we will discuss recent results obtained within this framework and report on progress regarding the inclusion of higher order corrections associated with the finite range of the underlying interaction.Comment: Commissioned article for Few-Body Systems, 47 pp, 16 fig

On Minisuperspace Models of S-branes

In this note we reconsider the minisuperspace toy models for rolling and bouncing tachyons. We show that the theories require to choose boundary conditions at infinity since particles in an exponentially unbounded potential fall to infinity in finite world-sheet time. Using standard techniques from operator theory, we determine the possible boundary conditions and we compute the corresponding energy spectra and minisuperspace 3-point functions. Based on this analysis we argue in particular that world-sheet models of S-branes possess a discrete spectrum of conformal weights containing both positive and negative values. Finally, some suggestions are made for possible relations with previous studies of the minisuperspace theory.Comment: 24 pages, 3 figure

On von Neumann and Bell theorems applied to quantumness tests

The issues, raised in arXiv:0809.011, concerning the relevance of the von Neumann theorem for the single-system's quantumness test proposed in arXiv:0704.1962 and performed for the case of single photon polarization in arXiv:0804.1646, and the usefulness of Bell's inequality for testing the idea of macroscopic quantum systems are discussed in some details. Finally, the proper quantum mechanical description of the experiment with polarized photon beams is presented.Comment: 6 pages, no figure

Multiscale Bone Remodelling with Spatial P Systems

Many biological phenomena are inherently multiscale, i.e. they are characterized by interactions involving different spatial and temporal scales simultaneously. Though several approaches have been proposed to provide "multilayer" models, only Complex Automata, derived from Cellular Automata, naturally embed spatial information and realize multiscaling with well-established inter-scale integration schemas. Spatial P systems, a variant of P systems in which a more geometric concept of space has been added, have several characteristics in common with Cellular Automata. We propose such a formalism as a basis to rephrase the Complex Automata multiscaling approach and, in this perspective, provide a 2-scale Spatial P system describing bone remodelling. The proposed model not only results to be highly faithful and expressive in a multiscale scenario, but also highlights the need of a deep and formal expressiveness study involving Complex Automata, Spatial P systems and other promising multiscale approaches, such as our shape-based one already resulted to be highly faithful.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005