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

Anisohydric but isohydrodynamic: seasonally constant plant water potential gradient explained by a stomatal control mechanism incorporating variable plant hydraulic conductance

Isohydric and anisohydric regulations of plant water status have been observed over several decades of field, glasshouse and laboratory studies, yet the functional significance and mechanism of both remain obscure. We studied the seasonal trends in plant water status and hydraulic properties in a natural stand of Eucalyptus gomphocephala through cycles of varying environmental moisture (rainfall, groundwater depth, evaporative demand) in order to test for isohydry and to provide physiological information for the mechanistic interpretation of seasonal trends in plant water status. Over a 16 month period of monitoring, spanning two summers, midday leaf water potential (Ψleaf) correlated with predawn Ψleaf, which was correlated with water table depth below ground level, which in turn was correlated with total monthly rainfall. Eucalyptus gomphocephala was therefore not seasonally isohydric. Despite strong stomatal down-regulation of transpiration rate in response to increasing evaporative demand, this was insufficient to prevent midday Ψleaf from falling to levels below −2 MPa in the driest month, well into the region likely to induce xylem air embolisms, based on xylem vulnerability curves obtained in the study. However, even though midday Ψleaf varied by over 1.2 MPa across seasons, the hydrodynamic (transpiration-induced) water potential gradient from roots to shoots (ΔΨplant), measured as the difference between predawn and midday Ψleaf, was relatively constant across seasons, averaging 0.67 MPa. This unusual pattern of hydraulic regulation, referred to here as isohydrodynamic, is explained by a hydromechanical stomatal control model where plant hydraulic conductance is dependent on transpiration rate