The recent renewed interest in the foundation of quantum statistical mechanics and in the dynamics of isolated quantum systems has led to a revival of the old approach by von Neumann to investigate the problem of thermalization only in terms of quantum dynamics in an isolated system [1, 2]. It has been demonstrated in some general or concrete settings that a pure initial state evolving under quantum dynamics indeed approaches an equilibrium state [3–9]. The underlying idea that a single pure (...) quantum state can fully describe thermal equilibrium has also become much more concrete [10–12]. (shrink)

Shōwashi e no renketsu -- Higashi Ajia kara no me -- Tennō to iu jiba -- Watashi no kaikōki -- Jikokuhyō katate ni ekisoba o.

本書は、2013年4月1日から2015年3月31日までの2年間、『みすず』誌に連載された「日記」を一書にしたものである。大学人としての仕事や作家として執筆に追われながら、政治学者として世の動向を分析し 、皇室の動きを観察し、鉄道旅行をする。日常から時代を解読する試み。.

We study the problem of the approach to equilibrium in a macroscopic quantum system in an abstract setting. We prove that, for a typical choice of “nonequilibrium subspace”, any initial state (from the energy shell) thermalizes, and in fact does so very quickly, on the order of the Boltzmann time τ B := h/(k B T ). This apparently unrealistic, but mathematically rigorous, conclusion has the important physical implication that the moderately slow decay observed in reality is not typical in (...) the present setting. (shrink)