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The generalized Gibbs ensemble (GGE), which involves multiple conserved quantities other than the Hamiltonian, has served as the statistical-mechanical description of the long-time behavior for several isolated integrable quantum systems. We argue that the GGE may involve a noncommutative set of conserved quantities in view of the maximum entropy principle and show that the GGE thus generalized (noncommutative GGE, NCGGE) gives a more qualitatively accurate description of the long-time behaviors than that of the conventional GGE. Providing a clear understanding of why the (NC)GGE well describes the long-time behaviors, we construct, for noninteracting models, the exact NCGGE that describes the long-time behaviors without an error even at finite system size. It is noteworthy that the NCGGE involves nonlocal conserved quantities, which can be necessary for describing long-time behaviors of local observables. We also give some extensions of the NCGGE and demonstrate how accurately they describe the long-time behaviors of few-body observables.

We have reconstructed a vacuum ultraviolet beamline BL-7 for solid state and surface science covering a photon energy range of 10-160 eV. A set of four spherical grating are used which are designed to cover the energy range of 10-20 eV, 20-40 eV, 40-80 eV, and 80-160 eV, respectively. The lower limit of the photon energy was extended for the investigation of surface electronic structures which typically have a photoexcitation cross section maxima at 10-20 eV. The higher limit was extended for the access of many important core levels such as 2p of Si and 3s/3d of transition metals. The photon flux was evaluated by the photocurrent measurement. The energy range were greatly extended compared to that of the previous one. The spot size of the zeroth-order light at the sample surface was 1.25 mm (horizontal) x 0.32 mm (vertical). Furthermore, a newly designed display-type spherical mirror analyzer was installed at the end station.