Relaxation rates and collision integrals for Bose-Einstein condensates

Near equilibrium, the rate of relaxation to equilibrium and the transport properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC) are determined by three collision integrals, $\mathcal{G}^{12}$, $\mathcal{G}^{22}$, and $\mathcal{G}^{31}$. All three collision integrals conserve momentum and energy during bogolon collisions, but only $\mathcal{G}^{22}$ conserves bogolon number. Previous works have considered the contribution of only two collision integrals, $\mathcal{G}^{22}$ and $\mathcal{G}^{12}$. In this work, we show that the third collision integral $\mathcal{G}^{31}$ makes a significant contribution to the bogolon number relaxation rate and needs to be retained when computing relaxation properties of the BEC. We provide values of relaxation rates in a form that can be applied to a variety of dilute Bose-Einstein condensates.Comment: 18 pages, 4 figures, accepted by Journal of Low Temperature Physics 7/201

Determinants of sustainability of ski resorts: do size and altitude matter?

© 2018, © 2018 European Association for Sport Management. Research questions: The research questions are aimed at increasing knowledge about ski resorts’ sustainability. Achieving and maintaining sustainable operations and meeting sustainability requirements may be more important for some resorts than others. RQ1: Which sustainability indicators are part of pillars and requirements of ski resort sustainability? RQ2: Which types of ski resorts are more effective in managing sustainability? Research methods: A survey of ski resort managers from Europe and North America was undertaken. Principal component analysis was conducted on each of the pillars and requirements of sustainability of ski resorts. Identified factors were then inputted into Kruskal–Wallis and Mann–Whitney U tests to search for differences between resorts with different lengths of pistes and altitudes. Finally, clustering was used to further define which types of ski resorts exhibit more sustainable behavior. Results and Findings: This study shows that larger ski resorts are capable of producing lesser environmental effect per visitor. Higher altitude forces ski resorts to behave more sustainably. There is a clear indication that resorts with longer pistes and higher altitudes are more inclined to implement sustainability management practices and enjoy higher quality environments. Implications: The results advance our knowledge of ski tourism and recreation as a special interest market segment as well as its potential for policy to support sustainable mountain tourism development. Identified advantages and situational conditions to be taken into account for efficient ski resort operations are discussed. A major policy implication of the present study is that big is not always bad when managing a ski resort