A mean field theory for the spin ladder system

In the present paper, we propose a mean field approach for spin ladders based upon the Jordan-Wigner transformation along an elaborately ordered path. We show on the mean field level that ladders with even number legs open a energy gap in their low energy excitation with a magnitude close to the corresponding experimental values, whereas the low energy excitation of the odd-number-leg ladders are gapless. It supports the validity of our approach. We then calculate the gap size and the excitation spectra of 2-leg-ladder system. Our result is in good agreement with both the experimental data and the numerical results.Comment: 14 pages,6 figure. submitted to Physical Review

Introduction

If Hong Kong were easy to simplify, this would have simplified things. Who is a ‘native’ resident? Or, to put the question another way, who is a ‘Hong Kong people’, a common second-language error here that raises interesting and rather profound questions when one unpacks the meaning underneath the Chinglish. Can people other than Cantonese-speaking Chinese fit the definition? Questions like these, as they have played out in the courts and the media, have led to shouting in the streets. And without the editors explicitly naming identity as a focus of this book (it is, after all, a fiction anthology, not a collection of essays in one of the social sciences), identity manifested as a theme in every story we accepted and quite a few that we did not

Bulk flow scaling for turbulent channel and pipe flows

We report a theory deriving bulk flow scaling for canonical wall-bounded flows. The theory accounts for the symmetries of boundary geometry (flat plate channel versus circular pipe) by a variational calculation for a large-scale energy length, which characterizes its bulk flow scaling by a simple exponent, i.e. $m=4$ for channel and 5 for pipe. The predicted mean velocity shows excellent agreement with several dozen sets of quality empirical data for a wide range of the Reynolds number (Re), with a universal bulk flow constant $\kappa\approx0.45$. Predictions for dissipation and turbulent transport in the bulk flow are also given, awaiting data verification.Comment: 4 pages, 4 figure