Landau-Zener Formula in a "Non-Adiabatic" regime for avoided crossings

We study a two-level transition probability for a finite number of avoided crossings with a small interaction. Landau-Zener formula, which gives the transition probability for one avoided crossing as $e^{-\pi\frac{\varepsilon^{2}}{h}}$, implies that the parameter $h$ and the interaction $\varepsilon$ play an opposite role when both tend to $0$. The exact WKB method produces a generalization of that formula under the optimal regime $\frac{h}{\varepsilon^2}$ tends to~0. In this paper, we investigate the case $\frac{\varepsilon^2}{h}$ tends to 0, called "non-adiabatic" regime. This is done by reducing the associated Hamiltonian to a microlocal branching model which gives us the asymptotic expansions of the local transfer matrices.Comment: 52 pages, 4 figures, accepted in Analysis and Mathematical Physics on 26 February 202

Zero Leakage Compressor Seals

Case StudiesDry gas seal is applied to refrigeration compressor. Some of configurations for dry gas seal system are shown in API 617 and 614, however those systems are designed with condition that leak gas from dry gas seal is released to atmosphere or flare system. In order to minimize emissions and refrigerant make up, this paper introduces the development of new concept of leakage recovery system by distillation column (process patented), and provides verification test results