Secular non-secular master equation

Redfield non-secular master equation governing relaxation of a spin in weak interaction with a thermal bath is studied. Using the fact that the relaxation follows the exponential law, we prove that in most cases the semi-secular approximation is sufficient to find the system relaxation rate. Based on this, a "secular" form of the non-secular master equation is for the first time developed which correctly set up one of most fundamental equations in relaxation investigation. This key secular form allows us to derive a general formula of the phonon-induced quantum tunneling rate which is valid for the entire range of temperature regardless of the basis. In incoherent tunneling regime and localized basis, this formula reduces to the ubiquitous incoherent tunneling rate. Meanwhile, in eigenstates basis, this tunneling rate is demonstrated to be equal to zero. From this secular form, we end the controversy surrounding the selection of basis for the secular approximation by figuring out the conditions for using this approximation in localized and eigenstates basis. Particularly, secular approximation in localized basis is justified in the regime of high temperature and small tunnel splittings. In contrast, a large ground doublet's tunnel splitting is required for the secular approximation in eigenstates basis. With these findings, this research lays a sound foundation for any treatments of the spin-phonon relaxation under any conditions provided that the non-secular master equation is relevant.Comment: 9 pages, 0 figure

OPTIMIZATION OF OPERATING PARAMETERS IN LNG AP-X PROCESS

Natural gas (NG) has been known as the cleanest fossil fuel since it releases low level of harmful products when being burnt. Natural gas can be transported either in pipelines or in liquefied natural gas (LNG) carriers. In LNG carriers, LNG is liquefied to the temperature of -162 degree Celsius at atmospheric pressure so that its volume can be reduced up to 600 times. There are a lot of techniques available for liquefying natural gas. The most potential technique developed by APCI is AP-X process. This is an improvement from C3MR process by using nitrogen in the subcooling loop at the end of the process. It is very beneficial to know the optimum refrigerant flow rate for the purpose of saving energy consumed in the process. Moreover, the operating refrigerant flow rate also is optimized with subject to the compensation with the compressor load and the energy efficiency. HYSYS software is utilized to model the nitrogen loop of AP-X process. LNG flow rate, compressor load and heat duties exchanged are taken from HYSYS model. In this study, the optimum pure nitrogen flow rate was found to be at around 2500 kg/h. Besides, the flow rate for 5% methane mixed refrigerant is 2375 kg/hr, so that the process is most beneficial in term of revenue as well as energy efficiency. The optimum capacity of LNG plant using AP-X process is found at 9.1 MTPA, according to around 13.5% increase in train capacity compared with the current operating train capacity in Qatar

Cosmological model with a local void and observational constraints.

Master'sMASTER OF SCIENC

OPTIMIZATION OF OPERATING PARAMETERS IN LNG AP-X PROCESS

Natural gas (NG) has been known as the cleanest fossil fuel since it releases low level of harmful products when being burnt. Natural gas can be transported either in pipelines or in liquefied natural gas (LNG) carriers. In LNG carriers, LNG is liquefied to the temperature of -162 degree Celsius at atmospheric pressure so that its volume can be reduced up to 600 times. There are a lot of techniques available for liquefying natural gas. The most potential technique developed by APCI is AP-X process. This is an improvement from C3MR process by using nitrogen in the subcooling loop at the end of the process. It is very beneficial to know the optimum refrigerant flow rate for the purpose of saving energy consumed in the process. Moreover, the operating refrigerant flow rate also is optimized with subject to the compensation with the compressor load and the energy efficiency. HYSYS software is utilized to model the nitrogen loop of AP-X process. LNG flow rate, compressor load and heat duties exchanged are taken from HYSYS model. In this study, the optimum pure nitrogen flow rate was found to be at around 2500 kg/h. Besides, the flow rate for 5% methane mixed refrigerant is 2375 kg/hr, so that the process is most beneficial in term of revenue as well as energy efficiency. The optimum capacity of LNG plant using AP-X process is found at 9.1 MTPA, according to around 13.5% increase in train capacity compared with the current operating train capacity in Qatar

Coherence/incoherence transition temperature in molecular spin

We examine the coherence/incoherence transition temperature of a generic molecular spin. Our results demonstrates that a molecular spin with a high coherence/incoherence transition temperature should possess a low spin number and low axiality, or high spin number and high axiality. Interestingly, the latter is better protected from the magnetic noises than the former and thus be the best candidate for a robust electron-based molecular spin qubit/qudit. The transition temperature can be further optimized if a large non-axial component of the spin Hamiltonian exists.Comment: 8 pages, 6 figure

Quantum tunneling of magnetization in molecular spin

We examine the quantum tunneling of magnetization in molecular spin in weak interaction with a bath subject to Redfield master equation. By designing a microscopic model for a multilevel spin system using only a generic Hamiltonian and applying stationary approximation for excited doublets/singlets, we derive a key equation of motion for the quantum tunneling of magnetization process which is applicable in the whole temperature domain. From this equation, we find that in general three tunneling rates are needed to accurately describe the quantum tunneling process. More importantly, behavior of the quantum tunneling in the intermediate temperature domain where there exists a transition between incoherent and coherent quantum tunneling is also unraveled for the first time. Limiting cases at low and high temperature and/or low magnetic field are also worked out where some popular well-known results are reproduced. Last but not least, a new interpretation of the quantum tunneling of magnetization is proposed where we reveal the similarity between this relaxation process with a driven damped harmonic oscillator.Comment: 11 pages, 5 figure

Dissipative Landau-Zener transition with decoherence rate

An innovative microscopic model with a minimal number of parameters: tunneling splitting gap, external field sweeping velocity, and decoherence rate is used to describe dynamics of the dissipative Landau-Zener transition in the presence of the decoherence. In limiting cases, the derived equation of motion gives rise to the well-known Landau-Zener and Kayanuma formula. In a general case, the description demonstrates a non-monotonic flipping probability with respect to the sweeping velocity, which is also found in some other models. This non-monotony can be explained by considering the competition and timescale of the quantum tunneling, crossing period, and decoherence process. The simplicity and robustness of the theory offer a practical and novel description of the Landau-Zener transition. In addition, it promises an alternative method to the electron paramagnetic resonance in measuring the effective decoherence rate of relevant quantum systems.Comment: 8 pages, 2 figure