Spin-Orbit Coupled Fermi Gases across a Feshbach Resonance

In this letter we study both ground state properties and the superfluid transition temperature of a spin-1/2 Fermi gas across a Feshbach resonance with a synthetic spin-orbit coupling, using mean-field theory and exact solution of two-body problem. We show that a strong spin-orbit coupling can significantly enhance the pairing gap for 1/(k_F a_s)<=0 due to increased density-of-state. Strong spin-orbit coupling also significantly enhances the superfluid transition temperature when 1/(k_F a_s)<=0, while suppresses it slightly when 1/(k_F a_s)>0. The universal interaction energy and pair size at resonance are also discussed.Comment: 4+3 pages, 4 figures, supplementary material adde

Stability Condition of a Strongly Interacting Boson-Fermion Mixture across an Inter-Species Feshbach Resonance

We study the properties of dilute bosons immersed in a single component Fermi sea across a broad boson-fermion Feshbach resonance. The stability of the mixture requires that the bare interaction between bosons exceeds a critical value, which is a universal function of the boson-fermion scattering length, and exhibits a maximum in the unitary region. We calculate the quantum depletion, momentum distribution and the boson contact parameter across the resonance. The transition from condensate to molecular Fermi gas is also discussed.Comment: 4 pages, 4 figure

Application Potential of Solar PV, Wind and Fuel Cells Technologies for Global Sustainability Improvement

This dissertation develops a systematic approach to comprehensively investigate the application potential of Solar PV, wind and fuel cells in reducing GHGs emissions for energy intensive global manufacturing industry. This systematic approach is developed by integrating the technological and economic characteristics of the clean energy technologies, as well as the local geographic conditions where the clean energy technologies may be deployed. This approach consists of the investigation on such aspects as: technological feasibility, capacity factor, FIT strength, Levelized energy cost, cost benefit and sensitivity. In this dissertation, the systematic approach developed is applied on the application potential analyses of solar PV, wind and fuel cells technologies in reducing GHGs for the global automotive manufacturers, at six global locations including Detroit, Mexico City, Sao Paulo, Shanghai, Cairo and Bochum. For the application potential of these three clean energy technologies in reducing GHGs emissions, the technological feasibility, capacity factor, Levelized energy cost, cost benefit and sensitivity analysis are conducted with different geographic and economic parameters. The cost benefit trends of solar PV, wind and fuel cells in reducing GHGs emissions from 2010-2035 are projected by using this developed approach, with the assumptions of two virtual cost cases. This approach is applied on the cost benefit range analysis in six selected countries to investigate the uncertainty of the GHGs reduction cost benefit due to the geographic difference. Potential cost benefit maps on GHGs emission reduction in the nationwide of the US lower 48 states are generated by using this systematic approach. The sensitivity analysis is applied for the solar PV and wind energies to investigate the linear relevance of different geographic and economic parameters with the cost benefit performance. In the FIT strength analysis of the case study, different geographic locations are selected due to the lack of data. This dissertation concludes with discussions on the application potential of three clean energy technologies at different global locations in reducing GHGs emission for global manufacturing industry. As there is lack of information support on the selection of appropriate clean energy technologies at specific locations to achieve GHGs emission reduction, this approach developed provides a comprehensive support for decision making

Bounded Projection Matrix Approximation with Applications to Community Detection

Community detection is an important problem in unsupervised learning. This paper proposes to solve a projection matrix approximation problem with an additional entrywise bounded constraint. Algorithmically, we introduce a new differentiable convex penalty and derive an alternating direction method of multipliers (ADMM) algorithm. Theoretically, we establish the convergence properties of the proposed algorithm. Numerical experiments demonstrate the superiority of our algorithm over its competitors, such as the semi-definite relaxation method and spectral clustering

Research on Optimizing National Mental Health Literacy from the Perspective of Health in China: Significance and Approach

Improving the level of national mental health and strengthening the construction of social psychological service system are the necessary and important ways to promote the implementation of the Healthy China strategy. However, the gap between the requirements of Healthy China strategy for social mental health service system and the current situation of mental health service in China is still widespread. Promoting the public to form an effective demand for psychological help and establishing a new mental health service model is the key to bridge this gap. Optimizing mental health literacy is an important starting point and breakthrough to solve this problem. At present, the research on mental health literacy is undergoing a transformation from the paradigm of psycho-epidemiology to the paradigm of psychology and sociology. Taking contemporary China as the background, the reconceptualization of mental health literacy and the exploration of the current situation of Chinese mental health literacy in the new era is one of the core task of current psychological path research. The significance of this study is mainly reflected in: (1) promote the formation of effective demand for help and improve the level of public mental health; (2) enhance cultural selfconfidence and construct the theory of mental health literacy of contemporary Chinese people; (3) guide the supply side structural reform of mental health services and promote mental health equity; (4) reduce the burden of mental illness and help build a well-off society in an all-round way; (5) help build a social and psychological service system

Spin Glass Correlation Length: a Caliper for Temperature Chaos

The spin glass correlation length is used as a caliper for the onset of temperature chaos in a Cu$_{0.94}$Mn$_{0.06}$ single crystal sample. From the values of the correlation length at different temperatures, we are able to calibrate the onset of the transition from reversible to chaotic behavior. We find that temperature chaos sets in abruptly as the chaos length scale $L^*$ becomes comparable to the spin glass correlation length $\xi$. We find the chaotic exponent for temperature chaos, $\zeta$, to be the order of unity assuming either fractal or compact glassy domains, in good agreement with previous theoretical analyses and numerical simulations

Accretion of the relativistic Vlasov gas onto a Kerr black hole

We study the accretion of relativistic Vlasov gas onto a Kerr black hole, regarding the particles as distributed throughout all the space, other than just in the equatorial plane. We solve the relativistic Liouville equation in the full $3+1$ dimensional framework of Kerr geometry. For the flow that is stationary and axial symmetric, we prove that the distribution function is independent of the conjugate coordinates. For an explicit distribution that can approximate to Maxwell-J\"{u}ttner distribution, we further calculate the particle current density, the stress energy momentum tensor and the unit accretion rates of mass, energy and angular momentum. The analytic results at large distance are shown to be consistent with the limits of the numerical ones computed at finite distance. Especially, we show that the unit mass accretion rate agrees with the Schwarzschild result in the case of low temperature limit. Furthermore, we find from the numerical results that the three unit accretion rates vary with the angle in Kerr metric and the accretion of Vlasov gas would slow down the Kerr black hole. The closer to the equator, the faster it slows down the black hole.Comment: 28 pages, 11 figures, accepted for publication in Physical Review