Exactly solvable models and ultracold Fermi gases

Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe Ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.Comment: based on an invited talk at Statphys24, Cairns (Australia) 2010. 16 pages, 6 figure

A Robust and Artifact Resistant Algorithm of Ultrawideband Imaging System for Breast Cancer Detection.

Goal: Ultrawideband radar imaging is regarded as one of the most promising alternatives for breast cancer detection. A range of algorithms reported in literature show satisfactory tumor detection capabilities. However, most of algorithms suffer significant deterioration or even fail when the early-stage artifact, including incident signals and skin-fat interface reflections, cannot be perfectly removed from received signals. Furthermore, fibro-glandular tissue poses another challenge for tumor detection, due to the small dielectric contrast between glandular and cancerous tissues. Methods: This paper introduces a novel Robust and Artifact Resistant (RAR) algorithm, in which a neighborhood pairwise correlation-based weighting is designed to overcome the adverse effects from both artifact and glandular tissues. In RAR, backscattered signals are time-shifted, summed, and weighted by the maximum combination of the neighboring pairwise correlation coefficients between shifted signals, forming the intensity of each point within an imaging area. Results: The effectiveness was investigated using 3-D anatomically and dielectrically accurate finite-difference-time-domain numerical breast models. The use of neighborhood pairwise correlation provided robustness against artifact, and enabled the detection of multiple scatterers. RAR is compared with four well-known algorithms: delay-and-sum, delay-multiply-and-sum, modified-weighted-delay-and-sum, and filtered-delay-and-sum. Conclusion: It has shown that RAR exhibits improved identification capability, robust artifact resistance, and high detectability over its counterparts in most scenarios considered, while maintaining computational efficiency. Simulated tumors in both homogeneous and heterogonous, from mildly to moderately dense breast phantoms, combining an entropy-based artifact removal algorithm, were successfully identified and localized. Significance: These results show the strong potential of RAR for breast cancer screening

An imprecise statistical method for accelerated life testing using the power-Weibull model

Accelerated life testing provides an interesting challenge for quantification of the uncertainties involved, in particular due to the required linking of the units’ failure times, or failure time distributions, at different stress levels. This paper provides an initial exploration of the use of statistical methods based on imprecise probabilities for accelerated life testing. We apply nonparametric predictive inference at the normal stress level, in combination with an estimated parametric power-Weibull model linking observations at different stress levels. To provide robustness with regard to this assumed link between different stress levels, we introduce imprecision by considering an interval around the parameter estimate, leading to observations at stress levels other than the normal level to be transformed to intervals at the normal level. The width of such intervals is increasing with the difference between the stress level at which a unit is tested and the normal level. The resulting inference method is predictive, so it explicitly considers the random failure time of a future unit tested at the normal level. We perform simulation studies to investigate the performance of our imprecise predictive method and to get insight into a suitable amount of imprecision for the linking between levels. We also explain how simulation studies can assist in choosing imprecision in order to provide robustness against specific biases or model misspecifications

Wilson ratio of Fermi gases in one dimension

We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-component Tomonaga-Luttinger liquid (TLL) phase. The ratio exhibits anomalous enhancement at the two critical points due to the sudden change in the density of states. Despite a breakdown of the quasiparticle description in one dimension, two important features of the Fermi liquid are retained, namely the specific heat is linearly proportional to temperature whereas the susceptibility is independent of temperature. In contrast to the phenomenological TLL parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two and three dimensions.Comment: 5+2 pages, 4+1 figures, Eq. (4) is proved, figures were refine

Cooling curves for neutron stars with hadronic matter and quark matter

The thermal evolution of isothermal neutron stars is studied with matter both in the hadronic phase as well as in the mixed phase of hadronic matter and strange quark matter. In our models, the dominant early-stage cooling process is neutrino emission via the direct Urca process. As a consequence, the cooling curves fall too fast compared to observations. However, when superfluidity is included, the cooling of the neutron stars is significantly slowed down. Furthermore, we find that the cooling curves are not very sensitive to the precise details of the mixing between the hadronic phase and the quark phase and also of the pairing that leads to superfluidity.Comment: 19 pages, 25 figure

Universal local pair correlations of Lieb-Liniger bosons at quantum criticality

The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for the strong coupling Bose gas at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that the local pair correlation has the universal value $g^{(2)}(0)\approx 2 p/(n\varepsilon)$ in the quantum critical regime, the TLL phase and the quasi-classical region, where $p$ is the pressure per unit length rescaled by the interaction energy $\varepsilon=\frac{\hbar^2}{2m} c^2$ with interaction strength $c$ and linear density $n$. This suggests the possibility to test finite temperature local pair correlations for the TLL in the relativistic dispersion regime and to probe quantum criticality with the local correlations beyond the TLL phase. Furthermore, thermodynamic properties at high temperatures are obtained by both high temperature and virial expansion of the Yang-Yang thermodynamic equation.Comment: 8 pages, 6 figures, additional text and reference