Molecule and polaron in a highly polarized two-dimensional Fermi gas with spin-orbit coupling

We show that spin-orbit coupling (SOC) gives rise to pairing instability in a highly polarized two-dimensional Fermi gas for arbitrary interaction strength. The pairing instability can lead to a Fulde-Ferrell-Larkin-Ovchinnikov-like molecular state, which undergoes a first-order transition into a pairing state with zero center-of-mass momentum as the parameters are tuned. These pairing states are metastable against a polaron state dressed by particle-hole fluctuations for small SOC. At large SOC, a polaron-molecule transition exists, which suggests a phase transition between the topological superfluid state and the normal state for a highly polarized Fermi gas in the thermodynamic limit. As polarization in a Fermi gas with SOC is induced by the effective Zeeman field, we also discuss the influences of the effective Zeeman field on the ground state of the system. Our findings may be tested directly in future experiments.Comment: final published versio

Ergodic SDEs on submanifolds and related numerical sampling schemes

In many applications, it is often necessary to sample the mean value of certain quantity with respect to a probability measure {\mu} on the level set of a smooth function $\xi: \mathbb{R}^d\rightarrow \mathbb{R}^k$, $1\le k < d$. A specially interesting case is the so-called conditional probability measure, which is useful in the study of free energy calculation and model reduction of diffusion processes. By Birkhoff's ergodic theorem, one approach to estimate the mean value is to compute the time average along an infinitely long trajectory of an ergodic diffusion process on the level set whose invariant measure is {\mu}. Motivated by the previous work of Ciccotti, Leli\`evre, and Vanden-Eijnden [11], as well as the work of Leli\`evre, Rousset, and Stoltz [33], in this paper we construct a family of ergodic diffusion processes on the level set of $\xi$ whose invariant measures coincide with the given one. For the conditional measure, in particular, we show that the corresponding SDEs of the constructed ergodic processes have relatively simple forms, and, moreover, we propose a consistent numerical scheme which samples the conditional measure asymptotically. The numerical scheme doesn't require computing the second derivatives of $\xi$ and the error estimates of its long time sampling efficiency are obtained.Comment: 45 pages. Accepted versio

Rational a priori or Emotional a priori? Husserl and Scheler’s Criticisms of Kant Regarding the Foundation of Ethics

Based on the dispute between Protagoras and Socrates on the origin of ethics, one can ask the question of whether the principle of ethics is reason orfeeling/emotion, or whether ethics is grounded on reason or feeling/emotion. The development of Kant’s thoughts on ethics shows the tension between reason and feeling/emotion. In Kant’s final critical ethics, he held to a principle of “rational a priori.” On the one hand, this is presented as the rational a priori principle being the binding principle of judgment. On the other hand, it is presented as the doctrine of “rational fact” as the ultimate argument of his ethics. Husserl believed that Kant’s doctrine of a rational a priori totally disregarded the a priori essential laws of feeling. Like Husserl, Scheler criticized Kant’s doctrine of a rational a priori, and therefore developed his own theory of an “emotional a priori”. Both of them focused their critiques on the grounding level of ethics. Scheler, however, did not follow Husserl all the way, but criticized him and reflected on his thoughts. At last, he revealed the primary status of a phenomenological material ethics of value

Inner Mongolia's Mongol Nomads

Film of 59 mins.Filmed in about 1988 in East Ujimqin Banner, Xilingol League, Inner Mongolia Autonomous Region, PR China. This ethnographic film focuses on nadam, food preparation including dairy properties, yurts, a wedding, and death

Preen Gland-Secreted Alkanols Enhance Male Attractiveness in Parrots

The skin glands are widely used in pheromone production throughout the vertebrate worlds. Growing evidences show that birds also have chemical communication, but the uropygial (also called preen or oil) glands, serving as only specialized skin glands of birds, have no sex pheromones characterized. Here, by combining GC-MS analysis and bioassay, we show with the budgerigar, Melopsittacus undulatus, that birds can used the preen gland-secreted volatiles (a blend of octadecanol, nonadecanol and eicosanol for male budgerigars) spread over body plumage when preening to convey sex information. Here, we first report the avian pheromones derived from the uropyginal gland and suggests that the gland has broader implications than previously known (e.g. plumage waterproofing and reflectance in sexual behaviour of birds