Universal impurity-induced bound state in topological superfluids

We predict a universal mid-gap bound state in topological superfluids, induced by either non-magnetic or magnetic impurities in the strong scattering limit. This universal state is similar to the lowest-energy Caroli-de Gennes-Martricon bound state in a vortex core, but is bound to localized impurities. We argue that the observation of such a universal bound state can be a clear signature for identifying topological superfluids. We theoretically examine our argument for a spin-orbit coupled ultracold atomic Fermi gas trapped in a two-dimensional harmonic potential, by performing extensive self-consistent calculations within the mean-field Bogoliubov-de Gennes theory. A realistic scenario for observing universal bound state in ultracold $^{40}$K atoms is proposed.Comment: 5 pages + 4 figures; published in PRL; see the relevant study in 1D: Phys. Rev. A 87, 013622 (2013); see also the accompanying Physics Synopsis: http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.02040

Duopoly innovation under product externalities

This study argues that product substitutability and complementary have major effects on the relationship between innovation and competition and some interesting conclusions are derived. First, innovative investment is reduced with market power. The total quantity of products and social welfare are increased with market power while decreased with increasing of substitutability or deceasing of complementary. Second, the equilibrium products and innovative investment are lower than those under social optimality. Finally, by comparison with Cournot quantity competition, Bertrand price competition is keener. But the main conclusions are the same under both kinds of competitions

A New Approach to Constrain Black Hole Spins in Active Galaxies Using Optical Reverberation Mapping

A tight relation between the size of the broad-line region (BLR) and optical luminosity has been established in about 50 active galactic nuclei studied through reverberation mapping of the broad Hbeta emission line. The R_blr-L relation arises from simple photoionization considerations. Using a general relativistic model of an optically thick, geometrically thin accretion disk, we show that the ionizing luminosity jointly depends on black hole mass, accretion rate, and spin. The non-monotonic relation between the ionizing and optical luminosity gives rise to a complicated relation between the BLR size and the optical luminosity. We show that the reverberation lag of Hbeta to the varying continuum depends very sensitively to black hole spin. For retrograde spins, the disk is so cold that there is a deficit of ionizing photons in the BLR, resulting in shrinkage of the hydrogen ionization front with increasing optical luminosity, and hence shortened Hbeta lags. This effect is specially striking for luminous quasars undergoing retrograde accretion, manifesting in strong deviations from the canonical R_blr-L relation. This could lead to a method to estimate black hole spins of quasars and to study their cosmic evolution. At the same time, the small scatter of the observed R_blr-L relation for the current sample of reverberation-mapped active galaxies implies that the majority of these sources have rapidly spinning black holes.Comment: 6 pages, 5 figures, to appear in ApJ

Nonadiabatic Holonomic Quantum Computation and Its Optimal Control

Geometric phase has the intrinsic property of being resistant to some types of local noises as it only depends on global properties of the evolution path. Meanwhile, the non-Abelian geometric phase is in the matrix form, and thus can naturally be used to implement high performance quantum gates, i.e., the so-called holonomic quantum computation. This article reviews recent advances in nonadiabatic holonomic quantum computation, and focuses on various optimal control approaches that can improve the gate performance, in terms of the gate fidelity and robustness. Besides, we also pay special attention to its possible physical realizations and some concrete examples of experimental realizations. Finally, with all these efforts, within state-of-the-art technology, the performance of the implemented holonomic quantum gates can outperform the conventional dynamical ones, under certain conditions

Effects of celebrity endorsement on firms’ competition: from industrial organisation perspective

Product endorsement is employed by many firms and most studies have proceeded based on management perspectives and ignored the strategic effects (or indirect effects). However, as a non-price competition, product endorsement behaviour’s strategic effects are valuable to be considered and convenient to be captured by industrial organisation perspective. So, this paper’s purpose is to reveal the strategic effects of product endorsement by industrial organisation perspective. First, the results of this paper show that celebrity endorsement decreases the rival’s benefits. Second, under a unique endorser, the lower efficiency (measured by marginal production cost) firm’s celebrity endorsement improves price difference and dispersion, which are direct effects of product endorsement. The higher efficiency firm’s endorsement promotes the producer surplus, consumer surplus and social welfare, which are called indirect effects. Finally, celebrity endorsement has trigger effects. If one firm launches celebrity endorsement, the rational reaction for its rivals is also to engage in a similar behaviour. This paper expands the celebrity endorsement issue from management to economics perspective

Risk factors and survival prediction of young breast cancer patients with liver metastases: a population-based study

BackgroundThe risk and prognosis of young breast cancer (YBC) with liver metastases (YBCLM) remain unclear. Thus, this study aimed to determine the risk and prognostic factors in these patients and construct predictive nomogram models.MethodsThis population-based retrospective study was conducted using data of YBCLM patients from the Surveillance, Epidemiology, and End Results database between 2010 and 2019. Multivariate logistic and Cox regression analyses were used to identify independent risk and prognostic factors, which were used to construct the diagnostic and prognostic nomograms. The concordance index (C-index), calibration plot, receiver operating characteristic (ROC) curve, and decision curve analysis (DCA) were used to assess the performances of the established nomogram models. Propensity score matching (PSM) analysis was used to balance the baseline characteristics between the YBCLM patients and non-young patients with BCLM when comparing overall survival (OS) and cancer-specific survival (CSS).ResultsA total of 18,275 YBC were identified, of whom 400 had LM. T stage, N stage, molecular subtypes, and bone, lung, and brain metastases were independent risk factors for LM developing in YBC. The established diagnostic nomogram showed that bone metastases contributed the most risk of LM developing, with a C-index of 0.895 (95% confidence interval 0.877–0.913) for this nomogram model. YBCLM had better survival than non-young patients with BCLM in unmatched and matched cohorts after propensity score matching analysis. The multivariate Cox analysis demonstrated that molecular subtypes, surgery and bone, lung, and brain metastases were independently associated with OS and CSS, chemotherapy was an independent prognostic factor for OS, and marital status and T stage were independent prognostic factors for CSS. The C-indices for the OS- and CSS-specific nomograms were 0.728 (0.69–0.766) and 0.74 (0.696–0.778), respectively. The ROC analysis indicated that these models had excellent discriminatory power. The calibration curve also showed that the observed results were consistent with the predicted results. DCA showed that the developed nomogram models would be effective in clinical practice.ConclusionThe present study determined the risk and prognostic factors of YBCLM and further developed nomograms that can be used to effectively identify high-risk patients and predict survival outcomes

Single Impurity In Ultracold Fermi Superfluids

The role of impurities as experimental probes in the detection of quantum material properties is well appreciated. Here we study the effect of a single classical magnetic impurity in trapped ultracold Fermi superfluids. Depending on its shape and strength, a magnetic impurity can induce single or multiple mid-gap bound states in a superfluid Fermi gas. The multiple mid-gap states could coincide with the development of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase within the superfluid. As an analog of the Scanning Tunneling Microscope, we propose a modified RF spectroscopic method to measure the local density of states which can be employed to detect these states and other quantum phases of cold atoms. A key result of our self consistent Bogoliubov-de Gennes calculations is that a magnetic impurity can controllably induce an FFLO state at currently accessible experimental parameters.Comment: 5 pages, 3 figures; added calculations for 3