Density and Spin Linear Response of Atomic Fermi Superfluids with Population Imbalance in BCS-BEC Crossover

We present a theoretical study of the density and spin (representing the two components) linear response of Fermi superfluids with tunable attractive interactions and population imbalance. In both linear response theories, we find that the fluctuations of the order parameter must be treated on equal footing with the gauge transformations associated with the symmetries of the Hamiltonian so that important constraints including various sum rules can be satisfied. Both theories can be applied to the whole BCS-Bose-Einstein condensation crossover. The spin linear responses are qualitatively different with and without population imbalance because collective-mode effects from the fluctuations of the order parameter survive in the presence of population imbalance, even though the associated symmetry is not broken by the order parameter. Since a polarized superfluid becomes unstable at low temperatures in the weak and intermediate coupling regimes, we found that the density and spin susceptibilities diverge as the system approaches the unstable regime, but the emergence of phase separation preempts the divergence.Comment: 15 pages, 5 figure

Adaptive Circuit Learning of Born Machine: Towards Realization of Amplitude Embedding and Data Loading

With the progress in the quantum algorithm in recent years, much of the existing literature claims the exponential quantum advantage against their classical counterpart. However, many of these successes hinge on the assumption that arbitrary states can be efficiently prepared in quantum circuits. In reality, crafting a circuit to prepare a generic $n$-qubit quantum state demands an operation count on the order of $\mathcal{O}(2^n)$, which is prohibitively demanding for the quantum algorithm to demonstrate its advantage against the classical one. To tackle this data-loading problem, numerous strategies have been put forward. Nonetheless, most of these approaches only consider a very simple and easy-to-implement circuit structure, which has been shown to suffer from serious optimization issues. In this study, we harness quantum circuits as Born machines to generate probability distributions. Drawing inspiration from methods used to investigate electronic structures in quantum chemistry and condensed matter physics, we present a novel algorithm "Adaptive Circuit Learning of Born Machine" (ACLBM) that dynamically expands the ansatz circuit. Our algorithm is tailored to selectively integrate two-qubit entangled gates that best capture the complex entanglement present within the target state. Empirical results underscore the proficiency of our approach in encoding real-world data through amplitude embedding, demonstrating not only compliance with but also enhancement over the performance benchmarks set by previous research.Comment: 14 pages, 11 figures, 1 tabl

LED Lighting System Reliability Modeling and Inference via Random Effects Gamma Process and Copula Function

Light emitting diode (LED) lamp has attracted increasing interest in the field of lighting systems due to its low energy and long lifetime. For different functions (i.e., illumination and color), it may have two or more performance characteristics. When the multiple performance characteristics are dependent, it creates a challenging problem to accurately analyze the system reliability. In this paper, we assume that the system has two performance characteristics, and each performance characteristic is governed by a random effects Gamma process where the random effects can capture the unit to unit differences. The dependency of performance characteristics is described by a Frank copula function. Via the copula function, the reliability assessment model is proposed. Considering the model is so complicated and analytically intractable, the Markov chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about actual LED lamps data is given to demonstrate the usefulness and validity of the proposed model and method

Effects of aromatizable and nonaromatizable androgens on the sex inversion of red-spotted grouper (Epinephelus akaara)

The effects of aromatizable 17α-methyltestosterone (MT) and non-aromatizable 17α-methyldihydrotestosterone (MDHT) on sex inversion in red-spotted grouper, Epinephelus akaara, were investigated. Fish were implanted with MT, MDHT and MT+AI (aromatase inhibitor, AI) respectively for one month. The results showed that the three treated groups turned into transitional stage with intersex gonads, which contained atretic oocytes and spermatogenic germ cells at all stages of spermatogenesis. The controls did not change sex. The gonads of more than half MT-implanted fish were in early transitional stages of sex inversion, whereas those of more than half MDHT and MT+AI-implanted fish were in late transitional stages of sex inversion. No difference in serum estradiol-17β (E2) levels between the controls and the treated groups were observed, whereas 11-ketotestosterone (11-KT) and testosterone (T) levels increased in all treated groups. Significantly lower gonadosomatic index (GSI) and gonadal aromatase activity were observed in the treated groups, which were in accordance with the lower mRNA expression of P450aromA. However, P450aromB mRNA expression increased in the MT group, while it did not change in the MDHT group. These results suggest that the sex inversion of red-spotted grouper by MT and MDHT implantation might be due to the suppression of P450aromA gene expression, and resulting in both the decrease of the ovarian estrogen –secretion, as well as the increase in the 11-KT levels. Furthermore, the main reason for MT being less effective than MDHT might be due to partial aromatization of MT to estrogen

General displacement arch-cantilever element method for stress analysis of arch dam

AbstractBased on the general displacement method and the basic hypothesis of the trial load method, a new advanced trial load method, the general displacement arch-cantilever element method, was proposed to derive the transformation relation of displacements and loads between the surface nodes and middle plane nodes. This method considers the nodes on upstream and downstream surfaces of the arch dam to be exit nodes (master nodes), and the middle plane nodes to be slave nodes. According to the derived displacement and load transformation matrices, the equilibrium equation treating the displacement of middle plane nodes as a basic unknown variable is transformed into one that treats the displacement of upstream and downstream nodes as a basic unknown variable. Because the surface nodes have only three degrees of freedom (DOF), this method can be directly coupled with the finite element method (FEM), which is used for foundation simulation to analyze the stress of the arch dam with consideration of dam-foundation interaction. Moreover, using the FEM, the nodal load of the arch dam can be easily obtained. Case studies of a typical cylindrical arch dam and the Wudongde arch dam demonstrate the robustness and feasibility of the proposed method

Single-photon transport and mechanical NOON state generation in microcavity optomechanics

We investigate the single-photon transport in a single-mode optical fiber coupled to an optomechanical system in the single-photon strong-coupling regime. The single-photon transmission amplitude is analytically obtained with a real-space approach and the effects of thermal noises are studied via master-equation simulations. The results provide an explicit understanding of optomechanical interaction and offer a useful guide for manipulating single photons in optomechanical systems. Based on the theoretical framework, we further propose a scheme to generate the mechanical NOON states with arbitrary phonon numbers by measuring the sideband photons. The probability for generating the NOON state with five phonons is over 0.15.Comment: 13 pages, 6 figure

Observation of Majorana fermions with spin selective Andreev reflection in the vortex of topological superconductor

Majorana fermion (MF) whose antiparticle is itself has been predicted in condensed matter systems. Signatures of the MFs have been reported as zero energy modes in various systems. More definitive evidences are highly desired to verify the existence of the MF. Very recently, theory has predicted MFs to induce spin selective Andreev reflection (SSAR), a novel magnetic property which can be used to detect the MFs. Here we report the first observation of the SSAR from MFs inside vortices in Bi2Te3/NbSe2 hetero-structure, in which topological superconductivity was previously established. By using spin-polarized scanning tunneling microscopy/spectroscopy (STM/STS), we show that the zero-bias peak of the tunneling differential conductance at the vortex center is substantially higher when the tip polarization and the external magnetic field are parallel than anti-parallel to each other. Such strong spin dependence of the tunneling is absent away from the vortex center, or in a conventional superconductor. The observed spin dependent tunneling effect is a direct evidence for the SSAR from MFs, fully consistent with theoretical analyses. Our work provides definitive evidences of MFs and will stimulate the MFs research on their novel physical properties, hence a step towards their statistics and application in quantum computing.Comment: 4 figures 15 page