Ground-state phase diagram and critical temperature of two-component Bose gases with Rashba spin-orbit coupling

Ground-state phase diagram of two-component Bose gases with Rashba spin-orbit coupling is determined via a variational approach. A phase in which the fully polarized condensate occupies zero momentum is identified. This zero-momentum phase competes with the spin density wave phase when interspecies interaction is stronger than intraspecies interaction, and the former one is always the ground state for weak spin-orbit coupling. When the energies of these two phases are close, there is a phase separation between them. At finite temperature, such a zero-momentum condensation can be induced by a ferromagnetic phase transition in normal state. The spontaneous spin polarization removes the degeneracy of quasiparticles' energy minima, and consequently the modified density of state accommodates a Bose condensation to appear below a critical temperature.Comment: 5 pages, 3 figures, final versio

Equation of state and phase transition in spin-orbit-coupled Bose gases at finite temperature: A perturbation approach

We study two-component Bose gases with Raman induced spin-orbit coupling via a perturbation approach at finite temperature. For weak coupling, free energy is expanded in terms of Raman coupling strength up to the second order, where the coefficient (referred to as Raman susceptibility) is determined according to linear response theory. The equation of state for the stripe phase and the plane-wave phase are obtained in Popov approximation, and the first order transition between these two phases is investigated. As temperature increases, we find the phase boundary bends toward the stripe phase side in most temperature regions, which implies the ferromagnetic order is more robust than the crystalline order in presence of thermal fluctuations. Our results qualitatively agree with the recent experimental observation in rubidium atomic gases. A method to measure the Raman susceptibility through the two-photon Bragg scattering experiment is also discussed.Comment: 7 pages, 5 figures; published in Phys. Rev.

Phase transitions and elementary excitations in spin-1 Bose gases with Raman-induced spin-orbit coupling

We study the ground state phase diagram and the quantum phase transitions in spin-1 Bose gases with Raman induced spin-orbit coupling. In addition to the Bose-Einstein condensates with uniform density, three types of stripe condensation phases that simultaneously break the U(1) symmetry and the translation symmetry are identified. The transitions between these phases are investigated, and the occurrences of the various tricritical points are predicted. The excitation spectra in the plane-wave phase and the zero-momentum phase show rich roton-maxon structures, and their instabilities indicate the tendency to develop the crystalline order. We propose the atomic gas of $^{23}$Na could be a candidate for observing the stripe condensate with high contrast fringes.Comment: 10 pages, 8 figures, published versio

Effects of Radial Distances on Small-scale Magnetic Flux Ropes in the Solar Wind

Small-scale magnetic flux ropes (SFRs), in the solar wind, have been studied for decades. Statistical analysis utilizing various in situ spacecraft measurements is the main observational approach which helps investigate the generation and evolution of these small-scale structures. Based on the Grad-Shafranov (GS) reconstruction technique, we use the automated detection algorithm to build the databases of these small-scale structures via various spacecraft measurements at different heliocentric distances. We present the SFR properties including the magnetic field and plasma parameters at different radial distances from the sun near the ecliptic plane. It is found that the event occurrence rate is still in the order of a few hundreds per month, the duration and scale size distributions follow power laws, and the flux rope axis orientations are approximately centered around the local Parker spiral directions. In general, most SFR properties exhibit radial decays. In addition, with various databases established, we derive scaling laws for the changes of average field magnitude, event counts, and SFR scale sizes, with respect to the radial distances, ranging from $\sim$ 0.3 au for Helios to $\sim$ 7 au for the Voyager spacecraft. The implications of our results for comparisons with the relevant theoretical works and for the application to the Parker Solar Probe (PSP) mission are discussed.Comment: Accepted by ApJ (22 March

A Survey on Multi-Task Learning

Multi-Task Learning (MTL) is a learning paradigm in machine learning and its aim is to leverage useful information contained in multiple related tasks to help improve the generalization performance of all the tasks. In this paper, we give a survey for MTL. First, we classify different MTL algorithms into several categories, including feature learning approach, low-rank approach, task clustering approach, task relation learning approach, and decomposition approach, and then discuss the characteristics of each approach. In order to improve the performance of learning tasks further, MTL can be combined with other learning paradigms including semi-supervised learning, active learning, unsupervised learning, reinforcement learning, multi-view learning and graphical models. When the number of tasks is large or the data dimensionality is high, batch MTL models are difficult to handle this situation and online, parallel and distributed MTL models as well as dimensionality reduction and feature hashing are reviewed to reveal their computational and storage advantages. Many real-world applications use MTL to boost their performance and we review representative works. Finally, we present theoretical analyses and discuss several future directions for MTL

Inverse Photoelectrochemical Cell

The splitting of water with sunlight using photoelectrochemical cell (PEC) to produce hydrogen is a promising avenue for sustainable energy production. The greatest virtue of PEC is that it uses sunlight as the only source to split water, but its efficiencies are still quite low due to poor performances of the available materials (such as SrTiO3). Consequently, another way of PEC research has been developed. By simultaneously using sunlight and electricity as energy source, PEC can get a larger current at a lower voltage, i.e., hydrogen can be made under the voltage below 1.23V, the minimum voltage required by electrolysis of water. But so far the efficiencies of the mainstream materials (such as TiO2) remain low. Where is the future development direction of PEC? Here we propose a new PEC model. Its operating principle is quite the opposite of the aforesaid conventional PEC, that is, the previous photoanode/photocathode is converted into the present photocathode/photoanode. It can also obtain high current under low voltage, even near zero voltage in extreme conditions. A basic single configuration and an improved n-p configuration were designed. We reselected materials for photoelectrodes, and confirmed its feasibility successfully. Two preliminary results were obtained from two contrasts: whether compared with water electrolysis or conventional PEC water splitting, the inverse PEC showed promising superiority.Comment: 11 pages, 5 figure

Layer-by-layer assembly of colloidal particles deposited onto the polymer-grafted elastic substrate

We demonstrate a novel route of spatially organizing the colloid arrangements on the polymer-grafted substrate by use of self-consistent field and density functional theories. We find that grafting of polymers onto a substrate can effectively control spatial dispersions of deposited colloids as a result of the balance between colloidal settling force and entropically elastic force of brushes, and colloids can form unexpected ordered structures on a grafting substrate. The depositing process of colloidal particles onto the elastic "soft" substrate includes two steps: brush-mediated one-dimensional arrangement of colloidal crystals and controlled layer-by-layer growth driven entropically by non-adsorbing polymer solvent with increasing the particles. The result indicates a possibility for the production of highly ordered and defect-free structures by simply using the grafted substrate instead of periodically patterned templates, under appropriate selection of colloidal size, effective depositing potential, and brush coverage density

Interactions between colloidal particles induced by polymer brushes grafted onto the substrate

We investigate the interaction energy between two colloidal particles on or immersed in nonadsorbing polymer brushes grafted onto the substrate as a function of the separation of the particles by use of self-consistent field theory calculation. Depending on the colloidal size and the penetration depth, we demonstrate an existence of repulsive energy barrier of several $k_{B}T$, which can be interpreted by separating the interaction energy into three parts: colloids-polymer interfacial energy, entropic contribution due to ``depletion zone" overlap of colloidal particles, and entropically elastic energy of grafted chains by compression of particles. The existence of repulsive barrier which is of entirely entropic origin, can lead to kinetic stabilization of the mixture rather than depletion flocculation or phase separation. Therefore, the present result may suggest an approach to control the self-assembling behavior of colloids for the formation of target structures, by tuning the colloidal interaction on the grafting substrate under appropriate selection of colloidal size, effective gravity (influencing the penetration depth), and brush coverage density

Origin of fermion generations from extended noncommutative geometry

We propose a way to understand the 3 fermion generations by the algebraic structures of noncommutative geometry, which is a promising framework to unify the standard model and general relativity. We make the tensor product extension and the quaternion extension on the framework. Each of the two extensions alone keeps the action invariant, and we consider them as the almost trivial structures of the geometry. We combine the two extensions, and show the corresponding physical effects, i.e., the emergence of 3 fermion generations and the mass relationships among those generations. We define the coordinate fiber space of the bundle of the manifold as the space in which the classical noncommutative geometry is expressed, then the tensor product extension explicitly shows the contribution of structures in the non-coordinate base space of the bundle to the action. The quaternion extension plays an essential role to reveal the physical effect of the structure in the non-coordinate base space.Comment: 17 latex pages, no figure. Final version for publicatio

Propagation Phenomena for A Reaction-Advection-Diffusion Competition Model in A Periodic Habitat

This paper is devoted to the study of propagation phenomena for a Lotka-Volterra reaction-advection-diffusion competition model in a periodic habitat. We first investigate the global attractivity of a semi-trival steady state for the periodic initial value problem. Then we establish the existence of the rightward spreading speed and its coincidence with the minimal wave speed for spatially periodic rightward traveling waves. We also obtain a set of sufficient conditions for the rightward spreading speed to be linearly determinate. Finally, we apply the obtained results to a prototypical reaction-diffusion model