The evolution of the magnetic inclination angle as an explanation of the long term red timing-noise of pulsars

We study the possibility that the long term red timing-noise in pulsars originates from the evolution of the magnetic inclination angle $\chi$. The braking torque under consideration is a combination of the dipole radiation and the current loss. We find that the evolution of $\chi$ can give rise to extra cubic and fourth-order polynomial terms in the timing residuals. These two terms are determined by the efficiency of the dipole radiation, the relative electric-current density in the pulsar tube and $\chi$. The following observation facts can be explained with this model: a) young pulsars have positive $\ddot{\nu}$; b) old pulsars can have both positive and negative $\ddot{\nu}$; c) the absolute values of $\ddot{\nu}$ are proportional to $-\dot{\nu}$; d) the absolute values of the braking indices are proportional to the characteristic ages of pulsars. If the evolution of $\chi$ is purely due to rotation kinematics, then it can not explain the pulsars with braking index less than 3, and thus the intrinsic change of the magnetic field is needed in this case. Comparing the model with observations, we conclude that the drift direction of $\chi$ might oscillate many times during the lifetime of a pulsar. The evolution of $\chi$ is not sufficient to explain the rotation behavior of the Crab pulsar, because the observed $\chi$ and $\dot{\chi}$ are inconsistent with the values indicated from the timing residuals using this model.Comment: 5 pages, 1 figure. Accepted for publication in MNRA

Tuning Feshbach resonance in cold atomic gases with inter-channel coupling

We show that the essential properties of a Feshbach resonance in cold atomic gases can be tuned by dressing the atomic states in different scattering channels through inter-channel couplings. Such a scheme can be readily implemented in the orbital Feshbach resonance of alkaline-earth-like atoms by coupling hyperfine states in the clock-state manifolds. Using $^{173}$Yb atoms as an example, we find that both the resonance position and the two-body bound-state energy depend sensitively on the inter-channel coupling strength, which offers control parameters in tuning the inter-atomic interactions. We also demonstrate the dramatic impact of the dressed Feshbach resonance on many-body processes such as the polaron to molecule transition and the BCS-BEC crossover.Comment: 6 pages, 4 figure

Two-body bound state of ultracold Fermi atoms with two-dimensional spin-orbit coupling

In a recent experiment, a two-dimensional spin-orbit coupling (SOC) was realized for fermions in the continuum [Nat. Phys. 12, 540 (2016)], which represents an important step forward in the study of synthetic gauge field using cold atoms. In the experiment, it was shown that a Raman-induced two-dimensional SOC exists in the dressed-state basis close to a Dirac point of the single-particle spectrum. By contrast, the short-range inter-atomic interactions of the system are typically expressed in the hyperfine-spin basis. The interplay between synthetic SOC and interactions can potentially lead to interesting few- and many-body phenomena but has so far eluded theoretical attention. Here we study in detail properties of two-body bound states of such a system. We find that, due to the competition between SOC and interaction, the stability region of the two-body bound state is in general reduced. Particularly, the threshold of the lowest two-body bound state is shifted to a positive, SOC-dependent scattering length. Furthermore, the center-of-mass momentum of the lowest two-body bound state becomes nonzero, suggesting the emergence of Fulde-Ferrell pairing states in a many-body setting. Our results reveal the critical difference between the experimentally realized two-dimensional SOC and the more symmetric Rashba or Dresselhaus SOCs in an interacting system, and paves the way for future characterizations of topological superfluid states in the experimentally relevant systems.Comment: 10 pages, 7 figure

Diffusion of an ellipsoid in bacterial suspensions

Active matter such as swarming bacteria and motile colloids exhibits exotic properties different from conventional equilibrium materials. Among these properties, the enhanced diffusion of tracer particles is generally deemed as a hallmark of active matter. Here, rather than spherical tracers, we investigate the diffusion of isolated ellipsoids in quasi-two-dimensional bacterial bath. Our study reveals a nonlinear enhancement of both translational and rotational diffusions. More importantly, we uncover an anomalous coupling between translation and rotation that is strictly prohibited in the classic Brownian diffusion. Combining experiments with theoretical modeling, we show that such an anomaly arises from generic stretching flows induced by swimming bacteria. Our work illustrates a universal organizing principle of active matter and sheds new light on fundamental transport processes in microbiological systems.Comment: 13 pages, 4 figure

The confinement induced resonance in spin-orbit coupled cold atoms with Raman coupling

We investigate the confinement induced resonance in spin-orbit coupled cold atoms with Raman coupling. We find that the quasi-bound levels induced by the spin-orbit coupling and Raman coupling result in the Feshbach-type resonances. For sufficiently large Raman coupling, the bound states in one dimension exist only for sufficiently strong attractive interaction. Furthermore, the bound states in quasi-one dimension exist only for sufficient large ratio of the length scale of confinement to three dimensional s-wave scattering length. The Raman coupling substantially changes the confinement-induced resonance position. We give a proposal to realize confinement induced resonance by increasing the Raman coupling strength in experiments.Comment: 5 pages, 4 figure

Detection of a Majorana-fermion zero mode by a T-shaped quantum-dot structure

Electron transport through the T-shaped quantum-dot (QD) structure is theoretically investigated, by considering a Majorana zero mode coupled to the terminal QD. It is found that in the double-QD case, the presence of the Majorana zero mode can efficiently dissolve the antiresonance point in the conductance spectrum and induce a conductance peak to appear at the same energy position whose value is equal to $e^2/2h$. This antiresonance-resonance change will be suitable to detect the Majorana bound states. Next in the multi-QD case, we observe that in the zero-bias limit, the conductances are always the same as the double-QD result, independent of the parity of the QD number. We believe that all these results can be helpful for understanding the properties of Majorana bound states

Radial alignment of elliptical galaxies by the tidal force of a cluster of galaxies

Unlike the random radial orientation distribution of field elliptical galaxies, galaxies in a cluster are expected to point preferentially towards the center of the cluster, as a result of the cluster's tidal force on its member galaxies. In this work an analytic model is formulated to simulate this effect. The deformation time scale of a galaxy in a cluster is usually much shorter than the time scale of change of the tidal force; the dynamical process of the tidal interaction within the galaxy can thus be ignored. An equilibrium shape of a galaxy is then assumed to be the surface of equipotential, which is the sum of the self-gravitational potential of the galaxy and the tidal potential of the cluster at this location. We use a Monte-Carlo method to calculate the radial orientation distribution of these galaxies, by assuming the NFW mass profile of the cluster and the initial ellipticity of field galaxies. The radial angles show a single peak distribution centered at zero. The Monte-Carlo simulations also show that a shift of the reference center from the real cluster center weakens the anisotropy of the radial angle distribution. Therefore, the expected radial alignment cannot be revealed if the distribution of spatial position angle is used instead of that of radial angle. The observed radial orientations of elliptical galaxies in cluster Abell~2744 are consistent with the simulated distribution.Comment: 8 pages, 6 figures, 2 tables. MNRAS in pres

Understanding the residual patterns of timing solutions of radio pulsars with a model of magnetic field oscillation

We explain some phenomena existing generally in the timing residuals: amplitude and sign of the second derivative of a pulsar's spin-frequency ($\ddot\nu$), some sophisticated residual patterns, which also change with the time span of data segments. The sample is taken from Hobbs et al.\,(2010), in which the pulsar's spin-frequency and its first derivative have been subtracted from the timing solution fitting. We first classify the timing residual patterns into different types based on the sign of $\ddot\nu$. Then we use the magnetic field oscillation model developed in our group \citep{zhang12a} to fit successfully the different kinds of timing residuals with the Markov Chain Monte Carlo method. Finally, we simulate the spin evolution over 20 years for a pulsar with typical parameters and analyze the data with the conventional timing solution fitting. By choosing different segments of the simulated data, we find that most of the observed residual patterns can be reproduced successfully. This is the first time that the observed residual patterns are fitted by a model and reproduced by simulations with very few parameters. From the distribution of the different residual patterns in the $P-\dot P$ diagram, we argue that (1) a single magnetic field oscillation mode exists commonly in all pulsars throughout their lifetimes; (2) there may be a transition period over the lifetimes of pulsars, in which multiple magnetic field oscillation modes exist.Comment: 21 pages, 22 figures, accepted for publication in MNRA

A "nearly parametric" solution to Selective Harmonic Elimination PWM

Selective Harmonic Elimination Pulse Width Modulation (SHEPWM) is an important technique to solve PWM problems, which control the output voltage of an inverter via selecting appropriate switching angles. Based on the Rational Univariate Representation (RUR) theory for solving polynomial systems, the paper presents an algorithm to compute a "nearly parametric" solution to a SHEPWM problem. When the number of switching angles N is fixed, a "nearly parametric" solution can be considered as functions of the modulation index m. So we can adapt the amplitude of the output voltage with the same source voltage by changing the modulation index. When m is given as a specific value, complete solutions to the SHEPWM problem can be obtained easily using univariate polynomial solving. Compared with other methods, m is considered as a symbolic parameter for the first time, and this can help avoid totally restarting when m changes. The average time for computing complete solutions associated to 460 modulation indexes based on a "nearly parametric" solution when N=5 is 0.0284s, so the algorithm is practical. Three groups of switching angles associated to N=5, m=0.75 is simulated in MATLAB, and it verifies the algorithm's correctness

BCS-BEC crossover and quantum phase transition in an ultracold Fermi gas under spin-orbit coupling

In this work, we study the BCS-BEC crossover and quantum phase transition in a Fermi gas under Rashba spin-orbit coupling close to a Feshbach resonance. By adopting a two-channel model, we take into account of the closed channel molecules, and show that combined with spin-orbit coupling, a finite background scattering in the open channel can lead to two branches of solution for both the two-body and the many-body ground states. The branching of the two-body bound state solution originates from the avoided crossing between bound states in the open and the closed channels, respectively. For the many-body states, we identify a quantum phase transition in the upper branch regardless of the sign of the background scattering length, which is in clear contrast to the case without spin-orbit coupling. For systems with negative background scattering length in particular, we show that the bound state in the open channel, and hence the quantum phase transition in the upper branch, are induced by spin-orbit coupling. We then characterize the critical detuning of the quantum phase transition for both positive and negative background scattering lengths, and demonstrate the optimal parameters for the critical point to be probed experimentally.Comment: 7 pages, 4 figure