Total versus quantum correlations in a two-mode Gaussian state

In Li and Luo(2007 Phys. Rev. A 76 032327), the inequality(1/2)T≥ Q was identified as a fundamental postulate for a consistent theory of quantum versus classical correlations for arbitrary measures of total T and quantum Q correlations in bipartite quantum states. Besides, Hayden et al(2006 Commun. Math. Phys. 265 95) have conjectured that, in some conditions within systems endowed with infinite-dimensional Hilbert spaces, quantum correlations may dominate not only half of total correlations but total correlations itself. Here, in a two-mode Gaussian state,quantifying T and Q respectively by the quantum mutual information I~G and the entanglement of formation(EoF) ε_F~G, we verify that ε_(F,R)~G,is always less than(1/2) I_R~G when I~G and ε_F~G are defined via the Rényi-2 entropy. While via the von Neumann entropy, ε_(F,V)~G,may even dominate I_V~G itself,which partly consolidates the Hayden conjecture, and partly, provides strong evidence hinting that the origin of this counterintuitive behavior should intrinsically be related to the von Neumann entropy by which the EoF ε_(F,V)~G,is defined, rather than related to the conceptual definition of the EoF ε_F. The obtained results show that—in the special case of mixed two-mode Gaussian states—quantum entanglement can be faithfully quantified by the Gaussian Rényi-2 EoF ε_(F,R)~G,.     

Notes on index of quantum integrability

A quantum integrability index was proposed in Komatsu et al(2019 SciPost Phys. 7 065). It systematizes the Goldschmidt and Witten's operator counting argument(Goldschmidt and Witten 1980 Phys. Lett. B 91 392) by using the conformal symmetry. In this work we compute the quantum integrability indexes for the symmetric coset models SU(N)/SO(N) and SO(2N)/SO(N)×SO(N). The indexes of these theories are all non-positive except for the case of SO(4)/SO(2)×SO(2). Moreover we extend the analysis to the theories with fermions and consider a concrete theory: the CP~N model coupled with a massless Dirac fermion. We find that the indexes for this class of models are non-positive as well.     

When null energy condition meets ADM mass

We give a conjecture on the lower bound of the ADM mass M by using the null energy condition. The conjecture includes a Penrose-like inequality $3M\geqslant \kappa { \mathcal A }/(4\pi )+\sqrt{{ \mathcal A }/4\pi }$ and the Penrose inequality $2M\geqslant \sqrt{{ \mathcal A }/4\pi }$ with ${ \mathcal A }$ the event horizon area and κ the surface gravity. Both the conjecture in the static spherically symmetric case and the Penrose inequality for a dynamical spacetime with spherical symmetry are proved by imposing the null energy condition. We then generalize the conjecture to a general dynamical spacetime. Our results raise a new challenge for the famous unsettled question in general relativity: in what general case can the null energy condition replace other energy conditions to ensure the Penrose inequality?     

Study of semileptonic decay of ${\bar{B}}_{s}^{0} \rightarrow \phi {l}^{+}{l}^{-}$ in QCD sum rule

In this work we study the semileptonic decay of ${\bar{B}}_{s}^{0}\to \phi {l}^{+}{l}^{-}$ (l=e, μ, τ) with the QCD sum rule method. We calculate the ${\bar{B}}_{s}^{0}\to \phi $ translation form factors relevant to this semileptonic decay, then the branching ratios of ${\bar{B}}_{s}^{0}\to \phi {l}^{+}{l}^{-}$ (l=e, μ, τ) decays are calculated with the form factors obtained here. Our result for the branching ratio of ${\bar{B}}_{s}^{0}\to \phi {\mu }^{+}{\mu }^{-}$ agree very well with the recent experimental data. For the unmeasured decay modes such as ${\bar{B}}_{s}^{0}\to \phi {e}^{+}{e}^{-}$ and ${\bar{B}}_{s}^{0}\to \phi {\tau }^{+}{\tau }^{-}$, we give theoretical predictions.     

激光冷却SH~–阴离子的理论研究

本文采用多组态相互作用及Davidson修正方法和全电子基组计算了SH~-阴离子的X~1∑~+,a~3∏和A~1∏态的势能曲线、电偶极矩和跃迁偶极矩.计算的光谱常数与实验值及已有的理论值符合得很好.在计算中考虑了自旋-轨道耦合效应.计算得到a~3∏_1(v'=0)?X~1∑_(0+)~+(v"=0)和A~1∏_1(v'=0)?X~1Σ_(0+)~+(v"=0)跃迁具有高对角分布的弗兰克-康登因子,分别为0.9990和0.9999;计算得到a~3∏_1和A~1∏_1态的自发辐射寿命分别为1.472和0.188 ms.A~1∏_1?X~1∑_(0+)~+跃迁存在中间态a~3∏_(0+)和a~3∏_1,但中间态对激光冷却SH~-阴离子的影响可以忽略.分别利用a~3∏_1(v'=0)? X~1∑_(0+)~+(v"=0)和A~1∏_1(v'=0)? X~1∑_(0+)~+(v"=0)跃迁构建了准闭合的能级系统,冷却所需的激光波长分别为492.27和478.57 nm.最后预测了激光冷却SH~-阴离子能达到的多普勒温度和反冲温度.这些结果为进一步实验提供了理论参数.     

Neutral meson oscillations and equivalence principle for particles and antiparticles

Oscillations of neutral meson (K ⁰-$ \overline {K^0 } $ \overline {K^0 } , D ⁰-$ \overline {D^0 } $ \overline {D^0 } , and B ⁰-$ \overline {B^0 } $ \overline {B^0 } are extremely sensitive to the meson and antimeson energies at rest. This energy is determined as mc ²—with the corresponding inertial mass—and as the energy of gravitational interaction. Assuming that the CPT theorem is correct for inertial masses and estimating the gravitational potential for which the largest contribution originates from the field of the galaxy center, we obtain the estimate from experimental data on K ⁰-$ \overline {K^0 } $ \overline {K^0 } oscillations:

Einfluß des Randes auf das effektive Verhalten heterogener Körper - Anwendung auf Rayleighwellen

Effective Elastic Properties of Finite Heterogeneous Media - Application to Rayleigh-waves Rayleigh waves in a heterogeneous material (multiphase mixtures, composite materials, polycrystals) are governed by integrodifferential equations derived by the aid of known methods for infinite heterogeneous media. According to this wave equation the velocity depends on the frequency, and the waves are damped. After some simplifications (isotropy, nonrandom elastic constants) the following is obtained: if the fluctuations of the mass density are restricted to the vicinity of the boundary, the frequency dependent part of the velocity behaves like \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^3 \omega ^3}}{{{\mathop c\limits^\circ} _t^3}} $\end{document} and the damping is proportional to \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^4 \omega ^5}}{{{\mathop c\limits^\circ} _t^5}} $\end{document}, whereas \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^2 \omega ^2}}{{{\mathop c\limits^\circ} _t^2}} $\end{document} respectively \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^3 \omega ^4}}{{{\mathop c\limits^\circ} _t^4}} $\end{document} is found if the fluctuations are present in the whole half-space. From this it is seen, what assumptions are necessary to describe the waves by differential equations with frequenc y-dependent mass density.     

The integrated density of states for the difference Laplacian on the modified Koch graph

We consider the integrated density of statesN(λ) of the difference Laplacian ?Δ on the modified Koch graph. We show thatN(λ) increases only with jumps and a set of jump points ofN(λ) is the set of eigenvalues of ?Δ with the infinite multiplicity. We establish also that $$0< C_1 \leqslant \mathop {\lim }\limits_{\lambda \to 0} \frac{{N(\lambda )}}{{\lambda ^{d_s /2} }}< \overline {\mathop {\lim }\limits_{\lambda \to 0} } \frac{{N(\lambda )}}{{\lambda ^{d_s /2} }} \leqslant C_2< \infty$$ whered _s =2log5/log(40/3) is the spectral dimension of MKG.     

Three-loop on-shell charge renormalization without integration:\Lambda _{QED}^{\overline {MS} } to four loops

Using algebraic methods, we find the three-loop relation between the bare and physical couplings of one-flavourD-dimensional QED, in terms of Γ functions and a singleF ₃₂ series, whose expansion nearD=4 is obtained, by wreath-product transformations, to the order required for five-loop calculations. Taking the limitD→4, we find that the \(\overline {MS} \) coupling \(\bar \alpha (\mu )\) satisfies the boundary condition $$\begin{gathered} \frac{{\bar \alpha (m)}}{\pi } = \frac{\alpha }{\pi } + \frac{{15}}{{16}}\frac{{\alpha ^3 }}{{\pi ^3 }} + \left\{ {\frac{{11}}{{96}}\zeta (3) - \frac{1}{3}\pi ^2 \log 2} \right. \hfill \\ \left. { + \frac{{23}}{{72}}\pi ^2 - \frac{{4867}}{{5184}}} \right\}\frac{{\alpha ^4 }}{{\pi ^4 }} + \mathcal{O}(\alpha ^5 ), \hfill \\ \end{gathered} $$ wherem is the physical lepton mass and α is the physical fine structure constant. Combining this new result for the finite part of three-loop on-shell charge renormalization with the recently revised four-loop term in the \(\overline {MS} \) β-function, we obtain $$\begin{gathered} \Lambda _{QED}^{\overline {MS} } \approx \frac{{me^{3\pi /2\alpha } }}{{(3\pi /\alpha )^{9/8} }}\left( {1 - \frac{{175}}{{64}}\frac{\alpha }{\pi } + \left\{ { - \frac{{63}}{{64}}\zeta (3)} \right.} \right. \hfill \\ \left. { + \frac{1}{2}\pi ^2 \log 2 - \frac{{23}}{{48}}\pi ^2 + \frac{{492473}}{{73728}}} \right\}\left. {\frac{{\alpha ^2 }}{{\pi ^2 }}} \right), \hfill \\ \end{gathered} $$ at the four-loop level of one-flavour QED.     

Application of kernel ridge regression in predicting neutron-capture reaction cross-sections

This article provides the first application of the machine-learning approach in the study of the cross-sections for neutron-capture reactions with the kernel ridge regression (KRR) approach. It is found that the KRR approach can reduce the root-mean-square (rms) deviation of the relative errors between the experimental data of the Maxwellian-averaged $(n,\gamma )$ cross-sections and the corresponding theoretical predictions from 69.8% to 35.4%. By including the data with different temperatures in the training set, the rms deviation can be further significantly reduced to 2.0%. Moreover, the extrapolation performance of the KRR approach along different temperatures is found to be effective and reliable.     

On the Essential Spectrum of a Class of Singular Matrix Differential Operators. I: Quasiregularity Conditions and Essential Self-adjointness

The essential spectrum of singular matrix differential operator determined by the operator matrix

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form $ V(r,\theta ) = \tfrac{1} {8}\kappa r_e^2 \left( {\tfrac{r} {{r_e }} - \tfrac{{r_e }} {r}} \right)^2 + \tfrac{{\beta cos^2 \theta }} {{r^2 sin^2 \theta }} A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form . The energy eigenvalues and eigenfunctions of the bound-states for the Schr?dinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions.      

High resolution spectroscopy of Rb in magnetic field by far-detuning electromagnetically induced transparency

We have presented a high resolution spectroscopy of Rb in magnetic field by far-detuning electromagnetically induced transparency (EIT). The EIT spectrum in the $\Xi$-type configuration is usually companied by a double resonance optical pumping (DROP) due to the strong optical coupling between the two upper states, leading to the spectral lines seriously deformed and widely broadened for complex relaxation processes in DROP. Here we demonstrate a high resolution spectroscopy by far-detuning EIT for $^{87}\rm{Rb}$ $\rm{5S_{1/2}\rightarrow5P_{3/2}\rightarrow5D_{5/2}}$ in magnetic fields. The method of far-detuning eliminates the relaxation in DROP to the most extent and decreases the spectral linewidth from more than 20 MHz down to its natural linewidth limit (6 MHz). The deformation of the spectral lines also disappears and the observed spectra are well in accordance with the theoretical calculation. Our work shows that far-detuning EIT is a reliable high resolution spectroscopic method when the relaxation in DROP cannot be neglected, especially for the case of transition to low excited states.     

碳离子治疗计划中的RBE加权剂量鲁棒优化方法

提出基于混合束模型的相对生物学效应(RBE)加权剂量鲁棒优化方法,用于减少碳离子束射程和摆位偏差对生物剂量分布的影响。建立概率组合鲁棒优化模型,利用二次型目标函数表达式,分别制定针对物理吸收剂量和RBE加权剂量的碳离子束治疗计划,并基于共轭梯度优化算法求解出各自最优的权重解,使得靶区和危及器官(OAR)实际剂量分布在射程和摆位偏差组合情况下尽量满足剂量要求。采用C型靶模型测试鲁棒优化方法的有效性。与基于计划靶区(PTV)的常规优化方法相比,针对物理吸收剂量的鲁棒优化计划临床靶区(CTV)的$ \Delta {D}_{95{\text{%}} } $减少10.00 cGy,OAR的$ \Delta {D}_{5{\text{%}} } $和$ \Delta {D}_{\mathrm{m}\mathrm{a}\mathrm{x}} $分别减少21.50和35.97 cGy,计划的鲁棒性得到了很好的提升。针对RBE加权剂量的鲁棒优化计划CTV的$ \Delta {D}_{95{\text{%}} } $降低14.00 cGy(RBE),OAR的$ \Delta {D}_{5{\text{%}} } $和$ \Delta {D}_{\mathrm{m}\mathrm{a}\mathrm{x}} $分别减少19.00和26.28 cGy(RBE),说明该方法不仅减少了CTV的生物剂量变化,也减少了OAR的生物剂量热点。该结果证明了基于混合束模型的RBE加权剂量鲁棒优化方法在有效提高碳离子放疗计划鲁棒性的同时使OAR也得到了很好的保护。     

非马尔科夫环境中各向异性海森堡自旋链的量子失协

利用量子失协方法研究在非马尔科夫环境中具有时变磁场的两比特各向异性海森堡XYZ模型量子失协的动力学演化。海森堡XYZ系统的初始态为最大纠缠态 $\left|\psi_{A B}\right\rangle=(1 / \sqrt{2})(|11\rangle+|00\rangle)$ , 利用非马尔科夫量子态扩散方法解析求解非马尔科夫主方程, 得出系统的约化密度矩阵; 然后代入量子失协公式得出系统量子失协的演化动力学。讨论自旋耦合强度、环境关联系数γ和余弦磁场强度B对量子失协动力学的影响。研究发现: 当环境关联系数γ较小时, 系统的量子失协明显呈现上升趋势, 因此可以表明非马尔科夫环境具有增加系统量子失协的作用。同时较大的自旋耦合系数J和J_Z以及余弦磁场强度B也具有增加系统量子失协的作用。     

Pion-induced ${K}^{* }$ production with ${{\rm{\Sigma }}}^{* }$ baryon off proton target

In this work, the reaction ${\pi }^{-}p\to {K}^{* }{{\rm{\Sigma }}}^{* }$ is investigated with an effective Lagrangian approach. The contributions from the Born terms, including the s, t, and u channel, are considered, and the Regge model and the Feynman model are applied to treat the t -channel contribution. The existing experimental data can be reproduced with the best-fitted χ ² being 2.38 and 1.54 for the Feynman and Regge models, respectively. Moreover, it is found that the contribution from the t channel is dominant in the cross-section. The contribution of the u channel is mainly distributed at backward angles, and the contribution from the s channel is small and negligible. In the Feynman model, the contribution of the t -channel K exchange is much larger than the contribution of the ${K}^{* }$ exchange, while in the Regge model the contribution of the t -channel K exchange is comparable to that of the ${K}^{* }$ exchange. Prediction about the differential cross-section of the ${\pi }^{-}p\to {K}^{* }{{\rm{\Sigma }}}^{* }$ reaction is also presented, which is helpful for clarifying the role of the Regge treatment. The current results suggest high-precision experimental measurements which can be performed at J-PARC and COMPASS.     

Weakly Non-Ergodic Statistical Physics

For weakly non ergodic systems, the probability density function of a time average observable is where is the value of the observable when the system is in state j=1,…L. p _j ^eq is the probability that a member of an ensemble of systems occupies state j in equilibrium. For a particle undergoing a fractional diffusion process in a binding force field, with thermal detailed balance conditions, p _j ^eq is Boltzmann’s canonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0<α<1 is the anomalous diffusion exponent 〈x ²〉∼t ^α found for free boundary conditions. When α→1 ergodic statistical mechanics is recovered . We briefly discuss possible physical applications in single particle experiments.     

Low-Pressure Helicon-Plasma Discharge Initiation via Magnetic Field Ramping

Discharge initiation at low pressures and flow rates is investigated in the Madison Helicon Experiment flowing helicon source. At low pressures (below 14-sccm flow rate), a threshold magnetic field exists for discharge initiation which depends on RF power and gas flow rate. Above the threshold magnetic field, RF discharges start only after a significant delay (approximately seconds) and sometimes will not start at all. This threshold magnetic field is interpreted using electron multipactor arguments. A technique is described for initiating discharges at low flow rates and pressures $(lambda_{{rm en}, {rm iz}} ≫ L_{rm system})$ and high magnetic fields (above the threshold value). Without a static magnetic field present, the RF power is turned on, and a lower density $(≪ 10^{11} hbox{cm}^{-3})$ unmagnetized discharge occurs. The magnetic field is then applied, and the discharge transitions to the higher density (up to $10^{13} hbox{cm}^{-3}$) regime. Using this method, magnetized discharges can be started at flow rates as low as 1 sccm ( $1.8 times 10^{-4} hbox{torr}$ at $z = -91 hbox{cm}$ , $1.7 times 10^{-5} hbox{torr}$ at $z = 105 hbox{cm}$) at 500 W in a 1.04-kG magnetic field. This technique can be used to initiate low-pressure helicon discharges for basic plasma science experiments and other applications.      

${{ \mathcal H }}_{\infty }$ synchronization of chaotic Hopfield networks with time-varying delay: a resilient DOF control approach*

This paper focuses on the issue of resilient dynamic output-feedback (DOF) control for ${{ \mathcal H }}_{\infty }$ synchronization of chaotic Hopfield networks with time-varying delay. The aim is to determine a DOF controller with gain perturbations ensuring that the ${{ \mathcal H }}_{\infty }$ norm from the external disturbances to the synchronization error is less than or equal to a prescribed bound. A delay-dependent criterion for the ${{ \mathcal H }}_{\infty }$ synchronization is derived by employing the Lyapunov functional method together with some recent inequalities. Then, with the help of some decoupling techniques, sufficient conditions on the existence of the resilient DOF controller are developed for both the time-varying and constant time-delay cases. Lastly, an example is used to illustrate the applicability of the results obtained.