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<jats:title>Abstract</jats:title> <jats:p>A conformal multi-symplectic method has been proposed for the damped Korteweg–de Vries (DKdV) equation, which is based on the conformal multi-symplectic structure. By using the Strang-splitting method and the Preissmann box scheme, we obtain a conformal multi-symplectic scheme for multi-symplectic partial differential equations (PDEs) with added dissipation. Applying it to the DKdV equation, we construct a conformal multi-symplectic algorithm for it, which is of second order accuracy in time. Numerical experiments demonstrate that the proposed method not only preserves the dissipation rate of mass exactly with periodic boundary conditions, but also has excellent long-time numerical behavior.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>With the development of attosecond science, tunneling time can now be measured experimentally with the attoclock technique. However, there are many different theoretical definitions of tunneling time and no consensus has been achieved. Here, we bridge the relationship between different definitions of tunneling time based on a quantum travel time in one-dimensional rectangular barrier tunneling problem. We find that the real quantum travel time <jats:italic>t</jats:italic> <jats:sub>Re</jats:sub> is equal to the Bohmian time <jats:italic>t</jats:italic> <jats:sub>Bohmian</jats:sub>, which is related to the resonance lifetime of a bound state. The total quantum travel time <jats:italic>τ</jats:italic> <jats:sub>t</jats:sub> can perfectly retrieve the transversal time <jats:italic>t</jats:italic> <jats:sub> <jats:italic>x</jats:italic> </jats:sub> and the Büttiker–Landauer time <jats:italic>τ</jats:italic> <jats:sub>BL</jats:sub> in two opposite limits, regardless of the particle energy.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The dynamics of two nanospheres nonlinearly coupling with non-Markovian reservoir is investigated. A master equation of the two nanospheres is derived by employing quantum state diffusion method. It is shown that the nonlinear coupling can improve the non-Markovianity. Due to the sharing of the common non-Markovian environment, the state transfer between the two nanospheres can be realized. The entanglement and the squeezing of the individual mode, as well as the jointed two-mode are analyzed. The present system can be realized by trapping two nanospheres in a wideband cavity, which might provide a method to study adjustable non-Markovian dynamics of mechanical motion.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We introduce a new consensus pattern, named a successive lag cluster consensus (SLCC), which is a generalized pattern of successive lag consensus (SLC). By applying delay-dependent impulsive control, the SLCC of first-order and second-order multi-agent systems is discussed. Furthermore, based on graph theory and stability theory, some sufficient conditions for the stability of SLCC on multi-agent systems are obtained. Finally, several numerical examples are given to verify the correctness of our theoretical results.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We investigate full counting statistics of quantum heat transfer in a collective-qubit system constructed by multi-qubits interacting with two thermal baths. The nonequilibrium polaron-transformed Redfield approach embedded with an auxiliary counting field is applied to obtain the steady state heat current and fluctuations, which enables us to study the impact of the qubit–bath interaction in a wide regime. The heat current, current noise, and skewness are all found to clearly unify the limiting results in the weak and strong couplings. Moreover, the superradiant heat transfer is clarified as a system-size-dependent effect, and large number of qubits dramatically suppress the nonequilibrium superradiant signature.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>It is well-known that reaction–diffusion systems are used to describe the pattern formation models. In this paper, we will investigate the pattern formation generated by the fractional reaction–diffusion systems. We first explore the mathematical mechanism of the pattern by applying the linear stability analysis for the fractional Gierer–Meinhardt system. Then, an efficient high-precision numerical scheme is used in the numerical simulation. The proposed method is based on an exponential time differencing Runge–Kutta method in temporal direction and a Fourier spectral method in spatial direction. This method has the advantages of high precision, better stability, and less storage. Numerical simulations show that the system control parameters and fractional order exponent have decisive influence on the generation of patterns. Our numerical results verify our theoretical results.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Carbon sulfide cation (CS<jats:sup>+</jats:sup>) plays a dominant role in some astrophysical atmosphere environments. In this work, the rovibrational transition lines are computed for the lowest three electronic states, in which the internally contracted multireference configuration interaction approach (MRCI) with Davison size-extensivity correction (+Q) is employed to calculate the potential curves and dipole moments, and then the vibrational energies and spectroscopic constants are extracted. The Frank–Condon factors are calculated for the bands of <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{X}}}^{2}{{\rm{\Sigma }}}^{+}\mbox{-}{{\rm{A}}}^{2}{\rm{\Pi }}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">X</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">Σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> <mml:mo>−</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">A</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mi mathvariant="normal">Π</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_5_053101_ieqn7.gif" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{X}}}^{2}{{\rm{\Sigma }}}^{+}\mbox{-}{{\rm{B}}}^{2}{{\rm{\Sigma }}}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">X</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">Σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> <mml:mo>−</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">B</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">Σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_5_053101_ieqn8.gif" xlink:type="simple" /> </jats:inline-formula> systems, and the band of <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{X}}}^{2}{{\rm{\Sigma }}}^{+}\mbox{-}{{\rm{A}}}^{2}{\rm{\Pi }}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">X</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">Σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> <mml:mo>−</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">A</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mi mathvariant="normal">Π</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_5_053101_ieqn9.gif" xlink:type="simple" /> </jats:inline-formula> is in good agreement with the available experimental results. Transition dipole moments and the radiative lifetimes of the low-lying three states are evaluated. The opacities of the CS<jats:sup>+</jats:sup> molecule are computed at different temperatures under the pressure of 100 atms. It is found that as temperature increases, the band systems associated with different transitions for the three states become dim because of the increased population on the vibrational states and excited electronic states at high temperature.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The first-order Raman spectroscopy of diamond exhibits splitting and redshift after the burst of high-pressure (160–200 GPa) and high-temperature (∼2000 K). The observed longitudinal optical (LO) and the transverse optical (TO) splitting of Raman phonon is related to the tensile-strain induced activation of the forbidden or silent Raman modes that arise in the proximity of the Brillouin zone center.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>By numerically solving the two-dimensional time-dependent Schrödinger equation under the frozen-nuclei approximation, we are able to study the molecular photoelectron-momentum distribution (MPMD) of <jats:inline-formula> <jats:tex-math> <?CDATA ${{\rm{H}}}_{2}^{+}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_5_053201_ieqn3.gif" xlink:type="simple" /> </jats:inline-formula> with different orientation angles driven by elliptically polarized laser pulse with varying ellipticities. Our numerical results show that the MPMD is sensitive to the orientation angle and the laser ellipticity, which can be explained by the attosecond perturbation ionization theory and the exactly solvable photoionization model. When the ellipticity <jats:italic>ε</jats:italic>=0, the final MPMD of <jats:italic>x</jats:italic>-oriented <jats:inline-formula> <jats:tex-math> <?CDATA ${{\rm{H}}}_{2}^{+}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_5_053201_ieqn4.gif" xlink:type="simple" /> </jats:inline-formula> shows a distinct six-lobe pattern that is different from that with <jats:italic>ε</jats:italic>=0.5 and <jats:italic>ε</jats:italic>=1. The evolutions of electron wave packet (EWP) and MPMD with <jats:italic>x</jats:italic>-oriented <jats:inline-formula> <jats:tex-math> <?CDATA ${{\rm{H}}}_{2}^{+}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_5_053201_ieqn5.gif" xlink:type="simple" /> </jats:inline-formula> are presented to interpret this distinct pattern.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We utilize an electromagnetically induced transparency (EIT) of a three-level cascade system involving Rydberg state in a room-temperature cell, formed with a cesium 6S<jats:sub>1/2</jats:sub>–6P<jats:sub>3/2</jats:sub>–66S<jats:sub>1/2</jats:sub> scheme, to investigate the Autler–Townes (AT) splitting resulting from a 15.21-GHz radio-frequency (RF) field that couples the <jats:inline-formula> <jats:tex-math> <?CDATA $|66{{\rm{S}}}_{1/2}\rangle \to |65{{\rm{P}}}_{1/2}\rangle $?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">|</mml:mo> <mml:mn>66</mml:mn> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">S</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="false">/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy="false">〉</mml:mo> <mml:mo>→</mml:mo> <mml:mo stretchy="false">|</mml:mo> <mml:mn>65</mml:mn> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">P</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="false">/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy="false">〉</mml:mo> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_28_5_053202_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> Rydberg transition. The radio-frequency electric field induced AT splitting, <jats:italic>γ</jats:italic> <jats:sub>AT</jats:sub>, is defined as the peak-to-peak distance of an EIT-AT spectrum. The dependence of AT splitting <jats:italic>γ</jats:italic> <jats:sub>AT</jats:sub> on the probe and coupling Rabi frequency, Ω<jats:sub>p</jats:sub> and Ω<jats:sub>c</jats:sub>, is investigated. It is found that the EIT-AT splitting strongly depends on the EIT linewidth that is related to the probe and coupling Rabi frequency in a weak RF-field regime. Using a narrow linewidth EIT spectrum would decrease the uncertainty of the RF field measurements. This work provides new experimental evidence for the theoretical framework in [<jats:italic>J. Appl. Phys.</jats:italic> <jats:bold>121</jats:bold>, 233106 (2017)].</jats:p>