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<jats:p>We consider an impurity problem in a quasi-two-dimensional Fermi gas, where a spin-down impurity is immersed in a Fermi sea of <jats:italic>N</jats:italic> spin-up atoms. Using a variational approach and an effective two-channel model, we obtain the energy for a wide range of interaction strength and for various different mass ratios between the impurity and the background fermion in the context of heteronuclear mixture. We demonstrate that in a quasi-two-dimensional Fermi gas there exists a transition of the ground state from polaron in the weakly interacting region to molecule in the strongly interacting region. The critical interaction strength of the polaron–molecule transition is non-universal and depends on the particle density of the background Fermi sea. We also investigate the excited repulsive polaron state, and find similar non-universal behavior.</jats:p>

<jats:p>We demonstrate that dual dark magnetic-optical-traps (MOTs) have great importance in the two-species <jats:sup>87</jats:sup>Rb and <jats:sup>40</jats:sup>K mixture compared with dual bright MOTs. The dark MOT has a little improvement in the trapping of single-species <jats:sup>87</jats:sup>Rb or <jats:sup>40</jats:sup>K gases compared with bright MOT. For the case of loading two-species <jats:sup>87</jats:sup>Rb and <jats:sup>40</jats:sup>K simultaneously, the improvement of <jats:sup>40</jats:sup>K in the dual dark MOTs is mainly from the reduction of light-assisted collision losses. The dual dark MOTs employ a pair of conical lenses to produce the hollow beam for repump laser with high efficiency. The number and density of <jats:sup>87</jats:sup>Rb and <jats:sup>40</jats:sup>K atoms after evaporative cooling in the hybrid magnetic trap with dark MOT loading are compared with those in bright MOT. The atoms with large number and high density make it easier to realize the quantum degenerate of Bose–Fermi mixture.</jats:p>

<jats:p>We propose schemes of direct concurrence measurement for two-qubit phononic states from quantized mechanical vibration. By combining the Mach–Zehnder interferometer with the optomechanical cross-Kerr nonlinear effect, direct concurrence measurement schemes for two-qubit phononic entangled states are achieved with the help of photon detection with respect to the output of the interferometer. For different types of entangled states, diversified quantum devices and operations are designed accordingly. The final analysis shows reasonable performance under the current parameter conditions. Our schemes may be useful for potential phonon-based quantum computation and information in the future.</jats:p>

<jats:p>Aiming at training the feed-forward threshold neural network consisting of nondifferentiable activation functions, the approach of noise injection forms a stochastic resonance based threshold network that can be optimized by various gradient-based optimizers. The introduction of injected noise extends the noise level into the parameter space of the designed threshold network, but leads to a highly non-convex optimization landscape of the loss function. Thus, the hyperparameter on-line learning procedure with respective to network weights and noise levels becomes of challenge. It is shown that the Adam optimizer, as an adaptive variant of stochastic gradient descent, manifests its superior learning ability in training the stochastic resonance based threshold network effectively. Experimental results demonstrate the significant improvement of performance of the designed threshold network trained by the Adam optimizer for function approximation and image classification.</jats:p>

<jats:p>We present a new cosine chaotic mapping proved by chaos theory test and analysis such that the system has good cryptography properties, wide chaos range, simple structure, and good sensitivity to initial value, and the mapping can meet the needs of chaotic image encryption. Based on the cosine chaotic system, we propose a new encryption method. First, according to the cyclic characteristics of the mapping, the cyclic information wave is simulated. Second, the quasi-Doppler effect is used to synchronously scramble and diffuse the image to obfuscate the original pixel. Finally, the XOR diffusion of image pixels is carried out by information wave to further enhance the encryption effect. Simulation experiment and security analysis show that the algorithm has good security, can resist the common attack mode, and has good efficiency.</jats:p>

<jats:p>We investigate the relationship between the synchronous transition and the power law behavior in spiking networks which are composed of inhibitory neurons and balanced by dc current. In the region of the synchronous transition, the avalanche size and duration distribution obey a power law distribution. We demonstrate the robustness of the power law for event sizes at different parameters and multiple time scales. Importantly, the exponent of the event size and duration distribution can satisfy the critical scaling relation. By changing the network structure parameters in the parameter region of transition, quasicriticality is observed, that is, critical exponents depart away from the criticality while still hold approximately to a dynamical scaling relation. The results suggest that power law statistics can emerge in networks composed of inhibitory neurons when the networks are balanced by external driving signal.</jats:p>

<jats:p>Astrocytes have a regulatory function on the central nervous system (CNS), especially in the temperature-sensitive hippocampal region. In order to explore the thermosensitive dynamic mechanism of astrocytes in the CNS, we establish a neuron–astrocyte minimum system to analyze the synchronization change characteristics based on the Hodgkin–Huxley model, in which a pyramidal cell and an interneuron are connected by an astrocyte. The temperature range is set as 0 °C–40 °C to juggle between theoretical calculation and the reality of a brain environment. It is shown that the synchronization of thermosensitive neurons exhibits nonlinear behavior with changes in astrocyte parameters. At a temperature range of 0 °C–18 °C, the effects of the astrocyte can provide a tremendous influence on neurons in synchronization. We find the existence of a value for inositol triphosphate (IP<jats:sub>3</jats:sub>) production rate and feedback intensities of astrocytes to neurons, which can ensure the weak synchronization of two neurons. In addition, it is revealed that the regulation of astrocytes to pyramidal cells is more sensitive than that to interneurons. Finally, it is shown that the synchronization and phase transition of neurons depend on the change in Ca<jats:sup>2+</jats:sup> concentration at the temperature of weak synchronization. The results in this paper provide some enlightenment on the mechanism of cognitive dysfunction and neurological disorders with astrocytes.</jats:p>

<jats:p>The dynamic polarizabilities of <jats:inline-formula> <jats:tex-math> <?CDATA ${3{\rm{s}}}^{{2}^{1}}{{\rm{S}}}_{0}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>3</mml:mn> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> </mml:msup> <mml:msub> <mml:mi mathvariant="normal">S</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_31_8_083102_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math> <?CDATA ${3{\rm{s}}3{\rm{p}}}^{3}{{\rm{P}}}_{0}^{{\rm{o}}}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>3</mml:mn> <mml:mi mathvariant="normal">s</mml:mi> <mml:mn>3</mml:mn> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> <mml:msubsup> <mml:mi mathvariant="normal">P</mml:mi> <mml:mn>0</mml:mn> <mml:mi mathvariant="normal">o</mml:mi> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_31_8_083102_ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> states of Al<jats:sup>+</jats:sup> are calculated using the hybrid configuration interaction and many-body perturbation theory method, and multiconfiguration Dirac–Hartree–Fock method in this work. Five ultraviolet magic wavelengths for the Al<jats:sup>+</jats:sup> clock transition <jats:inline-formula> <jats:tex-math> <?CDATA ${3{\rm{s}}}^{{2}^{1}}{{\rm{S}}}_{0}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>3</mml:mn> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:msup> <mml:mn>2</mml:mn> <mml:mn>1</mml:mn> </mml:msup> </mml:mrow> </mml:msup> <mml:msub> <mml:mi mathvariant="normal">S</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_31_8_083102_ieqn3.gif" xlink:type="simple" /> </jats:inline-formula>–<jats:inline-formula> <jats:tex-math> <?CDATA ${3{\rm{s}}3{\rm{p}}}^{3}{{\rm{P}}}_{0}^{{\rm{o}}}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>3</mml:mn> <mml:mi mathvariant="normal">s</mml:mi> <mml:mn>3</mml:mn> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> <mml:msubsup> <mml:mi mathvariant="normal">P</mml:mi> <mml:mn>0</mml:mn> <mml:mi mathvariant="normal">o</mml:mi> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_31_8_083102_ieqn4.gif" xlink:type="simple" /> </jats:inline-formula> are predicted. Although the suitable lasers are not available presently, the potential precision measurement on these magic wavelengths for the Al<jats:sup>+</jats:sup> clock transition would be used to extract the ratios of several certain transition matrix elements with high accuracy, and then help to improve the precision and reliability of the estimate of the BBR shift of the Al<jats:sup>+</jats:sup> clock transition. The differential dynamic polarizabilities at certain wavelengths are evaluated, which are useful to assess the ac Stark shift of the Al<jats:sup>+</jats:sup> clock transition frequency and helpful in the clock experiments to suppress the ac Stark shift of the clock transition as possible as it can.</jats:p>

<jats:p>The effect of conical intersection on the excited dynamics of benzene is studied by <jats:italic>ab initio</jats:italic> theory of electronic structure, which provides an important insight into photophysical and photochemical reactions. Based on the CASSCF(6,6)/6-31+G(d, p) method, the topological structures of conical intersections S<jats:sub>1</jats:sub>/S and S<jats:sub>2</jats:sub>/S<jats:sub>1</jats:sub> of benzene, as well as the optimal structures of the ground state (S) and excited states (S<jats:sub>1</jats:sub>, S<jats:sub>2</jats:sub>), are determined. The energy minima of the S<jats:sub>1</jats:sub> state and S<jats:sub>2</jats:sub> state are estimated at 4.608 eV and 6.889 eV, respectively. In addition, the energy values of the conical intersections of S<jats:sub>1</jats:sub>/S and S<jats:sub>2</jats:sub>/S<jats:sub>1</jats:sub> are predicted to be 5.600 eV and 6.774 eV. According to the topological structures and energy values of the S<jats:sub>2</jats:sub>/S<jats:sub>1</jats:sub> and S<jats:sub>1</jats:sub>/S conical intersections, the photophysical behavior of benzene excited to the S<jats:sub>2</jats:sub> state and the effects of the S<jats:sub>2</jats:sub>/S<jats:sub>1</jats:sub> and S<jats:sub>1</jats:sub>/S conical intersections are discussed in detail.</jats:p>

<jats:p>We investigate the dissociation dynamics of core-excited O<jats:sub>2</jats:sub> molecules using a high-resolution energy-resolved electron-ion coincidence experimental setup. The excited cationic states with two valence holes and one Rydberg electron are created after spectator Auger decay induced by O 1s → (<jats:inline-formula> <jats:tex-math> <?CDATA ${}^{4}{\Sigma }_{{\rm{u}}}^{-}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow /> <mml:mn>4</mml:mn> </mml:msup> <mml:msubsup> <mml:mo>Σ</mml:mo> <mml:mi mathvariant="normal">u</mml:mi> <mml:mo>−</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_31_8_083301_ieqn3.gif" xlink:type="simple" /> </jats:inline-formula>)3s<jats:italic>σ</jats:italic> core excitation in O<jats:sub>2</jats:sub>. From the energy correlation between the kinetic energy of the Auger electron and the ion kinetic energy release, we distinguish several dissociation channels. Rather complex dissociation channels of the spectator Auger final states are disclosed, which can be explained by the increased number of the crossing point due to the existence of Rydberg electron. The quantum system will evolve into different dissociation limits at each crossing point between the potential energy curves.</jats:p>