We derive the Schr?dinger equation of a particle constrained to move on a rotating curved surface $S$. Using the thin-layer quantization scheme to confine the particle on $S$, and with a proper choice of gauge transformation for the wave function, we obtain the well-known geometric potential $V_{\rm g}$ and an additive Coriolis-induced geometric potential in the co-rotational curvilinear coordinates. This novel effective potential, which is included in the surface Schr?dinger equation and is coupled with the mean curvature of $S$, contains an imaginary part in the general case which gives rise to a non-Hermitian surface Hamiltonian. We find that the non-Hermitian term vanishes when $S$ is a minimal surface or a revolution surface which is axially symmetric around the rolling axis.

We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser–Horne inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotational asymmetry of the quantum state, the ratio of 0s to 1s varies with the measurement bases. The experimental partners can then use their measurement outcomes to generate the biased random bit string. The bias of their bit string can be adjusted by altering their choices of measurement bases. When this protocol is implemented in a device-independent way, we show that the bias of the bit string can still be ensured under the collective attack.

Quantum random number generators adopting single photon detection have been restricted due to the non-negligible dead time of avalanche photodiodes (APDs). We propose a new approach based on an APD array to improve the generation rate of random numbers significantly. This method compares the detectors' responses to consecutive optical pulses and generates the random sequence. We implement a demonstration experiment to show its simplicity, compactness and scalability. The generated numbers are proved to be unbiased, post-processing free, ready to use, and their randomness is verified by using the national institute of standard technology statistical test suite. The random bit generation efficiency is as high as 32.8% and the potential generation rate adopting the 32$\times $32 APD array is up to tens of Gbits/s.

Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special case of the fifth Painlevé transcendent is then worked out explicitly.

In the framework of MSSM the probability of $Z^0$-boson decay to charginos in a strong electromagnetic field, $Z^0\rightarrow \chi ^{+} \chi ^{-}$, is analyzed. The method of calculations employs exact solutions of relativistic wave equations for charginos in a crossed electromagnetic field. Analytic expression for the decay width ${\it \Gamma}(Z^{0}\rightarrow \chi ^{+} \chi ^{-})$ is obtained at an arbitrary value of the parameter $\varkappa=e m_Z^{-3}\sqrt{-(F_{\mu\nu}q^\nu)^2}$, which characterizes the external-field strength $F_{\mu\nu}$ and $Z^0$-boson momentum $q^{\nu}$. The process $Z^0\rightarrow \chi ^{+} \chi ^{-}$ is forbidden in a vacuum for the case of relatively heavy charginos: $M_{\chi^{\pm}}>m_Z/2$. However, in an intense electromagnetic background this reaction could take place in the region of superstrong fields ($\varkappa>1$).

The equation of state for nuclear matter is presented within the Brueckner–Hartree–Fock (BHF) scheme, by using the realistic Argonne V18 or Bonn B two-nucleon potentials plus their corresponding microscopic three-nucleon forces. It is then applied to calculate the properties of finite nuclei within a simple liquid-drop model, and we compare the calculated volume, surface, and Coulomb parameters with the empirical ones from the liquid drop model. Nuclear density distributions and charge radii in good agreement with the experimental data are obtained, and we predict the neutron skin thickness of various nuclei.

We report a systematic method to perform calculations of spectral line broadening parameters in plasmas. This method is applied to calculate Stark-broadening line profiles of $P_{\alpha}(n=4\rightarrow n=3)$ transitions under certain specific plasma conditions, by treating this case as an example. In the framework of the fully relativistic Dirac R-matrix theory, we calculate the electron-impact broadening operators, which are assumed to be diagonal matrix to simplify the situation. The electric microfield distribution function is calculated by retaining Hooper's formalism. The dipole matrix elements and atomic structure parameters used in these calculations have been obtained from atomic structure GRASP code. Based on this required data, we calculate the Stark-broadened line profiles of the Paschen spectral lines in He II ions in a systematic manner. Overall, there is a very good agreement between our calculated Stark-broadened line profiles and other line broadening numerical simulation codes (SimU and MELS). Our reported spectral line-broadening data have real applications in plasma spectroscopy, plasma diagnosis and also play a fundamental role in plasma modeling.

We experimentally demonstrate the relation of Raman coupling strength with the external bias magnetic field in degenerate Fermi gas of $^{40}$K atoms. Two Raman lasers couple two Zeeman energy levels, whose energy splitting depends on the external bias magnetic field. The Raman coupling strength is determined by measuring the Rabi oscillation frequency. The characteristics of the Rabi oscillation is to be damped after several periods due to Fermi atoms in different momentum states oscillating with different Rabi frequencies. The experimental results show that the Raman coupling strength will decrease as the external bias magnetic field increases, which is in good agreement with the theoretical prediction.

FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS)

We demonstrate a stable Q-switched mode-locked erbium-doped fiber laser (EDFL) operating in dark regime based on the nonlinear polarization rotation technique. The EDFL produces a pulse train where the Q-switching envelope is formed by multiple dark pulses. The repetition rate of the Q-switched envelope can be increased from 0.96 kHz to 3.26 kHz, whereas the pulse width reduces from 211 μs to 86 μs. The highest pulse of 479 nJ is obtained at the pump power of 55 mW. It is also observed that the dark pulses inside the Q-switching envelope consist of two parts: square and trailing dark pulses. The shortest pulse width of the dark square pulse is obtained at 40.5 μs when the pump power is fixed at 145 mW. The repetition rate of trailing dark pulses can be increased from 27.62 kHz to 50 kHz as the pump power increases from 55 mW to 145 mW.

The wavelength-tunable and switchable narrow bandwidth mode-locking operation is demonstrated in an all fiber laser based on semiconductor-saturable absorber mirror (SESAM). Two narrow-band fiber Bragg gratings centered at 1029.9 nm and 1032 nm respectively with a polarization controller inserted between them are used to realize the wavelength switchable between 1029.9 nm and 1032 nm. The laser delivers different pulse widths of 7.5 ps for 1030 nm and 20 ps for 1032 nm. The maximum output power for both could reach $\sim$6.5 mW at single pulse operation. The output wavelength could be tuned to about 0.9 nm intervals ranging from 1030.2 nm to 1031.1 nm and from 1032.15 nm to 1033.7 nm with the temperature change of the fiber Bragg grating, respectively.

We experimentally demonstrate a novel ghost imaging experiment utilizing a classical light source, capable of resolving objects with a high visibility. The experimental results show that our scheme can indeed realize ghost imaging with high visibility for a relatively complicated object composed of three near-ellipse-shaped holes with different dimensions. In our experiment, the largest hole is $\sim$36 times of the smallest one in area. Each of the three holes exhibits high-visibility in excess of 80%. The high visibility and high spatial-resolution advantages of this technique could have applications in remote sensing.

Broad-band all-optical wavelength conversion of differential phase-shift keyed (DPSK) signal is experimentally demonstrated. This scheme is composed of a one-bit delay interferometer demodulation stage followed by a semiconductor optical amplifier (SOA) based nonlinear polarization switch. A wavelength converter for the 10 Gb/s DPSK signal is presented, which has a wide wavelength range of more than 30 nm. The converted signals experience small power penalties less than 1.4 dB compared with the original signal, at a bit error rate of 10$^{-9}$. Additionally, the optical spectra, the measured waveforms and the open eye diagrams of the converted signals show a high quality wavelength conversion performance.

Transverse localization of light is investigated numerically in a self-focusing Kerr medium with a complex-valued optical lattice featuring parity-time symmetry. It is demonstrated that the light localization exists below the threshold of the spatial frequency of the lattices, and is further enhanced with the decrease of the spatial frequency. The influence of defects on the transverse localization is also discussed in detail. The results show that both positive and negative defects in such a medium would enhance the localization.

A Bayesian source tracking approach is developed to track a moving acoustic source in an uncertain ocean environment. This approach treats the environmental parameters (e.g., water depth, sediment and bottom parameters) at the source location and the source parameters (e.g., source depth, range and speed) as unknown random variables that evolve as the source moves. To track a target with low signal-to-noise ratio (SNR), acoustic signals from a series of observations are treated in a simultaneous inversion. This allows real-time updating of the environment and accurate tracking of the moving source. The noise signals radiated from a surface ship target are processed and analyzed. It is found that the Bayesian source tracking method could enhance the localization accuracy in an uncertain water environment and low SNR.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

We consider the radiation from the beam electrons traveling in a strong uniform axial magnetic field and an axial alternating electric field of wavelength $\lambda_{\rm w}$ generated by a voltage-supplied pill-box cavity. The beam electrons emit genuine laser radiation that propagates only in the axial direction through free-electron two-quantum Stark radiation. We find that laser radiation takes place only at the expense of the axial kinetic energy when $\lambda_{\rm w}\ll c/(\omega_{\rm c}/\gamma)$, where $\omega_{\rm c}/\gamma$ is the relativistic electron–cyclotron frequency. We formulate the laser power based on quantum-wiggler electrodynamics, and envision a laser of length 10 m with estimated power 0.1 GW/(kA) in the $10^{-4}$ cm wavelength range.

During the laser foil interaction, the output ion beam quality including the energy spread and beam divergence can be improved by the target ablation, due to the direct laser acceleration (DLA) electrons generated in the ablation plasma. The acceleration field established at the target rear by these electrons, which is highly directional and triangle-envelope, is helpful for the beam quality. With the help of the target ablation, both the beam divergence and energy spread will be reduced. If the ablation is more sufficient, the impact of DLA-electron-caused field will be strengthened, and the beam quality will be better, confirmed by the particle-in-cell simulation.

Transmission measurements of warm dense iron plasma are reported over the photon energy range of 400–1200 eV, including the strong 2$p$–3$d$ structures. One-dimensional hydrodynamic simulation is performed to estimate the plasma conditions: temperatures of several eV and densities of about $0.1$ g/cm$^3$. By using the simulated temperature and density, the calculations of the transmission spectra are performed and compared with the time-resolved experimental results.

CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES

We report the observation of bubble generation and migration in a germanate glass during irradiation by a femtosecond laser of high repetition rate. Bubbles are formed around the focal area of the laser beam, and their movement indicates the presence of thermal gravity convection in the glass melt, which is beyond the existing theoretical model about temperature field of focal area. Inside the bubbles, oxygen molecules are observed by the confocal Raman micro-spectroscopy. The generation of molecular oxygen and bubbles is explained in terms of the spatial separation of Ge and O ions and micro-explosion inside the glass melt.

The spall tests under the plane tensile pulses for resistance spot weld (RSW) of QP980 steel are performed by using a gun system. The velocity histories of free surfaces of the RSW are measured with the laser velocity interferometer system for any reflector. The recovered specimens are investigated with an Olympus GX71 metallographic microscope and a scanning electron microscope (SEM). The measured velocity histories are explained and used to evaluate the tension stresses in the RSW applying the characteristic theory and the assumption of Gathers. The spall strength (1977–2784 MPa) of the RSW for QP980 steel is determined based on the measured and simulated velocity histories. The spall mechanism of the RSW is brittle fracture in view of the SEM investigation of the recovered specimen. The micrographs of the as-received QP980 steel, the initial and recovered RSW of this steel for the spall test are compared to reveal the microstructure evolution during the welding and spall process. It is indicated that during the welding thermal cycle, the local martensitic phase transformation is dependent on the location within the fusion zone and the heat affected zone. It is presented that the transformation at high strain rate may be cancelled by other phenomenon while the evolution of weld defects is obvious during the spall process. It may be the stress triaxiality and strain rate effect of the RSW strength or the dynamic load-carrying capacity of the RSW structure that the spall strength of the RSW for QP980 steel is much higher than the uniaxial compression yield strength (1200 MPa) of the martensite phase in QP980 steel. Due to the weld defects in the center of the RSW, the spall strength of the RSW should be less than the conventional spall strength or the dynamic load-carrying capacity of condensed structure.

Using the newly developed particle swarm optimization algorithm on crystal structural prediction, we predict a new class of boron nitride with stoichiometry of NB$_{2}$ at ambient pressure, which belongs to the tetragonal $I\bar{4}m2$ space group. Then, its structure, elastic properties, electronic structure, and chemical bonding are investigated by first-principles calculations with the density functional theory. The phonon calculation and elastic constants confirm that the predicted NB$_{2}$ is dynamically and mechanically stable, respectively. The large bulk modulus, large shear modulus, large Young's modulus, and small Poisson's ratio show that the $I\bar{4}m2$ NB$_{2}$ should be a new superhard material with a calculated theoretical Vickers hardness value of 66 GPa. Further analysis on density of states and electron localization function demonstrate that the strong B–B and B–N covalent bonds are the main reason for its high hardness in $I\bar{4}m2$ NB$_{2}$.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

In the framework of the tight-binding model, the excitons states and linear absorption spectra are calculated in the metallic single-walled carbon nanotubes, with the axial magnetic field applied. From our calculations, it is found that for the $M_{11}$ and $M_{22}$ transitions, the exciton states are split into four separate column states by the applied magnetic field due to the symmetry breaking. More interesting is that the splitting can be directly reflected from the linear absorption spectra, which are dominated by four main absorption peaks. In addition, the splitting with increasing the axial magnetic field is also calculated, which increases linearly with the applied magnetic field. The obtained results are expected to be detected by the future experiments.

The thermodynamic properties of the bilayer ruthenate compound Sr$_3$Ru$_2$O$_7$ at very low temperatures are investigated by using a tight-binding model yielding the realistic band structure combined with the on-site interactions treated at the mean-field level. We find that both the total density of states at the Fermi energy and the entropy exhibit a sudden increase near the critical magnetic field for the nematic phase, echoing the experimental findings. A new mechanism to explain the anisotropic transport properties is proposed based on scatterings at the anisotropic domain boundaries. Our results suggest that extra cares are necessary to isolate the contributions due to the quantum criticality from the band structure singularity in Sr$_3$Ru$_2$O$_7$.

We present a systematic analysis of the exciton-recombination zone within all-quantum-dot (QD) multilayer films using sensing QD layers in QD-based light-emitting diodes (QLEDs), and demonstrate the all-QD multilayer films with different sequences of layers prepared by inserting a sensing blue QD layer denoted as B at various positions within four red QD multilayers denoted as R. We also use different hole transporting layers (PVK, CBP as well as poly-TPD) to prevent the formation of leakage current and to improve the luminance. The results show that the total EL emission is mostly at the fourth (60%) and fifth (40%) QD monolayers, adjacent to ITO. This presents both decreasing current density and increasing brightness with different hole transporting layers, thus resulting in more efficient performance.

We investigate the tunneling magnetoresistance via $\delta$ doping in a graphene-based magnetic tunnel junction in detail. It is found that the transmission probability and the conductance oscillates with the position and the aptitude of the $\delta$ doping. Also, both the transmission probability and the conductance at the parallel configuration are suppressed by the magnetic field more obviously than that at the antiparallel configuration, which implies a large negative magnetoresistance for this device. The results show that the negative magnetoresistance of over 300% at $B=1.0$ T is observed by choosing suitable doped parameters, and the temperature plays an important role in the magnetoresistance. Thus it is possible to open a way to effectively manipulate the magnetoresistance devices, and to make a type of magnetoresistance device by controlling the structural parameter of the $\delta$ doping.

We investigate theoretically the spin caloritronic transport properties of a stable 1,3,5-triphenylverdazyl (TPV) radical sandwiched between Au electrodes through different connection fashions. Obvious spin Seebeck effect can be observed in the para-connection fashion. Furthermore, a pure spin current and a completely spin-polarized current can be realized by tuning the gate voltage. Furthermore, a 100% spin polarization without the need of gate voltage can be obtained in the meta-connection fashion. These results demonstrate that TPV radical is a promising material for spin caloritronic and spintronic applications.

We report on the single crystal growth and superconducting properties of PbTaSe$_2$ with the non-centrosymmetric crystal structure. By using the chemical vapor transport technique, centimeter-size single crystals are successfully obtained. The measurement of temperature dependence of electrical resistivity $\rho(T)$ in both normal and superconducting states indicates a quasi-two-dimensional electronic state in contrast to that of polycrystalline samples. Specific heat $C(T)$ measurement reveals a bulk superconductivity with $T_{\rm c}\simeq3.75$ K and a specific heat jump ratio of 1.42. All these results are in agreement with a moderately electron–phonon coupled, type-II Bardeen–Cooper–Schrieffer superconductor.

The zero-magnetic-field oscillation behavior of spin torque nano-oscillator (STNO) with a perpendicularly magnetized free layer with second-order uniaxial anisotropy is studied theoretically based on the Landau–Lifshitz–Gilbert–Slonczewski equation. It is demonstrated numerically that the second-order uniaxial anisotropy plays a significant role in the occurrence of a zero-magnetic-field steady-state precession, which can be understood in terms of the energy balance between the energy accumulation due to the spin torque and the energy dissipation due to the Gilbert damping. In particular, a relatively large zero-magnetic-field-oscillation current region, in which the corresponding microwave frequency is increased while the threshold current still maintains an almost constant value, can be obtained by modulating the second-order uniaxial anisotropy of the free layer. These results suggest a tunable zero-magnetic-field STNO, and it may be a promising configuration for STNO's applications in future wireless communications.

The magnetic structure of the spin-chain antiferromagnet SrCo$_{2}$V$_{2}$O$_{8}$ is determined by single-crystal neutron diffraction experiment. The system undergoes a long-range magnetic order below the critical temperature $T_{\rm N}$=4.96 K. The moment of $2.16 \mu_{_{\rm B}}$ per Co at $1.6$ K in the screw chain running along the $c$ axis alternates in the $c$ axis. The moments of neighboring screw chains are arranged antiferromagnetically along one in-plane axis and ferromagnetically along the other in-plane axis. This magnetic configuration breaks the four-fold symmetry of the tetragonal crystal structure and leads to two equally populated magnetic twins with the antiferromagnetic vector in the $a$ or $b$ axis. The very similar magnetic state to the isostructural BaCo$_{2}$V$_{2}$O$_{8}$ warrants SrCo$_{2}$V$_{2}$O$_{8}$ as another interesting half-integer spin-chain antiferromagnet for investigation on quantum antiferromagnetism.

The change of conductivity and transparency of silver nanowire (AgNW) films by adding silver nano-particles (AgNPs) onto their surface is studied. The results show that the conductivity of the AgNW film is greatly improved with its sheet resistance reduced about 78.7% to 51.9 $\Omega$/sq, and there is no obvious reduction of the transmittance. Further studies show that there is a self-assembling process pushing the AgNPs to concentrate at the intersecting points between AgNWs to weld them, which would reduce the intersection resistance between the AgNWs. This self-assembling behavior is led by the surface interactivities among the dispersing liquid of AgNPs, the surface of the substrate and AgNWs when the dispersing liquid is drying.

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

A simple uniaxial oedometric system is developed to test the elastic modulus of granular materials. The stress–strain relationship is first measured under conditions of uniaxial compression with additional lateral stress and strain, then the elastic modulus of the material is determined by the linear fitting method. It is found that the modulus is positively correlated to the grain size and negatively correlated to the container size. Arching and dragging are revealed to be the mechanism of such correlations by using the digital image correlation method and the pressure film technology based on the statistical method.

How to determine accurately the association states of solutes in aqueous systems is of fundamental importance in a variety of chemical, physical, and biological processes. We apply four widely used criteria to analyze the dynamic association processes of solutes, e.g., amphiphilic molecules, and to find the inappropriate selections of representative sites on solutes in these criteria may bring about appreciable influence on the estimation of dynamic association behaviors such as unrealistic packing radii and even misleading packing structures. It would be better to select dynamically representative sites on solute molecules based on the characteristic of solute associations. Our detailed discussions give a guide on how to determine an appropriate criterion to accurately analyze the association behaviors of solute molecules in aqueous solutions.

A cyclometalated greenish-yellow emitter 2,3-diphenylimidazo[1,2-a]pyridine iridium(III) complex is successfully synthesized and used to fabricate phosphorescent organic light-emitting diodes. The optimized device exhibits a greenish-yellow emission with the peak at 523 nm and a strong shoulder at 557 nm, corresponding to Commission Internationale de l'Eclairage coordinates of (0.38, 0.58). The full width at half maximum of the device is 93 nm, which is broader than the fac-tris(2-phenylpyridine)iridium [Ir(ppy)$_{3}$] based reference device of 78 nm. Meanwhile, a maximum current efficiency of 62.6 cd/A (47.5 lm/W) is obtained. This result is higher than a maximum current efficiency of 54.8 cd/A (43 lm/W) of the Ir(ppy)$_{3}$ based device. The results indicate that this new iridium complex may have potential applications in fabricating high color rendering index white organic light emitting diodes.

The electrical instability behaviors of amorphous-indium-gallium-zinc-oxide (a-IGZO) thin-film transistors (TFTs) under ultraviolet (UV) illumination are studied. As UV radiation dosage increases, the turn-on voltage of the TFT shows continuous negative shift, which is accompanied by enhanced degradation of sub-threshold swing and field-effect mobility. The electrical instability is caused by the increased carrier concentration and defect states within the device channel, which can be further attributed to additional oxygen vacancy generation and ionization of oxygen vacancy related defects upon UV illumination, respectively. Furthermore, the performance of the a-IGZO TFT treated with UV radiation can gradually recover to its initial state after long-time storage.

The relaxation oscillation of the phase change memory (PCM) devices based on the Ge$_{2}$Sb$_{2}$Te$_{5}$ material is investigated by applying square current pulses. The current pulses with different amplitudes could be accurately given by the independently designed current testing system. The relaxation oscillation across the PCM device could be measured using an oscilloscope. The oscillation duration decreases with time, showing an inner link with the shrinking threshold voltage $V_{\rm th}$. However, the relaxation oscillation would not terminate until the remaining voltage $V_{\rm on}$ reaches the holding voltage $V_{\rm h}$. This demonstrates that the relaxation oscillation might be controlled by $V_{\rm on}$. The increasing current amplitudes could only quicken the oscillation velocity but not be able to eliminate it, which indicates that the relaxation oscillation might be an inherent behavior for the PCM cell.

The mask-free SF$_{6}$/O$_{2}$ plasma etching technique is used to produce surface texturization of mc-silicon solar cells for efficient light trapping in this work. The SEM images and mc-silicon etching rate show the influence of plasma power, SF$_{6}$/O$_{2}$ flow ratios and etching time on textured surface. With the acidic-texturing samples as a reference, the reflection and IQE spectra are obtained under different experimental conditions. The IQE spectrum measurement shows an evident increase in the visible and infrared responses. By using the optimized plasma power, SF$_{6}$/O$_{2 }$flow ratios and etching time, the optimal efficiency of 15.7% on $50\times50$ mm$^{2}$ reactive ion etching textured mc-silicon silicon solar cells is achieved, mostly due to the improvement in the short-circuit current density. The corresponding open-circuit voltage, short-circuit current density and fill factor are 611 mV, 33.6 mA/cm$^{2}$, 76.5%, respectively. It is believed that such a low-cost and high-performance texturization process is promising for large-scale industrial silicon solar cell manufacturing.

Fractal and self similarity of complex networks have attracted much attention in recent years. The fractal dimension is a useful method to describe the fractal property of networks. However, the fractal features of mobile social networks (MSNs) are inadequately investigated. In this work, a box-covering method based on the ratio of excluded mass to closeness centrality is presented to investigate the fractal feature of MSNs. Using this method, we find that some MSNs are fractal at different time intervals. Our simulation results indicate that the proposed method is available for analyzing the fractal property of MSNs.

We study the consistency conditions of the generalized $f(R)$ gravity by extending $f(R)$ gravity with non-minimal coupling to the generalized $f(R)$ with arbitrary geometry-matter coupling. Specifically, we discuss the two particular models of generalized $f(R)$ by means of consistency conditions. It is found that the second model is not physically viable so as to be ruled out. Moreover, we further constrain the first model using the Dolgov–Kawasaki stability criterion, and give the value ranges of the parameters in the first model. It is worth stressing that our results include the ones in $f(R)$ gravity with non-minimal coupling as the special case of $Q(L_{\rm m})=L_{\rm m}$.