Modern Physics Letters B

The recent experimental, theoretical and computational advances in the field of F₁-ATPase single-molecule microscopy are briefly surveyed. The role of theory is revealed in the statistical analysis, interpretation and prediction of single-molecule experimental trajectories, and in linking them with atomistic simulations. In particular, a theoretical model of elastically coupled molecular group transfer is reviewed and a detailed method for its application in stalling and controlled rotation experiments is provided. It is shown how the model can predict, using previous experiments, the rates of ligand binding/release processes (steps) and their exponential dependence on rotor angle in these experiments. The concept of Brønsted slopes is reviewed in the context of the single-molecule experiments, and the rate versus rotor angle relations are explained using the elastic model. These experimental data are treated in terms of the effect of thermodynamic driving forces on the rates assuming that the rotor shaft is elastically coupled to stator ring subunits in which the steps occur. In the application of the group transfer model on an extended angular range processes leading up to the transfer are discussed. Implications for large-scale atomistic simulation are suggested for the treatment of torque-generating steps.

The description of qudits in a formalism based on a generalized variant of Weyl–Heisenberg algebras is discussed. The unitary phase operators for a multi-qudit system and the corresponding phase states (the eigenstates of the phase operator) are constructed. We discuss the dynamics of multi-qudit phase states governed by a generalized Hamiltonian involving one- and two-body interactions which offer a remarkable connection between phase states, generalized graph states and the mutually unbiased bases. The entangled phase states are shown to possess the following properties simultaneously, namely the mutually unbiasedness of phase states resulting from the one-body generalized oscillator Hamiltonian and the entanglement properties of generalized graph states resulting from the two-body interaction Hamiltonian.

Reviewing past researches on quantum image scaling, only 2D images are studied. And, in a quantum system, the processing speed increases exponentially since parallel computation can be realized with superposition state when compared with classical computer. Consequently, this paper proposes quantum multidimensional color image scaling based on nearest-neighbor interpolation for the first time. Firstly, flexible representation of quantum images (FRQI) is extended to multidimensional color model. Meantime, the nearest-neighbor interpolation is extended to multidimensional color image and cycle translation operation is designed to perform scaling up operation. Then, the circuits are designed for quantum multidimensional color image scaling, including scaling up and scaling down, based on the extension of FRQI. In addition, complexity analysis shows that the circuits in the paper have lower complexity. Examples and simulation experiments are given to elaborate the procedure of quantum multidimensional scaling.

In this work, a variational method is used to examine the problems relevant to the free polaron energy spectrum in a wurtzite Al${}_y$Ga${}_{1-y}$N/Al${}_x$Ga${}_{1-x}$N triangle quantum well structure. The numerical calculations for the ground state energy, transition energy and polaron energy shifts as the functions of well-width $d$ and composition $x$ are carried out by considering the anisotropies of the parameters, such as the optical phonon frequency, dielectric constant and electron effective mass, as well as their observed changes with coordinate $z$ in this system. The research results show that the polaron energy shift caused by the electron–optical phonon interaction is large, and leads to an obvious energy decrease in the Al${}_y$Ga${}_{1-y}$N/Al${}_x$Ga${}_{1-x}$N triangular quantum well structure. The contribution of the confined phonon is found to increase with the increasing of the well-width and composition $x$, while that of the half space phonon is observed to decrease with the increasing of the well-width and composition $x$. The total contribution of the phonon increases with the increasing composition $x$, while a minimum is found to occur to the total contribution of the phonon during the decreasing process with the well-width. As the $d$ increases, the free polaron energies and transition energies decrease. Meanwhile, with the increasing of the composition $x$, the energy and transition energy are found to be increased. In the Al${}_y$Ga${}_{1-y}$N/Al${}_x$Ga${}_{1-x}$N triangular quantum well structure, the trends of the free polaron energy, transition energy and polaron energy shifts with the well-width and composition $x$ are found to be similar to those in the GaN/Al${}_x$Ga${}_{1-x}$N square quantum well structure. However, the corresponding values in the triangular quantum well structure are obviously greater than those in the square quantum well structure.

As the key components of grating-based X-ray phase contrast imaging, absorption gratings are essential to be fabricated. In fact, the internal stress is one of the critical issues for the application of the electroplated gold deposit as the absorption metal for absorption gratings. It is common that high internal stress levels can cause the deposit cracking, blistering and peeling away from the substrate material. This study investigates the effect of current density on the internal stress by the bent strip method. The surface morphologies of gold deposits are examined using scanning electron microscopy (SEM) and the crystal structure of the electroplated deposit is analyzed by X-ray diffraction (XRD). The change of current density reverses the internal stress of the deposits from compressive to tensile. The value of deposit stress can be near zero by optimizing the current density.

In this paper, from the algebraic reductions from the Lie algebra $gl(n,ℂ)$ to its commutative subalgebra $Z_n$, we construct the general $Z_n$-sine-Gordon and $Z_n$-sinh-Gordon systems which contain many multi-component sine-Gordon type and sinh-Gordon type equations. Meanwhile, we give the Bäcklund transformations of the $Z_n$-sine-Gordon and $Z_n$-sinh-Gordon equations which can generate new solutions from seed solutions. To see the $Z_n$-systems clearly, we consider the $Z_2$-sine-Gordon and $Z_3$-sine-Gordon equations explicitly including their Bäcklund transformations, the nonlinear superposition formula and Lax pairs.

In this paper, we propose a scheme for manipulating the behavior of optical bistability (OB) and optical multistability (OM) in an N-type four-level atomic system. In the scheme, quantum interference is optimized by the left-handed and the right-handed fields of an elliptically polarized field (EPF). The threshold and the hysteresis cycle shape of OB and OM can be controlled by modulating the intensity of the EPF. Especially, the transition from OB to OM or vice versa can also be easily realized by proper tuning the phase difference between the left-handed and right-handed polarized fields under the optimal intensity of the EPF.

This paper proposed a single photon avalanche diodes (SPADs) designed with 0.18 $\mu \mathrm{\text{m}}$ standard CMOS process. One of the major challenges in CMOS SPADs is how to raise the low photon detection efficiency (PDE). In this paper, the device structure and process parameters of the CMOS SPAD are optimized so as to improve PDE properties which have been investigated in detail. The CMOS SPADs are designed in p+/n-well/deep n-well (DNW) structure with the p-sub and the p-well guard ring (GR). The simulation results show that with the p-well GR, the quantum efficiency (QE) is about 80% with the breakdown voltage of 12.7 V, the unit responsivity is as high as 0.38 A/W and the PDE of 51% and 53% is obtained when the excess bias is at 1 V and 2 V, respectively. The dark count rate (DCR) is 6.2 kHz when bias voltage is 14 V. With the p-sub GR, the breakdown voltage is 13 V, the unit responsivity is up to 0.26 A/W, the QE is 58%, the PDE is 33% and 37% at excess bias of 1 V and 2 V, respectively. The DCR is 3.4 kHz at reverse bias voltage of 14 V.

Microstructures, electrical transport and magnetic properties of Sr${}_2$Ti${}_{1-x}$Co${}_x$O${}_4(0\le x\le 0.3)$ ceramics are investigated. With Co doping, the Sr${}_2$Ti${}_{1-x}$Co${}_x$O${}_4$ ceramics remain tetragonal structure while the grain size is decreased with doping. Magnetic moment is enhanced with Co doping and ferromagnetism is observed at low temperatures for Co-doped Sr${}_2$TiO${}_4$. The Sr${}_2$Ti${}_{0.9}$Co${}_{0.1}$O${}_4$ and Sr${}_2$Ti${}_{0.7}$Co${}_{0.3}$O${}_4$ show semiconductor-like transport properties, which can be well fitted by Mott variable range hopping model. The results will provide an effective route to synthesize Sr${}_2$Ti${}_{1-x}$Co${}_x$O${}_4$ ceramics as well as to investigate the physical properties.

In this work, we use a method based on the concept of particle confinement time $({\tau }_p)$ uniqueness to calculate the electron density and temperature in ohmically heated, edge plasma of the Hefei tokamak-7. Here, with the help of the data taken from Johnson and Hinnov’s table, we have done an extensive work to find electron densities and temperatures that satisfy the ${\tau }_p$ uniqueness to evaluate the temporal evolution of electron density $(n_e)$ and temperature $(T_e)$. The results are in good agreement as measured from the Langmuir probe array in previous works.