Modern Physics Letters B

The motion of molecular motor is essential to the biophysical functioning of living cells. This motion can be regarded as a multiple chemical state process. So, mathematically, the motion of molecular motor can be described by several coupled one-dimensional hopping processes or by several coupled Fokker–Planck equations. To know the basic properties of molecular motor, in this paper, we will give detailed analysis about the simplest case in which there are only two chemical states. Actually, many of the existing models, such as the flashing ratchet model, can be regarded as a two-state model. From the explicit expression of the mean velocity, one can see that the mean velocity of molecular motor might be non-zero even if the potential in each state is periodic, which means that there is no energy input to the molecular motor in each of the two states. At the same time, the mean velocity might be zero even if there is non-trivial energy input. Generally, the velocity of molecular motor depends not only on the potentials (or corresponding forward and backward transition rates) in the two chemical states, but also on the transition rates between them.

This study deals with the investigation of diffusion process of one-dimensional system with steps for adsorbates interacting via the nearest-neighbor harmonic forces. The results are obtained from numerical studies, utilizing the method of stochastic Langevin dynamics. To study commensurability effects and the role of steps in the behavior of the diffusing particles, we have computed the diffusion coefficient for large concentrations and several interaction strengths. Our numerical results show that the diffusive behavior is reduced for commensurate structure case when the ground state has only one particle per one period of the substrate potential and enhanced for incommensurate density. Furthermore, the dynamic is qualitatively similar to that obtained in the case of no steps but with a clear reduction of the diffusion rate. Implications of these findings are discussed.

In this paper, we investigate the fluctuation of the energy in the canonical ensemble in the setting of unnormalized q-expectation value theory in Tsallis statistics. After obtaining the general expression, we compare it with the energy fluctuation deduced from the generalized fluctuation-dissipation theorem. The results show that they are the same. Then, we take the classical ideal gas model as an example to explore the energy fluctuations of it. It shows that if the value of q is not in the vicinity of unity, the relative fluctuation of the energy is large. Thus, the energy in the canonical ensemble greatly deviates from the mean value.

Starting with the interaction of interacting field and a two level atom we observe that the atom-interacting field system acquires a space parameter dependent Berry phase after the phase parameter slowly changes and ultimately returns to its initial form.

The complete high-order perturbation formulas are established by both crystal-field (CF) and charge-transfer (CT) mechanisms. The EPR g factors of MgTiO₃:Cr³⁺, SrTiO₃:Cr³⁺ and SrTiO₃:Mn⁴⁺ crystals are calculated from the formulas. The calculations of the EPR g factors are in agreement with the experimental values. The contribution rate of the CT mechanism (|Δg^T/Δg^F|) to EPR parameters, increases with the growth of the valence state for the 3dⁿ ions in the crystals. For the higher valence state 3d³ ion Mn⁴⁺ in crystals, the explanation of the EPR parameters reasonably involves both CF and CT mechanisms. The g values are also given from one-spin-orbit-parameter model and crystal-field (CF) mechanism for comparison.

We present here the electrical transport properties of RFe_1-xNi_xO₃ (x ≤ 0.5) where R = Nd, Sm and Gd and the correlation between these systems. The resistivity increases as the rare ion is changed from Nd to Sm. The resistivity increases from the magnitude of the order of 10³ to 10⁶ Ωcm at lower temperatures and from 10 to 10⁵ Ωcm as the temperature is increased. Also, the resistivity decreases as the concentration of Ni is increased within the ensemble showing a semiconducting behavior. The resistivity data is fitted with the Greaves Variable Range Hopping model which fits in the intermediate range of temperatures. There is decrease in gap parameter, increase in conductivity and increase in the density of states at Fermi level which clarify that the correlation length in the conducting network increases with the increase in Ni substitution. The Debye temperature decreases as the Ni concentration increases and follows the same trend as the rare earth ion is replaced.