Narrow Results

We consider the time-independent scattering theory for time evolution operators of one-dimensional two-state quantum walks. The scattering matrix associated with the position-dependent quantum walk naturally appears in the asymptotic behavior at the spatial infinity of generalized eigenfunctions. The asymptotic behavior of generalized eigenfunctions is a consequence of an explicit expression of the Green function associated with the free quantum walk. When the position-dependent quantum walk is a finite rank perturbation of the free quantum walk, we derive a kind of combinatorial construction of the scattering matrix by counting paths of quantum walkers. We also mention some remarks on the tunneling effect.

In this paper, tunneling effect of Cooper pairs in weak-link superconductor structure with multi-junctions under the condition for overstepping the Josephson approximation is discussed. The equations describing the electric current based on the tunneling effect of Cooper pairs in several kinds of weak-link superconductor structures with multi-junctions are obtained under the condition to overstep the Josephson approximation. For both SISISIS and a four junctions ring, when all junctions are in the zero voltage state, the exact solution of the equations is obtained. It is found that, because of the tunneling effect of the Cooper pairs, an alternating current exists which can be expressed by an elliptic function. For a four junctions ring, the relation between the period of the alternating current and flux is pointed out. At last, the condition for overstepping the Josephson approximation is discussed. The result shows that overstepping the Josephson approximation may be possible when the volumes of superconductors are small enough.

Originally, Parikh and Wilczek's work is only suitable for the massless particles' tunneling. But their work has been further extended to the cases of massive uncharged and charged particles' tunneling recently. In this paper, as a particular black hole solution, we apply this extended method to reconsider the tunneling effect of the Horowitz–Strominger Dilaton black hole. We investigate the behavior of both massive uncharged and charged particles, and respectively calculate the emission rate at the event horizon. Our result shows that their emission rates are also consistent with the unitary theory. Moreover, comparing with the case of massless particles' tunneling, we find that this conclusion is independent of the kind of particles. And it is probably caused by the underlying relationship between this method and the laws of black hole thermodynamics.

Carbon nanotubes (CNT) is turning out to be a replacement to all the existing traditional sensors due to their high gauge factor, multidirectional sensing capability, high flexibility, low mass density, high dynamic range and high sensitivity to strains at nano and macro- scales. The strain sensitivity of CNT-based strain sensors depends on number of parameters; quality and quantity of CNT used, type of polymer used, deposition and dispersion technique adopted and also on environmental conditions. Due to all these parameters, the piezoresistive behavior of CNT is diversified and it needs to be explored. This paper theoretically analyses the strain sensitivity of CNT-based strain sensors. The strain sensitivity response of CNT strain sensor is a result of change in total resistance of CNT network with respect to applied strain. The total resistance of CNT network consists of intrinsic resistance and inter-tube resistance. It has been found that the change in intrinsic resistance under strain is due to the variation of bandgap of individual, which depends on the chirality of the tube and it varies exponentially with strain. The inter-tube resistance of CNT network changes nonlinearly due to change in distance between neighboring CNTs with respect to applied strain. As the distance $d$ between CNTs increases due to applied strain, tunneling resistance $R_{\mathrm{\text{tunnel}}}$ increases nonlinearly in exponential manner. When the concentration of CNTs in composite is close to percolation threshold, then the change of inter-tube resistances is more dominant than intrinsic resistance. At percolation threshold, the total resistance of CNT networks changes nonlinearly and this effect of nonlinearity is due to tunneling effect. The strain sensitivity of CNT-based strain sensors also varies nonlinearly with the change in temperature. For the change of temperature from $-20^{\circ }$C to 50${}^{\circ }$C, there is more than 100% change in strain sensitivity of CNT/polymer composite strain sensor. This change is mainly due to the infiltration of polymer into CNTs.

The tunneling effect of two-dimensional Dirac fermions in a constant magnetic field is studied. This can be done by using the continuity equation at some points to determine the corresponding reflexion and transmission coefficients. For this, we consider a system made of graphene as superposition of two different regions where the second is characterized by an energy gap t'. In fact, we treat concrete systems to practically give two illustrations: barrier and diode. For each case, we discuss the transmission in terms of the ratio of the energy conservation and t'. Moreover, we analyze the resonant tunneling by introducing a scalar Lorentz potential where it is shown that a total transmission is possible.

Measurements of neutrino travel times reported last September by the OPERA collaboration have been analyzed franticly as possible evidence of superluminal propagation of a signal. Even in the likely scenario that the result ultimately does not stand up to further scrutiny, it will be worth taking notice of the few things that fundamental physics did learn in the process of studying the "OPERA anomaly".

In this paper, we discuss that the Painlevé coordinates are not required to study tunneling effect from black holes. If the Schwarzschild coordinates are used to calculate the tunneling rate by the Parikh's method, the tunneling rate is half of the standard result.