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We derive the Schrödinger 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 Vg and an additive Coriolis-induced geometric potential in the co-rotational curvilinear coordinates. This novel effective potential, which is included in the surface Schrödinger 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 study the curvature-induced bound states and the coherent transport properties for a particle constrained to move on a truncated cone-like surface. With longitudinal hard wall boundary condition, the probability densities and spectra energy shifts are calculated, and are found to be obviously affected by the surface curvature. The bound-state energy levels and energy differences decrease as increasing the vertex angle or the ratio of axial length to bottom radius of the truncated cone. In a two-dimensional (2D) GaAs substrate with this geometric structure, an estimation of the ground-state energy shift of ballistic transport electrons induced by the geometric potential (GP) is addressed, which shows that the fraction of the ground-state energy shift resulting from the surface curvature is unnegligible under some region of geometric parameters. Furthermore, we model a truncated cone-like junction joining two cylinders with different radii, and investigate the effect of the GP on the transmission properties by numerically solving the open-boundary 2D Schrödinger equation with GP on the junction surface. It is shown that the oscillatory behavior of the transmission coefficient as a function of the injection energy is more pronounced when steeper GP wells appear at the two ends of the junction. Moreover, at specific injection energy, the transmission coefficient is oscillating with the ratio of the cylinder radii at incoming and outgoing sides.

We investigate a 6d generalized Randall-Sundrum brane world scenario with a bulk cosmological constant. It is shown that each stress-energy tensor T i ab on the brane is similar to a constant vacuum energy. This is consistent with the Randall-Sundrum model in which each 3-brane Lagrangian separated out a constant vacuum energy. By adopting an anisotropic metric ansatz, we obtain the 5d Friedmann-Robertson-Walker field equations. At a little later period, the expansion of the universe is proportional to t 1 2 which is as similar as the period of the radiation-dominated. We also investigate the case with two a(t) and two b(t). In a large region of t, we obtain the 3d effective cosmological constant Λ ef f = −2Ω/3 > 0 which is independent of the integral constant. Here the scale factor is exponential expansion which is consistent with our present observation of the universe. Our results demonstrate that it is possible to construct a model which solves the dark energy problem, meanwhile guaranteeing a positive brane tension.

Recent investigations of fundamental electronic properties (especially the carrier transport mechanisms) of Si nanocrystal embedded in the amorphous SiC films are highly desired in order to further develop their applications in nano-electronic and optoelectronic devices. Here, Boron-doped Si nanocrystals embedded in the amorphous SiC films were prepared by thermal annealing of Boron-doped amorphous Si-rich SiC films with various Si/C ratios. Carrier transport properties in combination with microstructural characteristics were investigated via temperature dependence Hall effect measurements. It should be pointed out that Hall mobilities, carrier concentrations as well as conductivities in films were increased with Si/C ratio, which could be reached to the maximum of 7.2 cm2/V∙s, 4.6 × 1019 cm−3 and 87.5 S∙cm−1, respectively. Notably, different kinds of carrier transport behaviors, such as Mott variable-range hopping, multiple phonon hopping, percolation hopping and thermally activation conduction that play an important role in the transport process, were identified within different temperature ranges (10 K~400 K) in the films of different Si/C ratio. The changes from Mott variable-range hopping process to thermally activation conduction process with temperature were observed and discussed in detail.