Schrdinger Equation of a Particle on a Rotating Curved Surface

We derive the Schr6dinger 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 potentiM Vg and an additive Coriolis-induced geometric potential in the co-rotationM curvilinear coordinates. This novel effective potential, which is included in the surface Schr6dinger 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.

An Ideal Experiment to Determine the ’Past of a Particle’ in the Nested Mach-Zehnder Interferometer

An ideal experiment is designed to determine the past of a particle in the nested Mach-Zehnder interferometer （MZI） by using standard quantum mechanics with quantum non-demolition measurements. We find that when the photon reaches the detector, it only follows one arm of the outer interferometer and leaves no trace in the inner MZI. When it goes through the inner MZI, it cannot reach the detector. Our result obtained from the standard quantum mechanics contradicts the statement based on two-state vector formulism, ＇the photon did not enter the （inner） interferometer, the photon never left the interferometer, but it was there＇. Therefore, the statement and also the overlapping claim are incorrect.

THE SIZE EFFECT ON THE DISPERSION OF A PARTICLE IN A HOMOGENEOUS ISOTROPIC TURBULENCE

The mechanism of the response motion of a suspended particle to turbulent motion of its surrounding fluid is different according to si:e of turbulent eddies. The particle is dragged by the viscous force of large eddies, and meanwhile driven randomly by small eddies. Based on this understanding, the dispersion of a particle with finite size in a homogeneous isotropic turbulence is calculated in this study. Results show that there are two competing effects: when enhanced by the inertia of a particle, the long-term particle diffusivity is reduced by the finite size of the particle.

Two-fluid modeling of Geldart A particles in gas-solid micro-fluidized beds

The fiuidization behavior of Geldart A particles in a gas-solid micro-fluidized bed was investigated by Eulerian-Eulerian numerical simulation. The commonly used Gidaspow drag model was tested first. The simulation showed that the predicted minimum bubbling velocities were significantly lower than the experimental data even when an extremely fine grid size （of approximately one particle diameter） was used. The modified Gibilaro drag model was therefore tested next. The predicted minimum bubbling velocity and bed voidage were in reasonable agreement with the experimental data available in literature. The experimentally observed regime transition phenomena from bubbling to slugging were also reproduced successfully in the simulations. Parametric studies indicated that the solid-wall boundary conditions had a significant impact on the predicted gas and solid flow behavior.