The calculated performance of airplanes equipped with supercharging engines

In part one of this report are presented the theoretical performance curves of an airplane engine equipped with a supercharging compressor. In predicting the gross power of a supercharging engine, the writer uses temperature and pressure correction factors based on experiments made at the Bureau of Standards (NACA report nos. 45 and 46). Means for estimating the temperature rise in the compressor are outlined. Part two of this report presents an estimation of the performance curves of an airplane fitted with a supercharging engine. A supercharging installation suitable for commercial use is described, and it is shown that with the use of the compressor a great saving in fuel and a considerable increase in carrying capacity can be effected simultaneously. In an appendix the writer derives a theoretical formula for the correction of the thrust coefficient of an airscrew to offset the added resistance of the airplane due to the slip-stream effect

Calculation of low-pressure indicator diagrams

Report develops a fundamental conception and partial application of a method for calculating the pressure-volume relationships to be expected for any given engine design. It outlines a method of computing and interpreting low-pressure indicator cards

Determining a quantum state by means of a single apparatus

The unknown state \hrho of a quantum system S is determined by letting it interact with an auxiliary system A, the initial state of which is known. A one-to-one mapping can thus be realized between the density matrix \hrho and the probabilities of occurrence of the eigenvalues of a single and factorized observable of S+A, so that \hrho can be determined by repeated measurements using a single apparatus. If S and A are spins, it suffices to measure simultaneously their $z$-components after a controlled interaction. The most robust setups are determined in this case, for an initially pure or a completely disordered state of A. They involve an Ising or anisotropic Heisenberg coupling and an external field.Comment: 5 pages revte

Electrical expression of spin accumulation in ferromagnet/semiconductor structures

We treat the spin injection and extraction via a ferromagnetic metal/semiconductor Schottky barrier as a quantum scattering problem. This enables the theory to explain a number of phenomena involving spin-dependent current through the Schottky barrier, especially the counter-intuitive spin polarization direction in the semiconductor due to current extraction seen in recent experiments. A possible explanation of this phenomenon involves taking into account the spin-dependent inelastic scattering via the bound states in the interface region. The quantum-mechanical treatment of spin transport through the interface is coupled with the semiclassical description of transport in the adjoining media, in which we take into account the in-plane spin diffusion along the interface in the planar geometry used in experiments. The theory forms the basis of the calculation of spin-dependent current flow in multi-terminal systems, consisting of a semiconductor channel with many ferromagnetic contacts attached, in which the spin accumulation created by spin injection/extraction can be efficiently sensed by electrical means. A three-terminal system can be used as a magnetic memory cell with the bit of information encoded in the magnetization of one of the contacts. Using five terminals we construct a reprogrammable logic gate, in which the logic inputs and the functionality are encoded in magnetizations of the four terminals, while the current out of the fifth one gives a result of the operation.Comment: A review to appear in Mod. Phys. Lett.

Critical view of WKB decay widths

A detailed comparison of the expressions for the decay widths obtained within the semiclassical WKB approximation using different approaches to the tunneling problem is performed. The differences between the available improved formulae for tunneling near the top and the bottom of the barrier are investigated. Though the simple WKB method gives the right order of magnitude of the decay widths, a small number of parameters are often fitted. The need to perform the fitting procedure remaining consistently within the WKB framework is emphasized in the context of the fission model based calculations. Calculations for the decay widths of some recently found super heavy nuclei using microscopic alpha-nucleus potentials are presented to demonstrate the importance of a consistent WKB calculation. The half-lives are found to be sensitive to the density dependence of the nucleon-nucleon interaction and the implementation of the Bohr-Sommerfeld quantization condition inherent in the WKB approach.Comment: 18 pages, Late

Pauli problem for a spin of arbitrary length: A simple method to determine its wave function

The problem of determining a pure state vector from measurements is investigated for a quantum spin of arbitrary length. Generically, only a finite number of wave functions is compatible with the intensities of the spin components in two different spatial directions, measured by a Stern-Gerlach apparatus. The remaining ambiguity can be resolved by one additional well-defined measurement. This method combines efficiency with simplicity: only a small number of quantities have to be measured and the experimental setup is elementary. Other approaches to determine state vectors from measurements, also known as the ‘‘Pauli problem,’’ are reviewed for both spin and particle systems

How to determine a quantum state by measurements: The Pauli problem for a particle with arbitrary potential

The problem of reconstructing a pure quantum state ¿¿> from measurable quantities is considered for a particle moving in a one-dimensional potential V(x). Suppose that the position probability distribution ¿¿(x,t)¿2 has been measured at time t, and let it have M nodes. It is shown that after measuring the time evolved distribution at a short-time interval ¿t later, ¿¿(x,t+¿t)¿2, the set of wave functions compatible with these distributions is given by a smooth manifold M in Hilbert space. The manifold M is isomorphic to an M-dimensional torus, TM. Finally, M additional expectation values of appropriately chosen nonlocal operators fix the quantum state uniquely. The method used here is the analog of an approach that has been applied successfully to the corresponding problem for a spin system

Corrections to the universal behavior of the Coulomb-blockade peak splitting for quantum dots separated by a finite barrier

Building upon earlier work on the relation between the dimensionless interdot channel conductance g and the fractional Coulomb-blockade peak splitting f for two electrostatically equivalent dots, we calculate the leading correction that results from an interdot tunneling barrier that is not a delta-function but, rather, has a finite height V and a nonzero width xi and can be approximated as parabolic near its peak. We develop a new treatment of the problem for g much less than 1 that starts from the single-particle eigenstates for the full coupled-dot system. The finiteness of the barrier leads to a small upward shift of the f-versus-g curve at small values of g. The shift is a consequence of the fact that the tunneling matrix elements vary exponentially with the energies of the states connected. Therefore, when g is small, it can pay to tunnel to intermediate states with single-particle energies above the barrier height V. The correction to the zero-width behavior does not affect agreement with recent experimental results but may be important in future experiments.Comment: Title changed from ``Non-universal...'' to ``Corrections to the universal...'' No other changes. 10 pages, 1 RevTeX file with 2 postscript figures included using eps

Analytic results for Gaussian wave packets in four model systems: I. Visualization of the kinetic energy

Using Gaussian wave packet solutions, we examine how the kinetic energy is distributed in time-dependent solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium. We find, for specific choices of initial parameters, that as much as 90% of the kinetic energy can be localized (at least conceptually) in the `front half' of such Gaussian wave packets, and we visualize these effects.Comment: 22 pages, RevTeX, four .eps figures, to appear in Found. Phys. Lett. Vol. 17, Dec. 200

On the Global Existence of Bohmian Mechanics

We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the connection between the conditions necessary for global existence and the self-adjointness of the Schr\"odinger Hamiltonian.Comment: 35 pages, LaTe