A Convergent Iterative Solution of the Quantum Double-well Potential

We present a new convergent iterative solution for the two lowest quantum wave functions $\psi_{ev}$ and $\psi_{od}$ of the Hamiltonian with a quartic double well potential $V$ in one dimension. By starting from a trial function, which is by itself the exact lowest even or odd eigenstate of a different Hamiltonian with a modified potential $V+\delta V$, we construct the Green's function for the modified potential. The true wave functions, $\psi_{ev}$ or $\psi_{od}$, then satisfies a linear inhomogeneous integral equation, in which the inhomogeneous term is the trial function, and the kernel is the product of the Green's function times the sum of $\delta V$, the potential difference, and the corresponding energy shift. By iterating this equation we obtain successive approximations to the true wave function; furthermore, the approximate energy shift is also adjusted at each iteration so that the approximate wave function is well behaved everywhere. We are able to prove that this iterative procedure converges for both the energy and the wave function at all $x$.Comment: 76 pages, Latex, no figure, 1 tabl

Thermally-Assisted Current-Driven Domain Wall Motion

Starting from the stochastic Landau-Lifschitz-Gilbert equation, we derive Langevin equations that describe the nonzero-temperature dynamics of a rigid domain wall. We derive an expression for the average drift velocity of the domain wall as a function of the applied current, and find qualitative agreement with recent magnetic semiconductor experiments. Our model implies that at any nonzero temperature the average domain-wall velocity initially varies linearly with current, even in the absence of non-adiabatic spin torques.Comment: 4 pages, 2 figure

Measurements of admittances and characteristic combustion times of reactive gaseous propellant coaxial injectors

The results of an experimental investigation that was concerned with the quantitative determination of the capabilities of combustion processes associated with coaxial injectors to amplify and sustain combustor oscillations was described. The driving provided by the combustion process was determined by employing the modified standing-wave method utilizing coaxial injectors and air-acetylene mixtures. Analyses of the measured data indicate that the investigated injectors are capable of initiating and amplifying combustion instabilities under favorable conditions of injector-combustion coupling and over certain frequency ranges. These frequency ranges and the frequency at which an injector's driving capacity is maximum are observed to depend upon the equivalence ratio, the pressure drop across the injector orifices and the number of injector elements. The characteristic combustion times of coaxial injectors were determined from steady state temperature measurements

Characteristics of response factors of coaxial gaseous rocket injectors

The results of an experimental investigation undertaken to determine the frequency dependence of the response factors of various gaseous propellant rocket injectors subject to axial instabilities are presented. The injector response factors were determined, using the modified impedance-tube technique, under cold-flow conditions simulating those observed in unstable rocket motors. The tested injectors included a gaseous-fuel injector element, a gaseous-oxidizer injector element and a coaxial injector with both fuel and oxidizer elements. Emphasis was given to the determination of the dependence of the injector response factor upon the open-area ratio of the injector, the length of the injector orifice, and the pressure drop across the injector orifices. The measured data are shown to be in reasonable agreement with the corresponding injector response factor data predicted by the Feiler and Heidmann model

The Renormalization Group and the Superconducting Susceptibility of a Fermi Liquid

A free Fermi gas has, famously, a superconducting susceptibility that diverges logarithmically at zero temperature. In this paper we ask whether this is still true for a Fermi liquid and find that the answer is that it does {\it not}. From the perspective of the renormalization group for interacting fermions, the question arises because a repulsive interaction in the Cooper channel is a marginally irrelevant operator at the Fermi liquid fixed point and thus is also expected to infect various physical quantities with logarithms. Somewhat surprisingly, at least from the renormalization group viewpoint, the result for the superconducting susceptibility is that two logarithms are not better than one. In the course of this investigation we derive a Callan-Symanzik equation for the repulsive Fermi liquid using the momentum-shell renormalization group, and use it to compute the long-wavelength behavior of the superconducting correlation function in the emergent low-energy theory. We expect this technique to be of broader interest.Comment: 9 pages, 2 figure

Behavior of nozzles and acoustic liners in three-dimensional acoustic fields Quarterly report, 1 Sep. - 31 Dec. 1969

Theoretical studies and test facility installation for investigating behavior of rocket nozzles and acoustic liners in three dimensional acoustic field

Behavior of nozzles and acoustic liners in three-dimensional acoustic fields Quarterly report, 1 Dec. 1969 - 28 Feb. 1970

Frequency responses of supercritical nozzles and acoustic liner

Behavior of nozzles and acoustic liners in three-dimensional acoustic fields Quarterly report, 1 Jun. - 31 Aug. 1970

Updating computer program for determining nozzle admittances to eliminate double-root solution and to fit resultant admittance data curves by statistical mean

Behavior of nozzles and acoustic liners in three-dimensional acoustic fields Quarterly report, 1 Sep. - 31 Nov. 1970

Behavior of nozzles and acoustic liners in three dimensional acoustic field

A renormalized large-n solution of the U(n) x U(n) linear sigma model in the broken symmetry phase

Dyson-Schwinger equations for the U(n) x U(n) symmetric matrix sigma model reformulated with two auxiliary fields in a background breaking the symmetry to U(n) are studied in the so-called bare vertex approximation. A large n solution is constructed under the supplementary assumption so that the scalar components are much heavier than the pseudoscalars. The renormalizability of the solution is investigated by explicit construction of the counterterms.Comment: RevTeX4, 14 pages, 2 figures. Version published in Phys. Rev.