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

Turing jumps through provability

Fixing some computably enumerable theory $T$, the Friedman-Goldfarb-Harrington (FGH) theorem says that over elementary arithmetic, each $\Sigma_1$ formula is equivalent to some formula of the form $\Box_T \varphi$ provided that $T$ is consistent. In this paper we give various generalizations of the FGH theorem. In particular, for $n>1$ we relate $\Sigma_{n}$ formulas to provability statements $[n]_T^{\sf True}\varphi$ which are a formalization of "provable in $T$ together with all true $\Sigma_{n+1}$ sentences". As a corollary we conclude that each $[n]_T^{\sf True}$ is $\Sigma_{n+1}$-complete. This observation yields us to consider a recursively defined hierarchy of provability predicates $[n+1]^\Box_T$ which look a lot like $[n+1]_T^{\sf True}$ except that where $[n+1]_T^{\sf True}$ calls upon the oracle of all true $\Sigma_{n+2}$ sentences, the $[n+1]^\Box_T$ recursively calls upon the oracle of all true sentences of the form $\langle n \rangle_T^\Box\phi$. As such we obtain a `syntax-light' characterization of $\Sigma_{n+1}$ definability whence of Turing jumps which is readily extended beyond the finite. Moreover, we observe that the corresponding provability predicates $[n+1]_T^\Box$ are well behaved in that together they provide a sound interpretation of the polymodal provability logic ${\sf GLP}_\omega$

Q-stars and charged q-stars

We present the formalism of q-stars with local or global U(1) symmetry. The equations we formulate are solved numerically and provide the main features of the soliton star. We study its behavior when the symmetry is local in contrast to the global case. A general result is that the soliton remains stable and does not decay into free particles and the electrostatic repulsion preserves it from gravitational collapse. We also investigate the case of a q-star with non-minimal energy-momentum tensor and find that the soliton is stable even in some cases of collapse when the coupling to gravity is absent.Comment: Latex, 19pg, 12 figures. Accepted in Phys. Rev.

Extended bound states and resonances of two fermions on a periodic lattice

The high-$T_c$ cuprates are possible candidates for d-wave superconductivity, with the Cooper pair wave function belonging to a non-trivial irreducible representation of the lattice point group. We argue that this d-wave symmetry is related to a special form of the fermionic kinetic energy and does not require any novel pairing mechanism. In this context, we present a detailed study of the bound states and resonances formed by two lattice fermions interacting via a non-retarded potential that is attractive for nearest neighbors but repulsive for other relative positions. In the case of strong binding, a pair formed by fermions on adjacent lattice sites can have a small effective mass, thereby implying a high condensation temperature. For a weakly bound state, a pair with non-trivial symmetry tends to be smaller in size than an s-wave pair. These and other findings are discussed in connection with the properties of high-$T_c$ cuprate superconductors.Comment: 21 pages, RevTeX, 4 Postscript figures, arithmetic errors corrected. An abbreviated version (no appendix) appeared in PRB on March 1, 199

DNA DSB repair pathway choice: an orchestrated handover mechanism

DNA double strand breaks (DSBs) are potential lethal lesions but can also lead to chromosome rearrangements, a step promoting carcinogenesis. DNA non-homologous end-joining (NHEJ) is the major DSB rejoining process and occurs in all cell cycle stages. Homologous recombination (HR) can additionally function to repair irradiation-induced two-ended DSBs in G2 phase. In mammalian cells, HR predominantly uses a sister chromatid as a template for DSB repair; thus HR functions only in late S/G2 phase. Here, we review current insight into the interplay between HR and NHEJ in G2 phase. We argue that NHEJ represents the first choice pathway, repairing approximately 80% of X-ray-induced DSBs with rapid kinetics. However, a subset of DSBs undergoes end resection and repair by HR. 53BP1 restricts resection, thereby promoting NHEJ. During the switch fromNHEJ to HR, 53BP1 is repositioned to the periphery of enlarged irradiation-induced foci (IRIF) via a BRCA1-dependent process. K63-linked ubiquitin chains, which also form at IRIF, are also repositioned as well as receptor-associated protein 80 (RAP80), a ubiquitin binding protein. RAP80 repositioning requires POH1, a proteasome component. Thus, the interfacing barriers to HR, 53BP1 and RAP80 are relieved by POH1 and BRCA1, respectively. Removal of RAP80 from the IRIF core is required for loss of the ubiquitin chains and 53BP1, and for efficient replication protein A foci formation. We propose that NHEJ is used preferentially to HR because it is a compact process that does not necessitate extensive chromatin changes in the DSB vicinity

Relations Between Low-lying Quantum Wave Functions and Solutions of the Hamilton-Jacobi Equation

We discuss a new relation between the low lying Schroedinger wave function of a particle in a one-dimentional potential V and the solution of the corresponding Hamilton-Jacobi equation with -V as its potential. The function V is $\geq 0$, and can have several minina (V=0). We assume the problem to be characterized by a small anhamornicity parameter $g^{-1}$ and a much smaller quantum tunneling parameter $\epsilon$ between these different minima. Expanding either the wave function or its energy as a formal double power series in $g^{-1}$ and $\epsilon$, we show how the coefficients of $g^{-m}\epsilon^n$ in such an expansion can be expressed in terms of definite integrals, with leading order term determined by the classical solution of the Hamilton-Jacobi equation. A detailed analysis is given for the particular example of quartic potential $V={1/2}g^2(x^2-a^2)^2$.Comment: LaTex, 48 pages, no figur

Nuclear and Particle Physics applications of the Bohm Picture of Quantum Mechanics

Approximation methods for calculating individual particle/ field motions in spacetime at the quantum level of accuracy (a key feature of the Bohm Picture of Quantum Mechanics (BP)), are studied. Modern textbook presentations of Quantum Theory are used throughout, but only to provide the necessary, already existing, tested formalisms and calculational techniques. New coherent insights, reinterpretations of old solutions and results, and new (in principle testable) quantitative and qualitative predictions, can be obtained on the basis of the BP that complete the standard type of postdictions and predictions.Comment: 41 page

EYM equations in the presence of q-stars

We study Einstein-Yang-Mills equations in the presence of gravitating non-topological soliton field configurations, of q-ball type. We produce numerical solutions, stable with respect to gravitational collapse and to fission into free particles, and we study the effect of the field strength and the eigen-frequency to the soliton parameters. We also investigate the formation of such soliton stars when the spacetime is asymptotically anti de Sitter.Comment: 11 pages, to appear in Phys. Rev.

Electro-impulse de-icing testing analysis and design

Electro-Impulse De-Icing (EIDI) is a method of ice removal by sharp blows delivered by a transient electromagnetic field. Detailed results are given for studies of the electrodynamic phenomena. Structural dynamic tests and computations are described. Also reported are ten sets of tests at NASA's Icing Research Tunnel and flight tests by NASA and Cessna Aircraft Company. Fabrication of system components are described and illustrated. Fatigue and electromagnetic interference tests are reported. Here, the necessary information for the design of an EIDI system for aircraft is provided

Indications for Criticality at Zero Curvature in a 4d Regge Model of Euclidean Quantum Gravity

We re-examine the approach to four-dimensional Euclidean quantum gravity based on the Regge calculus. A cut-off on the link lengths is introduced and consequently the gravitational coupling and the cosmological constant become independent parameters. We determine the zero curvature, $=0$, line in the coupling constant plane by numerical simulations. When crossing this line we find a strong, probably first order, phase transition line with indications of a second order endpoint. Beyond the endpoint the transition through the $=0$ line appears to be a crossover. Previous investigations, using the Regge or the Dynamical Triangulation approach, dealt with a limit in which the first order transition prevails.Comment: Contribution to the lattice 2003 Tsukuba symposiu