4,023 research outputs found
A Convergent Iterative Solution of the Quantum Double-well Potential
We present a new convergent iterative solution for the two lowest quantum
wave functions and of the Hamiltonian with a quartic
double well potential 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 , we construct the Green's
function for the modified potential. The true wave functions, or
, 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 , 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 .Comment: 76 pages, Latex, no figure, 1 tabl
Turing jumps through provability
Fixing some computably enumerable theory , the
Friedman-Goldfarb-Harrington (FGH) theorem says that over elementary
arithmetic, each formula is equivalent to some formula of the form
provided that is consistent. In this paper we give various
generalizations of the FGH theorem. In particular, for we relate
formulas to provability statements which
are a formalization of "provable in together with all true
sentences". As a corollary we conclude that each is
-complete. This observation yields us to consider a recursively
defined hierarchy of provability predicates which look a lot
like except that where calls upon the
oracle of all true sentences, the recursively
calls upon the oracle of all true sentences of the form . As such we obtain a `syntax-light' characterization of
definability whence of Turing jumps which is readily extended
beyond the finite. Moreover, we observe that the corresponding provability
predicates are well behaved in that together they provide a
sound interpretation of the polymodal provability logic
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- 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- 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 , and can have several minina (V=0). We assume the problem to be
characterized by a small anhamornicity parameter and a much smaller
quantum tunneling parameter between these different minima.
Expanding either the wave function or its energy as a formal double power
series in and , we show how the coefficients of
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 .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, , 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 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
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