2,795 research outputs found
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
Boson-fermion model beyond mean-field approximation
A model of hybridized bosons and fermions is studied beyond the mean field
approximation. The divergent boson self-energy at zero temperature makes the
Cooper pairing of fermions impossible.The frequency and momentum dependence of
the self- energy and the condensation temperature of initially
localized bosons are calculated analytically. The value of the boson
condensation temperature is below which rules out the
boson-fermion model with the initially localized bosons as a phenomenological
explanation of high-temperature superconductivity. The intra-cell
density-density fermion-boson interaction dominates in the fermion self-energy.
The model represents a normal metal with strongly damped bosonic excitations.
The latter play the role of normal impurities.Comment: 16 pages, Latex, 5 figures available upon reques
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.
Q-stars in extra dimensions
We study q-stars with global and local U(1) symmetry in extra dimensions in
asymptotically anti de Sitter or flat spacetime. The behavior of the mass,
radius and particle number of the star is quite different in 3 dimensions, but
in 5, 6, 8 and 11 dimensions is similar to the behavior in 4.Comment: 18 pages, to appear in Phys. Rev.
Comment on "Boson-fermion model beyond the mean-field approximation"
In a recent paper [A.S.Alexandrov, J.Phys.:Condens.Matter 8, 6923 (1996);
cond-mat/9603111], it has been suggested that there is no Cooper pairing in
boson-fermion models of superconductivity. We show that this conjecture is
based on an inconsistent approximation that violates an exact identity. Quite
generally, the divergence of the fermion t-matrix (the Thouless criterion) is
accompanied by the condensation of a boson mode.Comment: LaTeX, 5 pages, 2style files included, 4 embedded EPS figures,
submitted to J.Phys.:Condens.Matte
A New Approach to Solve the Low-lying States of the Schroedinger Equation
We review a new iterative procedure to solve the low-lying states of the
Schroedinger equation, done in collaboration with Richard Friedberg. For the
groundstate energy, the order iterative energy is bounded by a finite
limit, independent of ; thereby it avoids some of the inherent difficulties
faced by the usual perturbative series expansions. For a fairly large class of
problems, this new procedure can be proved to give convergent iterative
solutions. These convergent solutions include the long standing difficult
problem of a quartic potential with either symmetric or asymmetric minima.Comment: 54 pages, 3 figures given separatel
The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary
We consider the dimer-monomer problem for the rectangular lattice. By mapping
the problem into one of close-packed dimers on an extended lattice, we rederive
the Tzeng-Wu solution for a single monomer on the boundary by evaluating a
Pfaffian. We also clarify the mathematical content of the Tzeng-Wu solution by
identifying it as the product of the nonzero eigenvalues of the Kasteleyn
matrix.Comment: 4 Pages to appear in the Physical Review E (2006
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