5 research outputs found
A Characterization of Bispecial Sturmian Words
A finite Sturmian word w over the alphabet {a,b} is left special (resp. right
special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial
Sturmian word is a Sturmian word that is both left and right special. We show
as a main result that bispecial Sturmian words are exactly the maximal internal
factors of Christoffel words, that are words coding the digital approximations
of segments in the Euclidean plane. This result is an extension of the known
relation between central words and primitive Christoffel words. Our
characterization allows us to give an enumerative formula for bispecial
Sturmian words. We also investigate the minimal forbidden words for the set of
Sturmian words.Comment: Accepted to MFCS 201
Towards an S-matrix Description of Gravitational Collapse
Extending our previous results on trans-Planckian () scattering
of light particles in quantum string-gravity we present a calculation of the
corresponding S-matrix from the region of large impact parameters () down to the regime where classical gravitational collapse
is expected to occur. By solving the semiclassical equations of a previously
introduced effective-action approximation, we find that the perturbative
expansion around the leading eikonal result diverges at a critical value , signalling the onset of a new (black-hole related?)
regime. We then discuss the main features of our explicitly unitary S-matrix --
and of the associated effective metric -- down to (and in the vicinity of) , and present some ideas and results on its extension all the way to the region. We find that for the physical field solutions are
complex-valued and the S-matrix shows additional absorption, related to a new
production mechanism. The field solutions themselves are, surprisingly,
everywhere regular, suggesting a quantum-tunneling -- rather than a
singular-geometry -- situation.Comment: 39 pages, 5 figures; added discussion sect. 7, added references,
acknowledgement