9 research outputs found
Perturbation of the Ground Varieties of C = 1 String Theory
We discuss the effect of perturbations on the ground rings of string
theory at the various compactification radii defining the points of the
moduli space. We argue that perturbations by plus-type moduli define ground
varieties which are equivalent to the unperturbed ones under redefinitions of
the coordinates and hence cannot smoothen the singularity. Perturbations by the
minus-type moduli, on the other hand, lead to semi-universal deformations of
the singular varieties that can smoothen the singularity under certain
conditions. To first order, the cosmological perturbation by itself can remove
the singularity only at the self-dual () point.}Comment: 15 pages, TIFR/TH/93-36, phyzzx macro.(A clarification added in
Introduction, and a few references added
String Field Theory of Two Dimensional QCD on a Cylinder: A Realization of W-infinity Current Algebra
We consider 2-dimensional QCD on a cylinder, where space is a circle of
length . We formulate the theory in terms of gauge-invariant gluon operators
and multiple-winding meson (open string) operators. The meson bilocal operators
satisfy a current algebra. The gluon sector (closed strings)
contains purely quantum mechanical degrees of freedom. The description of this
sector in terms of non-relativistic fermions leads to a algebra. The
spectrum of excitations of the full theory is therefore organized according to
two different algebras: a wedge subalgebra of current algebra in the
meson sector and a wedge subalgebra of algebra in the glueball
sector. In the large limit the theory becomes semiclassical and an
effective description for the gluon degrees of freedom can be obtained. We have
solved the effective theory of the gluons in the small limit. We get a
glueball spectrum which coincides with the `discrete states' of the (Euclidean)
string theory. We remark on the implications of these results for (a) QCD
at finite temperature and (b) string theory.Comment: 28 pages, TIFR-TH-94/1
The Computational Complexity of Symbolic Dynamics at the Onset of Chaos
In a variety of studies of dynamical systems, the edge of order and chaos has
been singled out as a region of complexity. It was suggested by Wolfram, on the
basis of qualitative behaviour of cellular automata, that the computational
basis for modelling this region is the Universal Turing Machine. In this paper,
following a suggestion of Crutchfield, we try to show that the Turing machine
model may often be too powerful as a computational model to describe the
boundary of order and chaos. In particular we study the region of the first
accumulation of period doubling in unimodal and bimodal maps of the interval,
from the point of view of language theory. We show that in relation to the
``extended'' Chomsky hierarchy, the relevant computational model in the
unimodal case is the nested stack automaton or the related indexed languages,
while the bimodal case is modeled by the linear bounded automaton or the
related context-sensitive languages.Comment: 1 reference corrected, 1 reference added, minor changes in body of
manuscrip
Universal Cellular Automata and Class 4
Wolfram has provided a qualitative classification of cellular automata(CA)
rules according to which, there exits a class of CA rules (called Class 4)
which exhibit complex pattern formation and long-lived dynamical activity (long
transients). These properties of Class 4 CA's has led to the conjecture that
Class 4 rules are Universal Turing machines i.e. they are bases for
computational universality. We describe an embedding of a ``small'' universal
Turing machine due to Minsky, into a cellular automaton rule-table. This
produces a collection of cellular automata, all of which are
computationally universal. However, we observe that these rules are distributed
amongst the various Wolfram classes. More precisely, we show that the
identification of the Wolfram class depends crucially on the set of initial
conditions used to simulate the given CA. This work, among others, indicates
that a description of complex systems and information dynamics may need a new
framework for non-equilibrium statistical mechanics.Comment: Latex, 10 pages, 5 figures uuencode
Spatial stochastic resonance in 1D Ising systems
The 1D Ising model is analytically studied in a spatially periodic and
oscillatory external magnetic field using the transfer-matrix method. For low
enough magnetic field intensities the correlation between the external magnetic
field and the response in magnetization presents a maximum for a given
temperature. The phenomenon can be interpreted as a resonance phenomenon
induced by the stochastic heatbath. This novel "spatial stochastic resonance"
has a different origin from the classical stochastic resonance phenomenon.Comment: REVTex, 5 pages, 3 figure