132 research outputs found
On a model mechanism for the spatial patterning of teeth primordia in the Alligator
We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator,Alligator mississippiensis. Detailed embryological studies by Westergaard & Ferguson (1986, 1987, 1990) show that jaw growth plays a crucial role in the developmental patterning of the tooth initiation process. Based on biological data we develop a reaction-diffusion mechanism, which crucially includes domain growth. The model can reproduce the spatial pattern development of the first seven teeth primordia in the lower half jaw ofA. mississippiensis. The results for the precise spatio-temporal sequence compare well with detailed developmental experiments
Quantum chaos, random matrix theory, and statistical mechanics in two dimensions - a unified approach
We present a theory where the statistical mechanics for dilute ideal gases
can be derived from random matrix approach. We show the connection of this
approach with Srednicki approach which connects Berry conjecture with
statistical mechanics. We further establish a link between Berry conjecture and
random matrix theory, thus providing a unified edifice for quantum chaos,
random matrix theory, and statistical mechanics. In the course of arguing for
these connections, we observe sum rules associated with the outstanding
counting problem in the theory of braid groups. We are able to show that the
presented approach leads to the second law of thermodynamics.Comment: 23 pages, TeX typ
Monopole operators in three-dimensional N=4 SYM and mirror symmetry
We study non-abelian monopole operators in the infrared limit of
three-dimensional SU(N_c) and N=4 SU(2) gauge theories. Using large N_f
expansion and operator-state isomorphism of the resulting superconformal field
theories, we construct monopole operators which are (anti-)chiral primaries and
compute their charges under the global symmetries. Predictions of
three-dimensional mirror symmetry for the quantum numbers of these monopole
operators are verified.Comment: 23 pages, LaTex; v2: section 3.4 modified, section 3.5 extended,
references adde
Information erasure and the generalized second law of black hole thermodynamics
We consider the generalized second law of black hole thermodynamics in the light of quantum information theory, in particular information erasure and Landauer’s principle (namely, that erasure of information produces at least the equivalent amount of entropy). A small quantum system outside a black hole in the Hartle-Hawking state is studied, and the quantum system comes into thermal equilibrium with the radiation surrounding the black hole. For this scenario, we present a simple proof of the generalized second law based on quantum relative entropy. We then analyze the corresponding information erasure process, and confirm our proof of the generalized second law by applying Landauer’s principle
Localization of Events in Space-Time
The present paper deals with the quantum coordinates of an event in
space-time, individuated by a quantum object. It is known that these
observables cannot be described by self-adjoint operators or by the
corresponding spectral projection-valued measure. We describe them by means of
a positive-operator-valued (POV) measure in the Minkowski space-time,
satisfying a suitable covariance condition with respect to the Poincare' group.
This POV measure determines the probability that a measurement of the
coordinates of the event gives results belonging to a given set in space-time.
We show that this measure must vanish on the vacuum and the one-particle
states, which cannot define any event. We give a general expression for the
Poincare' covariant POV measures. We define the baricentric events, which lie
on the world-line of the centre-of-mass, and we find a simple expression for
the average values of their coordinates. Finally, we discuss the conditions
which permit the determination of the coordinates with an arbitrary accuracy.Comment: 31 pages, latex, no figure
Global Topology and Local Violation of Discrete Symmetries
Cosmological models that are locally consistent with general relativity and
the standard model in which an object transported around the universe undergoes
P, C and CP transformations, are constructed. This leads to generalization of
the gauge fields that describe electro-weak and strong interactions by
enlarging the gauge groups to include anti-unitary transformations. Gedanken
experiments show that if all interactions obey Einstein causality then P, C and
CP cannot be violated in these models. But another model, which would violate
charge superselection rule even for an isolated system, is allowed. It is
suggested that the fundamental physical laws must have these discrete
symmetries which are broken spontaneously, or they must be non causal.Comment: 12 pages, 1 figure, latex, Revtex. Charge conjugation which is
physically implemented in a cosmology with the appropriate topology is
described in more detail. Some minor errors are corrected. Shortened to meet
the page limit of Physical Review Letters to which this paper was submitte
Average Entropy of a Subsystem from its Average Tsallis Entropy
In the nonextensive Tsallis scenario, Page's conjecture for the average
entropy of a subsystem[Phys. Rev. Lett. {\bf 71}, 1291(1993)] as well as its
demonstration are generalized, i.e., when a pure quantum system, whose Hilbert
space dimension is , is considered, the average Tsallis entropy of an
-dimensional subsystem is obtained. This demonstration is expected to be
useful to study systems where the usual entropy does not give satisfactory
results.Comment: Revtex, 6 pages, 2 figures. To appear in Phys. Rev.
Shortest paths on systems with power-law distributed long-range connections
We discuss shortest-path lengths on periodic rings of size L
supplemented with an average of pL randomly located long-range links whose
lengths are distributed according to P_l \sim l^{-\xpn}. Using rescaling
arguments and numerical simulation on systems of up to sites, we show
that a characteristic length exists such that for
. For small p we find
that the shortest-path length satisfies the scaling relation
\ell(r,\xpn,p)/\xi = f(\xpn,r/\xi). Three regions with different asymptotic
behaviors are found, respectively: a) \xpn>2 where , b)
1<\xpn<2 where 0<\theta_s(\xpn)<1/2 and, c) \xpn<1 where
behaves logarithmically, i.e. . The characteristic length is
of the form with \nu=1/(2-\xpn) in region b), but depends
on L as well in region c). A directed model of shortest-paths is solved and
compared with numerical results.Comment: 10 pages, 10 figures, revtex4. Submitted to PR
Modelling the spatial patterning of the primordia in the lower jaw of alligator mississippiensis
We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator, Alligator mississippiensis. Detailed embryological studies12–14 have shown that jaw growth plays a crucial role in the developmental patterning of the tooth initiation process. The development of the spatial pattern occurs on a timescale comparable to jaw growth. Based on biological data we develop a dynamic patterning mechanism, which crucially includes domain growth. The mechanism can reproduce the spatial pattern development of the first seven teeth primordia in the lower jaw of A. mississippiensis. The results for the precise spatio-temporal sequence compare well with experiment
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