96,461 research outputs found

### SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants

We complete the realisation by braided subfactors, announced by Ocneanu, of
all SU(3)-modular invariant partition functions previously classified by
Gannon.Comment: 47 pages, minor changes, to appear in Reviews in Mathematical Physic

### New observations regarding deterministic, time reversible thermostats and Gauss's principle of least constraint

Deterministic thermostats are frequently employed in non-equilibrium
molecular dynamics simulations in order to remove the heat produced
irreversibly over the course of such simulations. The simplest thermostat is
the Gaussian thermostat, which satisfies Gauss's principle of least constraint
and fixes the peculiar kinetic energy. There are of course infinitely many ways
to thermostat systems, e.g. by fixing $\sum\limits_i{|{p_i}|^{\mu + 1}}$. In
the present paper we provide, for the first time, convincing arguments as to
why the conventional Gaussian isokinetic thermostat ($\mu=1$) is unique in this
class. We show that this thermostat minimizes the phase space compression and
is the only thermostat for which the conjugate pairing rule (CPR) holds.
Moreover it is shown that for finite sized systems in the absence of an applied
dissipative field, all other thermostats ($\mu=1$) perform work on the system
in the same manner as a dissipative field while simultaneously removing the
dissipative heat so generated. All other thermostats ($\mu=1$) are thus
auto-dissipative. Among all $\mu$-thermostats, only the $\mu=1$ Gaussian
thermostat permits an equilibrium state.Comment: 27 pages including 10 figures; submitted for publication Journal of
Chemical Physic

### Modular invariants from subfactors

In these lectures we explain the intimate relationship between modular
invariants in conformal field theory and braided subfactors in operator
algebras. A subfactor with a braiding determines a matrix $Z$ which is obtained
as a coupling matrix comparing two kinds of braided sector induction
("alpha-induction"). It has non-negative integer entries, is normalized and
commutes with the S- and T-matrices arising from the braiding. Thus it is a
physical modular invariant in the usual sense of rational conformal field
theory. The algebraic treatment of conformal field theory models, e.g.
$SU(n)_k$ models, produces subfactors which realize their known modular
invariants. Several properties of modular invariants have so far been noticed
empirically and considered mysterious such as their intimate relationship to
graphs, as for example the A-D-E classification for $SU(2)_k$. In the subfactor
context these properties can be rigorously derived in a very general setting.
Moreover the fusion rule isomorphism for maximally extended chiral algebras due
to Moore-Seiberg, Dijkgraaf-Verlinde finds a clear and very general proof and
interpretation through intermediate subfactors, not even referring to
modularity of $S$ and $T$. Finally we give an overview on the current state of
affairs concerning the relations between the classifications of braided
subfactors and two-dimensional conformal field theories. We demonstrate in
particular how to realize twisted (type II) descendant modular invariants of
conformal inclusions from subfactors and illustrate the method by new examples.Comment: Typos corrected and a few minor changes, 37 pages, AMS LaTeX, epic,
eepic, doc-class conm-p-l.cl

### Modular invariants and subfactors

In this lecture we explain the intimate relationship between modular
invariants in conformal field theory and braided subfactors in operator
algebras. Our analysis is based on an approach to modular invariants using
braided sector induction ("$\alpha$-induction") arising from the treatment of
conformal field theory in the Doplicher-Haag-Roberts framework. Many properties
of modular invariants which have so far been noticed empirically and considered
mysterious can be rigorously derived in a very general setting in the subfactor
context. For example, the connection between modular invariants and graphs (cf.
the A-D-E classification for $SU(2)_k$) finds a natural explanation and
interpretation. We try to give an overview on the current state of affairs
concerning the expected equivalence between the classifications of braided
subfactors and modular invariant two-dimensional conformal field theories.Comment: 25 pages, AMS LaTeX, epic, eepic, doc-class fic-1.cl

### Diffusion and Velocity Auto-Correlation in Shearing Granular Media

We perform numerical simulations to examine particle diffusion at steady
shear in a model granular material in two dimensions at the jamming density and
zero temperature. We confirm findings by others that the diffusion constant
depends on shear rate as $D\sim\dot\gamma^{q_D}$ with $q_D<1$, and set out to
determine a relation between $q_D$ and other exponents that characterize the
jamming transition. We then examine the the velocity auto-correlation function,
note that it is governed by two processes with different time scales, and
identify a new fundamental exponent, $\lambda$, that characterizes an algebraic
decay of correlations with time

### Asymmetric velocity correlations in shearing media

A model of soft frictionless disks in two dimensions at zero temperature is
simulated with a shearing dynamics to study various kinds of asymmetries in
sheared systems. We examine both single particle properties, the spatial
velocity correlation function, and a correlation function designed to separate
clockwise and counter-clockwise rotational fields from one another. Among the
rich and interesting behaviors we find that the velocity correlation along the
two different diagonals corresponding to compression and dilation,
respectively, are almost identical and, furthermore, that a feature in one of
the correlation functions is directly related to irreversible plastic events

### Modular Invariants, Graphs and $\alpha$-Induction for Nets of Subfactors I

We analyze the induction and restriction of sectors for nets of subfactors
defined by Longo and Rehren. Picking a local subfactor we derive a formula
which specifies the structure of the induced sectors in terms of the original
DHR sectors of the smaller net and canonical endomorphisms. We also obtain a
reciprocity formula for induction and restriction of sectors, and we prove a
certain homomorphism property of the induction mapping.
Developing further some ideas of F. Xu we will apply this theory in a
forthcoming paper to nets of subfactors arising from conformal field theory, in
particular those coming from conformal embeddings or orbifold inclusions of
SU(n) WZW models. This will provide a better understanding of the labeling of
modular invariants by certain graphs, in particular of the A-D-E classification
of SU(2) modular invariants.Comment: 36 pages, latex, several corrections, a strong additivity assumption
had to be adde

### Modular Invariants from Subfactors: Type I Coupling Matrices and Intermediate Subfactors

A braided subfactor determines a coupling matrix Z which commutes with the S-
and T-matrices arising from the braiding. Such a coupling matrix is not
necessarily of "type I", i.e. in general it does not have a block-diagonal
structure which can be reinterpreted as the diagonal coupling matrix with
respect to a suitable extension. We show that there are always two intermediate
subfactors which correspond to left and right maximal extensions and which
determine "parent" coupling matrices Z^\pm of type I. Moreover it is shown that
if the intermediate subfactors coincide, so that Z^+=Z^-, then Z is related to
Z^+ by an automorphism of the extended fusion rules. The intertwining relations
of chiral branching coefficients between original and extended S- and
T-matrices are also clarified. None of our results depends on non-degeneracy of
the braiding, i.e. the S- and T-matrices need not be modular. Examples from
SO(n) current algebra models illustrate that the parents can be different,
Z^+\neq Z^-, and that Z need not be related to a type I invariant by such an
automorphism.Comment: 25 pages, latex, a new Lemma 6.2 added to complete an argument in the
proof of the following lemma, minor changes otherwis

### Characteristics and classification of A-type supergiants in the Small Magellanic Cloud

We address the relationship between spectral type and physical properties for
A-type supergiants in the SMC. We first construct a self-consistent
classification scheme for A supergiants, employing the calcium K to H epsilon
line ratio as a temperature-sequence discriminant. Following the precepts of
the `MK process', the same morphological criteria are applied to Galactic and
SMC spectra with the understanding there may not be a correspondence in
physical properties between spectral counterparts in different environments. We
then discuss the temperature scale, concluding that A supergiants in the SMC
are systematically cooler than their Galactic counterparts at the same spectral
type, by up to ~10%. Considering the relative line strengths of H gamma and the
CH G-band we extend our study to F and early G-type supergiants, for which
similar effects are found. We note the implications for analyses of
extragalactic luminous supergiants, for the flux-weighted gravity-luminosity
relationship and for population synthesis studies in unresolved stellar
systems.Comment: 14 pages, 14 figures, accepted by MNRAS; minor section removed prior
to final publicatio

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