5,501 research outputs found
Normalizers of Operator Algebras and Reflexivity
The set of normalizers between von Neumann (or, more generally, reflexive)
algebras A and B, (that is, the set of all operators x such that xAx* is a
subset of B and x*Bx is a subset of A) possesses `local linear structure': it
is a union of reflexive linear spaces. These spaces belong to the interesting
class of normalizing linear spaces, namely, those linear spaces U for which
UU*U is a subset of U. Such a space is reflexive whenever it is ultraweakly
closed, and then it is of the form U={x:xp=h(p)x, for all p in P}, where P is a
set of projections and h a certain map defined on P. A normalizing space
consists of normalizers between appropriate von Neumann algebras A and B.
Necessary and sufficient conditions are found for a normalizing space to
consist of normalizers between two reflexive algebras. Normalizing spaces which
are bimodules over maximal abelian selfadjoint algebras consist of operators
`supported' on sets of the form [f=g] where f and g are appropriate Borel
functions. They also satisfy spectral synthesis in the sense of Arveson.Comment: 20 pages; to appear in the Proceedings of the London Mathematical
Societ
A Unified Conformal Field Theory Description of Paired Quantum Hall States
The wave functions of the Haldane-Rezayi paired Hall state have been
previously described by a non-unitary conformal field theory with central
charge c=-2. Moreover, a relation with the c=1 unitary Weyl fermion has been
suggested. We construct the complete unitary theory and show that it
consistently describes the edge excitations of the Haldane-Rezayi state.
Actually, we show that the unitary (c=1) and non-unitary (c=-2) theories are
related by a local map between the two sets of fields and by a suitable change
of conjugation. The unitary theory of the Haldane-Rezayi state is found to be
the same as that of the 331 paired Hall state. Furthermore, the analysis of
modular invariant partition functions shows that no alternative unitary
descriptions are possible for the Haldane-Rezayi state within the class of
rational conformal field theories with abelian current algebra. Finally, the
known c=3/2 conformal theory of the Pfaffian state is also obtained from the
331 theory by a reduction of degrees of freedom which can be physically
realized in the double-layer Hall systems.Comment: Latex, 42 pages, 2 figures, 3 tables; minor corrections to text and
reference
Are current-induced forces conservative?
The expression for the force on an ion in the presence of current can be
derived from first principles without any assumption about its conservative
character. However, energy functionals have been constructed that indicate that
this force can be written as the derivative of a potential function. On the
other hand, there exist compelling specific arguments that strongly suggest the
contrary. We propose physical mechanisms that invalidate such arguments and
demonstrate their existence with first-principles calculations. While our
results do not constitute a formal resolution to the fundamental question of
whether current-induced forces are conservative, they represent a substantial
step forward in this direction.Comment: 4 pages, 4 Figures, submitted to PR
Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics
Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested
Magneto-mechanical interplay in spin-polarized point contacts
We investigate the interplay between magnetic and structural dynamics in
ferromagnetic atomic point contacts. In particular, we look at the effect of
the atomic relaxation on the energy barrier for magnetic domain wall migration
and, reversely, at the effect of the magnetic state on the mechanical forces
and structural relaxation. We observe changes of the barrier height due to the
atomic relaxation up to 200%, suggesting a very strong coupling between the
structural and the magnetic degrees of freedom. The reverse interplay is weak,
i.e. the magnetic state has little effect on the structural relaxation at
equilibrium or under non-equilibrium, current-carrying conditions.Comment: 5 pages, 4 figure
Getting to know you: Accuracy and error in judgments of character
Character judgments play an important role in our everyday lives. However, decades of empirical research on trait attribution suggest that the cognitive processes that generate these judgments are prone to a number of biases and cognitive distortions. This gives rise to a skeptical worry about the epistemic foundations of everyday characterological beliefs that has deeply disturbing and alienating consequences. In this paper, I argue that this skeptical worry is misplaced: under the appropriate informational conditions, our everyday character-trait judgments are in fact quite trustworthy. I then propose a mindreading-based model of the socio-cognitive processes underlying trait attribution that explains both why these judgments are initially unreliable, and how they eventually become more accurate
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