4,121 research outputs found
Ranges of bimodule projections and reflexivity
We develop a general framework for reflexivity in dual Banach spaces,
motivated by the question of when the weak* closed linear span of two reflexive
masa-bimodules is automatically reflexive. We establish an affirmative answer
to this question in a number of cases by examining two new classes of
masa-bimodules, defined in terms of ranges of masa-bimodule projections. We
give a number of corollaries of our results concerning operator and spectral
synthesis, and show that the classes of masa-bimodules we study are operator
synthetic if and only if they are strong operator Ditkin
Multidimensional operator multipliers
We introduce multidimensional Schur multipliers and characterise them
generalising well known results by Grothendieck and Peller. We define a
multidimensional version of the two dimensional operator multipliers studied
recently by Kissin and Shulman. The multidimensional operator multipliers are
defined as elements of the minimal tensor product of several C*-algebras
satisfying certain boundedness conditions. In the case of commutative
C*-algebras, the multidimensional operator multipliers reduce to continuous
multidimensional Schur multipliers. We show that the multipliers with respect
to some given representations of the corresponding C*-algebras do not change if
the representations are replaced by approximately equivalent ones. We establish
a non-commutative and multidimensional version of the characterisations by
Grothendieck and Peller which shows that universal operator multipliers can be
obtained as certain weak limits of elements of the algebraic tensor product of
the corresponding C*-algebras.Comment: A mistake in the previous versio
Chiral zero modes of the SU(n) Wess-Zumino-Novikov-Witten model
We define the chiral zero modes' phase space of the G=SU(n)
Wess-Zumino-Novikov-Witten model as an (n-1)(n+2)-dimensional manifold M_q
equipped with a symplectic form involving a special 2-form - the Wess-Zumino
(WZ) term - which depends on the monodromy M. This classical system exhibits a
Poisson-Lie symmetry that evolves upon quantization into an U_q(sl_n) symmetry
for q a primitive even root of 1. For each constant solution of the classical
Yang-Baxter equation we write down explicitly a corresponding WZ term and
invert the symplectic form thus computing the Poisson bivector of the system.
The resulting Poisson brackets appear as the classical counterpart of the
exchange relations of the quantum matrix algebra studied previously. We argue
that it is advantageous to equate the determinant D of the zero modes' matrix
to a pseudoinvariant under permutations q-polynomial in the SU(n) weights,
rather than to adopt the familiar convention D=1.Comment: 30 pages, LaTeX, uses amsfonts; v.2 - small corrections, Appendix and
a reference added; v.3 - amended version for J. Phys.
A Quantum Gauge Group Approach to the 2D SU(n) WZNW Model
The canonical quantization of the WZNW model provides a complete set of
exchange relations in the enlarged chiral state spaces that include the Gauss
components of the monodromy matrices. Regarded as new dynamical variables, the
elements of the latter cannot be identified -- they satisfy different exchange
relations. Accordingly, the two dimensional theory expressed in terms of the
left and right movers' fields does not automatically respect monodromy
invariance. Continuing our recent analysis of the problem by gauge theory
methods we conclude that physical states (on which the two dimensional field
acts as a single valued operator) are invariant under the (permuted) coproduct
of the left and right . They satisfy additional constraints fully
described for n=2.Comment: 10 pages, LATEX (Proposition 4.2 corrected, one reference added
On the Newtonian origin of the spin motive force in ferromagnetic atomic wires
We demonstrate numerically the existence of a spin-motive force acting on
spin-carriers when moving in a time and space dependent internal field. This is
the case of electrons in a one-dimensional wires with a precessing domain wall.
The effect can be explained solely by considering adiabatic dynamics and it is
shown to exist for both classical and quantum systems.Comment: 5 pages, 7 figures, added figure 7 and tex
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
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
Operator realization of the SU(2) WZNW model
Decoupling the chiral dynamics in the canonical approach to the WZNW model
requires an extended phase space that includes left and right monodromy
variables. Earlier work on the subject, which traced back the quantum qroup
symmetry of the model to the Lie-Poisson symmetry of the chiral symplectic
form, left some open questions: - How to reconcile the monodromy invariance of
the local 2D group valued field (i.e., equality of the left and right
monodromies) with the fact that the latter obey different exchange relations? -
What is the status of the quantum group symmetry in the 2D theory in which the
chiral fields commute? - Is there a consistent operator formalism in the chiral
and in the extended 2D theory in the continuum limit? We propose a constructive
affirmative answer to these questions for G=SU(2) by presenting the chiral
quantum fields as sums of chiral vertex operators and q-Bose creation and
annihilation operators.Comment: 18 pages, LATE
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