389 research outputs found
Anomalous magneto-oscillations and spin precession
A semiclassical analysis based on concepts developed in quantum chaos reveals
that anomalous magneto-oscillations in quasi two-dimensional systems with
spin-orbit interaction reflect the non-adiabatic spin precession of a classical
spin vector along the cyclotron orbits.Comment: 4 pages, 2 figure
Subalgebras with Converging Star Products in Deformation Quantization: An Algebraic Construction for \complex \mbox{\LARGE P}^n
Based on a closed formula for a star product of Wick type on \CP^n, which
has been discovered in an earlier article of the authors, we explicitly
construct a subalgebra of the formal star-algebra (with coefficients contained
in the uniformly dense subspace of representative functions with respect to the
canonical action of the unitary group) that consists of {\em converging} power
series in the formal parameter, thereby giving an elementary algebraic proof of
a convergence result already obtained by Cahen, Gutt, and Rawnsley. In this
subalgebra the formal parameter can be substituted by a real number :
the resulting associative algebras are infinite-dimensional except for the case
, a positive integer, where they turn out to be isomorphic to
the finite-dimensional algebra of linear operators in the th energy
eigenspace of an isotropic harmonic oscillator with degrees of freedom.
Other examples like the -torus and the Poincar\'e disk are discussed.Comment: 16 pages, LaTeX with AMS Font
Natural History Of Atopic Disease In Early Childhood: Is Cord Blood IgE A Prognostic Factor?
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68008/2/10.1177_000992289203100411.pd
Semiclassical Time Evolution and Trace Formula for Relativistic Spin-1/2 Particles
We investigate the Dirac equation in the semiclassical limit \hbar --> 0. A
semiclassical propagator and a trace formula are derived and are shown to be
determined by the classical orbits of a relativistic point particle. In
addition, two phase factors enter, one of which can be calculated from the
Thomas precession of a classical spin transported along the particle orbits.
For the second factor we provide an interpretation in terms of dynamical and
geometric phases.Comment: 8 pages, no figure
Complexification of Gauge Theories
For the case of a first-class constrained system with an equivariant momentum
map, we study the conditions under which the double process of reducing to the
constraint surface and dividing out by the group of gauge transformations
is equivalent to the single process of dividing out the initial phase space by
the complexification of . For the particular case of a phase space
action that is the lift of a configuration space action, conditions are found
under which, in finite dimensions, the physical phase space of a gauge system
with first-class constraints is diffeomorphic to a manifold imbedded in the
physical configuration space of the complexified gauge system. Similar
conditions are shown to hold in the infinite-dimensional example of Yang-Mills
theories. As a physical application we discuss the adequateness of using
holomorphic Wilson loop variables as (generalized) global coordinates on the
physical phase space of Yang-Mills theory.Comment: 25pp., LaTeX, Syracuse SU-GP-93/6-2, Lisbon DF/IST 6.9
Direct Detection of Electroweak-Interacting Dark Matter
Assuming that the lightest neutral component in an SU(2)L gauge multiplet is
the main ingredient of dark matter in the universe, we calculate the elastic
scattering cross section of the dark matter with nucleon, which is an important
quantity for the direct detection experiments. When the dark matter is a real
scalar or a Majorana fermion which has only electroweak gauge interactions, the
scattering with quarks and gluon are induced through one- and two-loop quantum
processes, respectively, and both of them give rise to comparable contributions
to the elastic scattering cross section. We evaluate all of the contributions
at the leading order and find that there is an accidental cancellation among
them. As a result, the spin-independent cross section is found to be
O(10^-(46-48)) cm^2, which is far below the current experimental bounds.Comment: 19 pages, 7 figures, published versio
Nonlinear stochastic evolution equations of second order with damping
Convergence of a full discretization of a second order stochastic evolution
equation with nonlinear damping is shown and thus existence of a solution is
established. The discretization scheme combines an implicit time stepping
scheme with an internal approximation. Uniqueness is proved as well.Comment: This is the version of the article accepted for publication. The
final publication is available at http://link.springer.co
Phase Space Reduction for Star-Products: An Explicit Construction for CP^n
We derive a closed formula for a star-product on complex projective space and
on the domain using a completely elementary
construction: Starting from the standard star-product of Wick type on and performing a quantum analogue of Marsden-Weinstein
reduction, we can give an easy algebraic description of this star-product.
Moreover, going over to a modified star-product on ,
obtained by an equivalence transformation, this description can be even further
simplified, allowing the explicit computation of a closed formula for the
star-product on \CP^n which can easily transferred to the domain
.Comment: LaTeX, 17 page
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