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 $\alpha$: the resulting associative algebras are infinite-dimensional except for the case $\alpha=1/K$, $K$ a positive integer, where they turn out to be isomorphic to the finite-dimensional algebra of linear operators in the $K$th energy eigenspace of an isotropic harmonic oscillator with $n+1$ degrees of freedom. Other examples like the $2n$-torus and the Poincar\'e disk are discussed.Comment: 16 pages, LaTeX with AMS Font

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 $SU(n+1)/S(U(1)\times U(n))$ using a completely elementary construction: Starting from the standard star-product of Wick type on $C^{n+1} \setminus \{ 0 \}$ 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 $C^{n+1} \setminus \{ 0 \}$, 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 $SU(n+1)/S(U(1)\times U(n))$.Comment: LaTeX, 17 page

High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows

We relate high-energy limits of Laplace-type and Dirac-type operators to frame flows on the corresponding manifolds, and show that the ergodicity of frame flows implies quantum ergodicity in an appropriate sense for those operators. Observables for the corresponding quantum systems are matrix-valued pseudodifferential operators and therefore the system remains non-commutative in the high-energy limit. We discuss to what extent the space of stationary high-energy states behaves classically.Comment: 26 pages, latex2

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

Zitterbewegung and semiclassical observables for the Dirac equation

In a semiclassical context we investigate the Zitterbewegung of relativistic particles with spin 1/2 moving in external fields. It is shown that the analogue of Zitterbewegung for general observables can be removed to arbitrary order in \hbar by projecting to dynamically almost invariant subspaces of the quantum mechanical Hilbert space which are associated with particles and anti-particles. This not only allows to identify observables with a semiclassical meaning, but also to recover combined classical dynamics for the translational and spin degrees of freedom. Finally, we discuss properties of eigenspinors of a Dirac-Hamiltonian when these are projected to the almost invariant subspaces, including the phenomenon of quantum ergodicity

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