40,672 research outputs found
Classical and quantum ergodicity on orbifolds
We extend to orbifolds classical results on quantum ergodicity due to
Shnirelman, Colin de Verdi\`ere and Zelditch, proving that, for any positive,
first-order self-adjoint elliptic pseudodifferential operator P on a compact
orbifold X with positive principal symbol p, ergodicity of the Hamiltonian flow
of p implies quantum ergodicity for the operator P. We also prove ergodicity of
the geodesic flow on a compact Riemannian orbifold of negative sectional
curvature.Comment: 14 page
Ergodicity and Mixing in Quantum Dynamics
After a brief historical review of ergodicity and mixing in dynamics,
particularly in quantum dynamics, we introduce definitions of quantum
ergodicity and mixing using the structure of the system's energy levels and
spacings. Our definitions are consistent with usual understanding of ergodicity
and mixing. Two parameters concerning the degeneracy in energy levels and
spacings are introduced. They are computed for right triangular billiards and
the results indicate a very close relation between quantum ergodicity (mixing)
and quantum chaos. At the end, we argue that, besides ergodicity and mixing,
there may exist a third class of quantum dynamics which is characterized by a
maximized entropy.Comment: 10 pages, 6 figures and 1 tabl
On the ergodicity bounds for a constant retrial rate queueing model
We consider a Markovian single-server retrial queueing system with a constant
retrial rate. Conditions of null ergodicity and exponential ergodicity for the
correspondent process, as well as bounds on the rate of convergence are
obtained
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