59,796 research outputs found
Energetic and dynamic properties of a quantum particle in a spatially random magnetic field with constant correlations along one direction
We consider an electrically charged particle on the Euclidean plane subjected
to a perpendicular magnetic field which depends only on one of the two
Cartesian co-ordinates. For such a ``unidirectionally constant'' magnetic field
(UMF), which otherwise may be random or not, we prove certain spectral and
transport properties associated with the corresponding one-particle
Schroedinger operator (without scalar potential) by analysing its ``energy-band
structure''. In particular, for an ergodic random UMF we provide conditions
which ensure that the operator's entire spectrum is almost surely absolutely
continuous. This implies that, along the direction in which the random UMF is
constant, the quantum-mechanical motion is almost surely ballistic, while in
the perpendicular direction in the plane one has dynamical localisation. The
conditions are verified, for example, for Gaussian and Poissonian random UMF's
with non-zero mean-values. These results may be viewed as ``random analogues''
of results first obtained by A. Iwatsuka [Publ. RIMS, Kyoto Univ. 21 (1985)
385] and (non-rigorously) by J. E. Mueller [Phys. Rev. Lett. 68 (1992) 385]
Monoids over which all weakly flat acts are flat
If R is a ring with identity and M is a left R-module then it is well known that the following statements are equivalent: (1) M is flat. (2) The functor—⊗ M preserves embeddings of right ideals into R. This paper investigates situations in which the analogous statements are equivalent in the context of S-sets over a monoid S
Wave Packet Dynamics, Ergodicity, and Localization in Quasiperiodic Chains
In this paper, we report results for the wave packet dynamics in a class of
quasiperiodic chains consisting of two types of weakly coupled clusters. The
dynamics are studied by means of the return probability and the mean square
displacement. The wave packets show anomalous diffusion in a stepwise process
of fast expansion followed by time intervals of confined wave packet width.
Applying perturbation theory, where the coupling parameter v is treated as
perturbation, the properties of the eigenstates of the system are investigated
and related to the structure of the chains. The results show the appearance of
non-localized states only in sufficiently high orders of the perturbation
expansions. Further, we compare these results to the exact solutions obtained
by numerical diagonalization. This shows that eigenstates spread across the
entire chain for v>0, while in the limit v->0 ergodicity is broken and
eigenstates only spread across clusters of the same type, in contradistinction
to trivial localization for v=0. Caused by this ergodicity breaking, the wave
packet dynamics change significantly in the presence of an impurity offering
the possibility to control its long-term dynamics.Comment: 10 pages, 9 figure
Localization, quantum resonances and ratchet acceleration in a periodically-kicked -symmetric quantum rotator
We consider wave transport phenomena in a -symmetric extension
of the periodically-kicked quantum rotator model and reveal that dynamical
localization assists the unbroken phase. In the delocalized
(quantum resonance) regime, symmetry is always in the broken
phase and ratchet acceleration arises as a signature of unidirectional
non-Hermitian transport. An optical implementation of the periodically-kicked
-symmetric Hamiltonian, based on transverse beam propagation in a
passive optical resonator with combined phase and loss gratings, is suggested
to visualize acceleration modes in fractional Talbot cavities.Comment: 11 pages, 7 figure
- …