182,768 research outputs found
Cut time in sub-Riemannian problem on Engel group
The left-invariant sub-Riemannian problem on the Engel group is considered.
The problem gives the nilpotent approximation to generic nonholonomic systems
in four-dimensional space with two-dimensional control, for instance to a
system which describes motion of mobile robot with a trailer. The global
optimality of extremal trajectories is studied via geometric control theory.
The global diffeomorphic structure of the exponential mapping is described. As
a consequence, the cut time is proved to be equal to the first Maxwell time
corresponding to discrete symmetries of the exponential mapping
Electron Bloch Oscillations and Electromagnetic Transparency of Semiconductor Superlattices in Multi-Frequency Electric Fields
We examine phenomenon of electromagnetic transparency in semiconductor
superlattices (having various miniband dispersion laws) in the presence of
multi-frequency periodic and non-periodic electric fields. Effects of induced
transparency and spontaneous generation of static fields are discussed. We paid
a special attention on a self-induced electromagnetic transparency and its
correlation to dynamic electron localization. Processes and mechanisms of the
transparency formation, collapse, and stabilization in the presence of external
fields are studied. In particular, we present the numerical results of the time
evolution of the superlattice current in an external biharmonic field showing
main channels of transparency collapse and its partial stabilization in the
case of low electron density superlattices
Cooper pairing of electrons and holes in graphene bilayer: Correlation effects
Cooper pairing of spatially separated electrons and holes in graphene bilayer
is studied beyond the mean-field approximation. Suppression of the screening at
large distances, caused by appearance of the gap, is considered
self-consistently. A mutual positive feedback between appearance of the gap and
enlargement of the interaction leads to a sharp transition to correlated state
with greatly increased gap above some critical value of the coupling strength.
At coupling strength below the critical, this correlation effect increases the
gap approximately by a factor of two. The maximal coupling strength achievable
in experiments is close to the critical value. This indicated importance of
correlation effects in closely-spaced graphene bilayers at weak substrate
dielectric screening. Another effect beyond mean-field approximation considered
is an influence of vertex corrections on the pairing, which is shown to be very
weak.Comment: 6 pages, 5 figures; some references were adde
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