7,231 research outputs found
Existence and smoothness of the stable foliation for sectional hyperbolic attractors
We prove the existence of a contracting invariant topological foliation in a
full neighborhood for partially hyperbolic attractors. Under certain bunching
conditions it can then be shown that this stable foliation is smooth.
Specialising to sectional hyperbolic attractors, we give a verifiable condition
for bunching. In particular, we show that the stable foliation for the
classical Lorenz equation (and nearby vector fields) is better than which
is crucial for recent results on exponential decay of correlations. In fact the
foliation is at least .Comment: Corrected estimate for smoothness of stable foliation. Clarification
of which results hold for general partially hyperbolic attractors. Some minor
typos fixed. Accepted for publication in Bull. London Math. So
Hall conductivity as bulk signature of topological transitions in superconductors
Topological superconductors may undergo transitions between phases with
different topological numbers which, like the case of topological insulators,
are related to the presence of gapless (Majorana) edge states. In
topological insulators the charge Hall conductivity is quantized, being
proportional to the number of gapless states running at the edge. In a
superconductor, however, charge is not conserved and, therefore,
is not quantized, even in the case of a topological
superconductor. Here it is shown that while the evolves
continuously between different topological phases of a topological
superconductor, its derivatives display sharp features signaling the
topological transitions. We consider in detail the case of a triplet
superconductor with p-wave symmetry in the presence of Rashba spin-orbit (SO)
coupling and externally applied Zeeman spin splitting. Generalization to the
cases where the pairing vector is not aligned with that of the SO coupling is
given. We generalize also to the cases where the normal system is already
topologically non-trivial.Comment: 10 pages, 10 figure
- …