1,922 research outputs found
Chaotic quasi-collision trajectories in the 3-centre problem
We study a particular kind of chaotic dynamics for the planar 3-centre
problem on small negative energy level sets. We know that chaotic motions
exist, if we make the assumption that one of the centres is far away from the
other two (see Bolotin and Negrini, J. Diff. Eq. 190 (2003), 539--558): this
result has been obtained by the use of the Poincar\'e-Melnikov theory. Here we
change the assumption on the third centre: we do not make any hypothesis on its
position, and we obtain a perturbation of the 2-centre problem by assuming its
intensity to be very small. Then, for a dense subset of possible positions of
the perturbing centre on the real plane, we prove the existence of uniformly
hyperbolic invariant sets of periodic and chaotic almost collision orbits by
the use of a general result of Bolotin and MacKay (see Cel. Mech. & Dyn. Astr.
77 (2000), 49--75). To apply it, we must preliminarily construct chains of
collision arcs in a proper way. We succeed in doing that by the classical
regularisation of the 2-centre problem and the use of the periodic orbits of
the regularised problem passing through the third centre.Comment: 22 pages, 6 figure
Phase-space correlations of chaotic eigenstates
It is shown that the Husimi representations of chaotic eigenstates are
strongly correlated along classical trajectories. These correlations extend
across the whole system size and, unlike the corresponding eigenfunction
correlations in configuration space, they persist in the semiclassical limit. A
quantitative theory is developed on the basis of Gaussian wavepacket dynamics
and random-matrix arguments. The role of symmetries is discussed for the
example of time-reversal invariance.Comment: Published version with minor corrections to version
Hidden area and mechanical nonlinearities in freestanding graphene
We investigated the effect of out-of-plane crumpling on the mechanical
response of graphene membranes. In our experiments, stress was applied to
graphene membranes using pressurized gas while the strain state was monitored
through two complementary techniques: interferometric profilometry and Raman
spectroscopy. By comparing the data obtained through these two techniques, we
determined the geometric hidden area which quantifies the crumpling strength.
While the devices with hidden area obeyed linear mechanics with
biaxial stiffness N/m, specimens with hidden area in the range
were found to obey an anomalous Hooke's law with an exponent
Anisotropic magnetoresistance in nanocontacts
We present ab initio calculations of the evolution of anisotropic
magnetoresistance (AMR) in Ni nanocontacts from the ballistic to the tunnel
regime. We find an extraordinary enhancement of AMR, compared to bulk, in two
scenarios. In systems without localized states, like chemically pure break
junctions, large AMR only occurs if the orbital polarization of the current is
large, regardless of the anisotropy of the density of states. In systems that
display localized states close to the Fermi energy, like a single electron
transistor with ferromagnetic electrodes, large AMR is related to the variation
of the Fermi energy as a function of the magnetization direction.Comment: 7 pages, 4 figures; revised for publication, new figures in greyscal
Observation of the Fractional Quantum Hall Effect in Graphene
When electrons are confined in two dimensions and subjected to strong
magnetic fields, the Coulomb interactions between them become dominant and can
lead to novel states of matter such as fractional quantum Hall liquids. In
these liquids electrons linked to magnetic flux quanta form complex composite
quasipartices, which are manifested in the quantization of the Hall
conductivity as rational fractions of the conductance quantum. The recent
experimental discovery of an anomalous integer quantum Hall effect in graphene
has opened up a new avenue in the study of correlated 2D electronic systems, in
which the interacting electron wavefunctions are those of massless chiral
fermions. However, due to the prevailing disorder, graphene has thus far
exhibited only weak signatures of correlated electron phenomena, despite
concerted experimental efforts and intense theoretical interest. Here, we
report the observation of the fractional quantum Hall effect in ultraclean
suspended graphene, supporting the existence of strongly correlated electron
states in the presence of a magnetic field. In addition, at low carrier density
graphene becomes an insulator with an energy gap tunable by magnetic field.
These newly discovered quantum states offer the opportunity to study a new
state of matter of strongly correlated Dirac fermions in the presence of large
magnetic fields
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