120 research outputs found
Anomalous magneto-oscillations and spin precession
A semiclassical analysis based on concepts developed in quantum chaos reveals
that anomalous magneto-oscillations in quasi two-dimensional systems with
spin-orbit interaction reflect the non-adiabatic spin precession of a classical
spin vector along the cyclotron orbits.Comment: 4 pages, 2 figure
Hermitian Young Operators
Starting from conventional Young operators we construct Hermitian operators
which project orthogonally onto irreducible representations of the (special)
unitary group.Comment: 15 page
Intermediate statistics in quantum maps
We present a one-parameter family of quantum maps whose spectral statistics
are of the same intermediate type as observed in polygonal quantum billiards.
Our central result is the evaluation of the spectral two-point correlation form
factor at small argument, which in turn yields the asymptotic level
compressibility for macroscopic correlation lengths
Level spacings and periodic orbits
Starting from a semiclassical quantization condition based on the trace
formula, we derive a periodic-orbit formula for the distribution of spacings of
eigenvalues with k intermediate levels. Numerical tests verify the validity of
this representation for the nearest-neighbor level spacing (k=0). In a second
part, we present an asymptotic evaluation for large spacings, where consistency
with random matrix theory is achieved for large k. We also discuss the relation
with the method of Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472] for
two-point correlations.Comment: 4 pages, 2 figures; major revisions in the second part, range of
validity of asymptotic evaluation clarifie
Beyond the Heisenberg time: Semiclassical treatment of spectral correlations in chaotic systems with spin 1/2
The two-point correlation function of chaotic systems with spin 1/2 is
evaluated using periodic orbits. The spectral form factor for all times thus
becomes accessible. Equivalence with the predictions of random matrix theory
for the Gaussian symplectic ensemble is demonstrated. A duality between the
underlying generating functions of the orthogonal and symplectic symmetry
classes is semiclassically established
Spectral Statistics for the Dirac Operator on Graphs
We determine conditions for the quantisation of graphs using the Dirac
operator for both two and four component spinors. According to the
Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry
the energy level statistics are expected, in the semiclassical limit, to
correspond to those of random matrices from the Gaussian symplectic ensemble.
This is confirmed by numerical investigation. The scattering matrix used to
formulate the quantisation condition is found to be independent of the type of
spinor. We derive an exact trace formula for the spectrum and use this to
investigate the form factor in the diagonal approximation
Is there an unmet medical need for improved hearing restoration?
Hearing impairment, the most prevalent sensory deficit, affects more than 466 million people worldwide (WHO). We presently lack causative treatment for the most common form, sensorineural hearing impairment; hearing aids and cochlear implants (CI) remain the only means of hearing restoration. We engaged with CI users to learn about their expectations and their willingness to collaborate with health care professionals on establishing novel therapies. We summarize upcoming CI innovations, gene therapies, and regenerative approaches and evaluate the chances for clinical translation of these novel strategies. We conclude that there remains an unmet medical need for improving hearing restoration and that we are likely to witness the clinical translation of gene therapy and major CI innovations within this decade
Parabolic maps with spin: Generic spectral statistics with non-mixing classical limit
We investigate quantised maps of the torus whose classical analogues are
ergodic but not mixing. Their quantum spectral statistics shows non-generic
behaviour, i.e.it does not follow random matrix theory (RMT). By coupling the
map to a spin 1/2, which corresponds to changing the quantisation without
altering the classical limit of the dynamics on the torus, we numerically
observe a transition to RMT statistics. The results are interpreted in terms of
semiclassical trace formulae for the maps with and without spin respectively.
We thus have constructed quantum systems with non-mixing classical limit which
show generic (i.e. RMT) spectral statistics. We also discuss the analogous
situation for an almost integrable map, where we compare to Semi-Poissonian
statistics.Comment: 29 pages, 20 figure
Semiclassical Time Evolution and Trace Formula for Relativistic Spin-1/2 Particles
We investigate the Dirac equation in the semiclassical limit \hbar --> 0. A
semiclassical propagator and a trace formula are derived and are shown to be
determined by the classical orbits of a relativistic point particle. In
addition, two phase factors enter, one of which can be calculated from the
Thomas precession of a classical spin transported along the particle orbits.
For the second factor we provide an interpretation in terms of dynamical and
geometric phases.Comment: 8 pages, no figure
Semiclassical form factor for chaotic systems with spin 1/2
We study the properties of the two-point spectral form factor for classically
chaotic systems with spin 1/2 in the semiclassical limit, with a suitable
semiclassical trace formula as our principal tool. To this end we introduce a
regularized form factor and discuss the limit in which the so-called diagonal
approximation can be recovered. The incorporation of the spin contribution to
the trace formula requires an appropriate variant of the equidistribution
principle of long periodic orbits as well as the notion of a skew product of
the classical translational and spin dynamics. Provided this skew product is
mixing, we show that generically the diagonal approximation of the form factor
coincides with the respective predictions from random matrix theory.Comment: 20 pages, no figure
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