599 research outputs found
Quantum Andreev Map: A Paradigm of Quantum Chaos in Superconductivity. .
We introduce quantum maps with particle-hole conversion (Andreev reflection) and particle-hole symmetry, which exhibit the same excitation gap as quantum dots in the proximity to a superconductor. Computationally, the Andreev maps are much more efficient than billiard models of quantum dots. This makes it possible to test analytical predictions of random-matrix theory and semiclassical chaos that were previously out of reach of computer simulations. We have observed the universal distribution of the excitation gap for a large Lyapunov exponent and the logarithmic reduction of the gap when the Ehrenfest time becomes comparable to the quasiparticle dwell time
Effect of chiral symmetry on chaotic scattering from Majorana zero modes
In many of the experimental systems that may host Majorana zero modes, a
so-called chiral symmetry exists that protects overlapping zero modes from
splitting up. This symmetry is operative in a superconducting nanowire that is
narrower than the spin-orbit scattering length, and at the Dirac point of a
superconductor/topological insulator heterostructure. Here we show that chiral
symmetry strongly modifies the dynamical and spectral properties of a chaotic
scatterer, even if it binds only a single zero mode. These properties are
quantified by the Wigner-Smith time-delay matrix ,
the Hermitian energy derivative of the scattering matrix, related to the
density of states by . We compute the
probability distribution of and , dependent on the number of
Majorana zero modes, in the chiral ensembles of random-matrix theory. Chiral
symmetry is essential for a significant -dependence.Comment: 5 pages, 3 figures + appendix (3 pages, 1 figure
Effect of a tunnel barrier on the scattering from a Majorana bound state in an Andreev billiard
We calculate the joint distribution of the scattering matrix and
time-delay matrix of a chaotic quantum dot coupled
by point contacts to metal electrodes. While and are statistically
independent for ballistic coupling, they become correlated for tunnel coupling.
We relate the ensemble averages of and and thereby obtain the average
density of states at the Fermi level. We apply this to a calculation of the
effect of a tunnel barrier on the Majorana resonance in a topological
superconductor. We find that the presence of a Majorana bound state is hidden
in the density of states and in the thermal conductance if even a single
scattering channel has unit tunnel probability. The electrical conductance
remains sensitive to the appearance of a Majorana bound state, and we calculate
the variation of the average conductance through a topological phase
transition.Comment: Contribution for the special issue of Physica E in memory of Markus
B\"{u}ttiker. 13 pages, 7 figure
Selective enhancement of topologically induced interface states in a dielectric resonator chain
The recent realization of topological phases in insulators and
superconductors has advanced the quest for robust quantum technologies. The
prospects to implement the underlying topological features controllably has
given incentive to explore optical platforms for analogous realizations. Here
we realize a topologically induced defect state in a chain of dielectric
microwave resonators and show that the functionality of the system can be
enhanced by supplementing topological protection with non-hermitian symmetries
that do not have an electronic counterpart. We draw on a characteristic
topological feature of the defect state, namely, that it breaks a sublattice
symmetry. This isolates the state from losses that respect parity-time
symmetry, which enhances its visibility relative to all other states both in
the frequency and in the time domain. This mode selection mechanism naturally
carries over to a wide range of topological and parity-time symmetric optical
platforms, including couplers, rectifiers and lasers.Comment: 5 pages, 4 figures, + supplementary information (3 pages, 4 figures
Influence of the Coulomb potential on above-threshold ionization: a quantum-orbit analysis beyond the strong-field approximation
We perform a detailed analysis of how the interplay between the residual
binding potential and a strong laser field influences above-threshold
ionization (ATI), employing a semi-analytical, Coulomb-corrected strong-field
approximation (SFA) in which the Coulomb potential is incorporated in the
electron propagation in the continuum. We find that the Coulomb interaction
lifts the degeneracy of some SFA trajectories, and we identify a set of orbits
which, for high enough photoelectron energies, may be associated with
rescattering. Furthermore, by performing a direct comparison with the standard
SFA, we show that several features in the ATI spectra can be traced back to the
influence of the Coulomb potential on different electron trajectories. These
features include a decrease in the contrast, a shift towards lower energies in
the interference substructure, and an overall increase in the photoelectron
yield. All features encountered exhibit a very good agreement with the \emph{ab
initio} solution of the time-dependent Schr\"odinger equation.Comment: 12 pages, 10 figure
Formation and interaction of resonance chains in the open 3-disk system
In ballistic open quantum systems one often observes that the resonances in
the complex-energy plane form a clear chain structure. Taking the open 3-disk
system as a paradigmatic model system, we investigate how this chain structure
is reflected in the resonance states and how it is connected to the underlying
classical dynamics. Using an efficient scattering approach we observe that
resonance states along one chain are clearly correlated while resonance states
of different chains show an anticorrelation. Studying the phase space
representations of the resonance states we find that their localization in
phase space oscillate between different regions of the classical trapped set as
one moves along the chains and that these oscillations are connected to a
modulation of the resonance spacing. A single resonance chain is thus no WKB
quantization of a single periodic orbits, but the structure of several
oscillating chains arises from the interaction of several periodic orbits. We
illuminate the physical mechanism behind these findings by combining the
semiclassical cycle expansion with a quantum graph model.Comment: 25 pages, 15 figure
Single-mode delay time statistics for scattering by a chaotic cavity
We investigate the low-frequency dynamics for transmission or reflection of a
wave by a cavity with chaotic scattering. We compute the probability
distribution of the phase derivative phi'=d phi/d omega of the scattered wave
amplitude, known as the single-mode delay time. In the case of a cavity
connected to two single-mode waveguides we find a marked distinction between
detection in transmission and in reflection: The distribution P(phi') vanishes
for negative phi' in the first case but not in the second case.Comment: 10 pages including 3 figures; to be published in Physica Scripta
(proceedings Nobel Symposium on Quantum Chaos
Classical orbit bifurcation and quantum interference in mesoscopic magnetoconductance
We study the magnetoconductance of electrons through a mesoscopic channel
with antidots. Through quantum interference effects, the conductance maxima as
functions of the magnetic field strength and the antidot radius (regulated by
the applied gate voltage) exhibit characteristic dislocations that have been
observed experimentally. Using the semiclassical periodic orbit theory, we
relate these dislocations directly to bifurcations of the leading classes of
periodic orbits.Comment: 4 pages, including 5 figures. Revised version with clarified
discussion and minor editorial change
Significance of Ghost Orbit Bifurcations in Semiclassical Spectra
Gutzwiller's trace formula for the semiclassical density of states in a
chaotic system diverges near bifurcations of periodic orbits, where it must be
replaced with uniform approximations. It is well known that, when applying
these approximations, complex predecessors of orbits created in the bifurcation
("ghost orbits") can produce pronounced signatures in the semiclassical spectra
in the vicinity of the bifurcation. It is the purpose of this paper to
demonstrate that these ghost orbits themselves can undergo bifurcations,
resulting in complex, nongeneric bifurcation scenarios. We do so by studying an
example taken from the Diamagnetic Kepler Problem, viz. the period quadrupling
of the balloon orbit. By application of normal form theory we construct an
analytic description of the complete bifurcation scenario, which is then used
to calculate the pertinent uniform approximation. The ghost orbit bifurcation
turns out to produce signatures in the semiclassical spectrum in much the same
way as a bifurcation of real orbits would.Comment: 20 pages, 6 figures, LATEX (IOP style), submitted to J. Phys.
Spectral Features of the Proximity Effect
We calculate the local density of states (LDOS) of a superconductor-normal
metal sandwich at arbitrary impurity concentration. The presence of the
superconductor induces a gap in the normal metal spectrum that is proportional
to the inverse of the elastic mean free path for rather clean systems. For
a mean free path much shorter than the thickness of the normal metal, we find a
gap size proportional to that approaches the behavior predicted by the
Usadel equation (diffusive limit).Comment: LT22 proceeding
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