671 research outputs found
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
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
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
Many-body localization characterized from a one-particle perspective
We show that the one-particle density matrix can be used to
characterize the interaction-driven many-body localization transition in closed
fermionic systems. The natural orbitals (the eigenstates of ) are
localized in the many-body localized phase and spread out when one enters the
delocalized phase, while the occupation spectrum (the set of eigenvalues of
) reveals the distinctive Fock-space structure of the many-body
eigenstates, exhibiting a step-like discontinuity in the localized phase. The
associated one-particle occupation entropy is small in the localized phase and
large in the delocalized phase, with diverging fluctuations at the transition.
We analyze the inverse participation ratio of the natural orbitals and find
that it is independent of system size in the localized phase.Comment: 5 pages, 3 figures; v2: added two appendices and a new figure panel
in main text; v3: updated figur
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
Kinetic theory of shot noise in nondegenerate diffusive conductors
Journal ArticleWe investigate current fluctuations in nondegenerate semiconductors, on length scales intermediate between the elastic and inelastic mean free paths. We present an exact solution of the nonlinear kinetic equations in the regime of space-charge limited conduction, without resorting to the drift approximation of previous work. By including the effects of a finite voltage and carrier density in the contact region, a quantitative agreement is obtained with Monte Carlo simulations by Gonzalez et al., for a model of an energy-independent elastic scattering rate. The shot-noise power P is suppressed below the Poisson value PPoisson52eI (at mean current I) by the Coulomb repulsion of the carriers. The exact suppression factor is close to 1/3 in a three-dimensional system, in agreement with the simulations and with the drift approximation. Including an energy dependence of the scattering rate has a small effect on the suppression factor for the case of short-range scattering by uncharged impurities or quasielastic scattering by acoustic phonons. Long-range scattering by charged impurities remains an open problem
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