12,971 research outputs found
Localization of Eigenfunctions in the Stadium Billiard
We present a systematic survey of scarring and symmetry effects in the
stadium billiard. The localization of individual eigenfunctions in Husimi phase
space is studied first, and it is demonstrated that on average there is more
localization than can be accounted for on the basis of random-matrix theory,
even after removal of bouncing-ball states and visible scars. A major point of
the paper is that symmetry considerations, including parity and time-reversal
symmetries, enter to influence the total amount of localization. The properties
of the local density of states spectrum are also investigated, as a function of
phase space location. Aside from the bouncing-ball region of phase space,
excess localization of the spectrum is found on short periodic orbits and along
certain symmetry-related lines; the origin of all these sources of localization
is discussed quantitatively and comparison is made with analytical predictions.
Scarring is observed to be present in all the energy ranges considered. In
light of these results the excess localization in individual eigenstates is
interpreted as being primarily due to symmetry effects; another source of
excess localization, scarring by multiple unstable periodic orbits, is smaller
by a factor of .Comment: 31 pages, including 10 figure
Controllable quantum scars in semiconductor quantum dots
Quantum scars are enhancements of quantum probability density along classical
periodic orbits. We study the recently discovered phenomenon of strong,
perturbation-induced quantum scarring in the two-dimensional harmonic
oscillator exposed to a homogeneous magnetic field. We demonstrate that both
the geometry and the orientation of the scars are fully controllable with a
magnetic field and a focused perturbative potential, respectively. These
properties may open a path into an experimental scheme to manipulate electric
currents in nanostructures fabricated in a two-dimensional electron gas.Comment: 5 pages, 4 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
Observing trajectories with weak measurements in quantum systems in the semiclassical regime
We propose a scheme allowing to observe the evolution of a quantum system in
the semiclassical regime along the paths generated by the propagator. The
scheme relies on performing consecutive weak measurements of the position. We
show how weak trajectories" can be extracted from the pointers of a series of
measurement devices having weakly interacted with the system. The properties of
these "weak trajectories" are investigated and illustrated in the case of a
time-dependent model system.Comment: v2: Several minor corrections were made. Added Appendix (that will
appear as Suppl. Material). To be published in Phys Rev Let
Beyond the First Recurrence in Scar Phenomena
The scarring effect of short unstable periodic orbits up to times of the
order of the first recurrence is well understood. Much less is known, however,
about what happens past this short-time limit. By considering the evolution of
a dynamically averaged wave packet, we show that the dynamics for longer times
is controlled by only a few related short periodic orbits and their interplay.Comment: 4 pages, 4 Postscript figures, submitted to Phys. Rev. Let
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