2,524 research outputs found
Scarring in open quantum systems
We study scarring phenomena in open quantum systems. We show numerical
evidence that individual resonance eigenstates of an open quantum system
present localization around unstable short periodic orbits in a similar way as
their closed counterparts. The structure of eigenfunctions around these
classical objects is not destroyed by the opening. This is exposed in a
paradigmatic system of quantum chaos, the cat map.Comment: 4 pages, 4 figure
Short periodic orbits theory for partially open quantum maps
We extend the semiclassical theory of short periodic orbits [Phys. Rev. E
{\bf 80}, 035202(R) (2009)] to partially open quantum maps. They correspond to
classical maps where the trajectories are partially bounced back due to a
finite reflectivity . These maps are representative of a class that has many
experimental applications. The open scar functions are conveniently redefined,
providing a suitable tool for the investigation of these kind of systems. Our
theory is applied to the paradigmatic partially open tribaker map. We find that
the set of periodic orbits that belong to the classical repeller of the open
map () are able to support the set of long-lived resonances of the
partially open quantum map in a perturbative regime. By including the most
relevant trajectories outside of this set, the validity of the approximation is
extended to a broad range of values. Finally, we identify the details of
the transition from qualitatively open to qualitatively closed behaviour,
providing an explanation in terms of short periodic orbits.Comment: 6 pages, 4 figure
Localization of resonance eigenfunctions on quantum repellers
We introduce a new phase space representation for open quantum systems. This
is a very powerful tool to help advance in the study of the morphology of their
eigenstates. We apply it to two different versions of a paradigmatic model, the
baker map. This allows to show that the long-lived resonances are strongly
scarred along the shortest periodic orbits that belong to the classical
repeller. Moreover, the shape of the short-lived eigenstates is also analyzed.
Finally, we apply an antiunitary symmetry measure to the resonances that
permits to quantify their localization on the repeller.Comment: 4 pages, 4 figure
OTOC, complexity and entropy in bi-partite systems
There is a remarkable interest in the study of Out-of-time ordered
correlators (OTOCs) that goes from many body theory and high energy physics to
quantum chaos. In this latter case there is a special focus on the comparison
with the traditional measures of quantum complexity such as the spectral
statistics, for example. The exponential growth has been verified for many
paradigmatic maps and systems. But less is known for multi-partite cases. On
the other hand the recently introduced Wigner separability entropy (WSE) and
its classical counterpart (CSE) provide with a complexity measure that treats
equally quantum and classical distributions in phase space. We have compared
the behavior of these measures in a system consisting of two coupled and
perturbed cat maps with different dynamics: double hyperbolic (HH), double
elliptic (EE) and mixed (HE). In all cases, we have found that the OTOCs and
the WSE have essentially the same behavior, providing with a complete
characterization in generic bi-partite systems and at the same time revealing
them as very good measures of quantum complexity for phase space distributions.
Moreover, we establish a relation between both quantities by means of a
recently proven theorem linking the second Renyi entropy and OTOCs.Comment: 6 pages, 5 figure
Entanglement Across a Transition to Quantum Chaos
We study the relation between entanglement and quantum chaos in one- and
two-dimensional spin-1/2 lattice models, which exhibit mixing of the
noninteracting eigenfunctions and transition from integrability to quantum
chaos. Contrary to what occurs in a quantum phase transition, the onset of
quantum chaos is not a property of the ground state but take place for any
typical many-spin quantum state. We study bipartite and pairwise entanglement
measures, namely the reduced Von Neumann entropy and the concurrence, and
discuss quantum entanglement sharing. Our results suggest that the behavior of
the entanglement is related to the mixing of the eigenfunctions rather than to
the transition to chaos.Comment: 14 pages, 14 figure
Classical to quantum correspondence in dissipative directed transport
We compare the quantum and classical properties of the (Quantum) Isoperiodic
Stable Structures -- (Q)ISSs -- which organize the parameter space of a
paradigmatic dissipative ratchet model, i.e. the dissipative modified kicked
rotator. We study the spectral behavior of the corresponding classical
Perron-Frobenius operators with thermal noise and the quantum superoperators
without it for small values. We find a remarkable similarity
between the classical and quantum spectra. This finding significantly extends
previous results -- obtained for the mean currents and asymptotic distributions
only -- and on the other hand unveils a classical to quantum correspondence
mechanism where the classical noise is qualitatively different from the quantum
one. This is crucial not only for simple attractors but also for chaotic ones,
where just analyzing the asymptotic distribution reveals insufficient.
Moreover, we provide with a detailed characterization of relevant eigenvectors
by means of the corresponding Weyl-Wigner distributions, in order to better
identify similarities and differences. Finally, this model being generic, it
allows us to conjecture that this classical to quantum correspondence mechanism
is a universal feature of dissipative systems.Comment: 7 pages, 6 figure
Transient features of quantum open maps
We study families of open chaotic maps that classically share the same
asymptotic properties -- forward and backwards trapped sets, repeller
dimensions, escape rate -- but differ in their short time behavior. When these
maps are quantized we find that the fine details of the distribution of
resonances and the corresponding eigenfunctions are sensitive to the initial
shape and size of the openings. We study phase space localization of the
resonances with respect to the repeller and find strong delocalization effects
when the area of the openings is smaller than .Comment: 7 pages, 7 figure
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