42 research outputs found
Universal wave functions structure in mixed systems
When a regular classical system is perturbed, non-linear resonances appear as
prescribed by the KAM and Poincar\`{e}-Birkhoff theorems. Manifestations of
this classical phenomena to the morphologies of quantum wave functions are
studied in this letter. We reveal a systematic formation of an universal
structure of localized wave functions in systems with mixed classical dynamics.
Unperturbed states that live around invariant tori are mixed when they collide
in an avoided crossing if their quantum numbers differ in a multiple to the
order of the classical resonance. At the avoided crossing eigenstates are
localized in the island chain or in the vicinity of the unstable periodic orbit
corresponding to the resonance. The difference of the quantum numbers
determines the excitation of the localized states which is reveled using the
zeros of the Husimi distribution.Comment: 6 pages, 4 figure
Loschmidt Echo and the Local Density of States
Loschmidt echo (LE) is a measure of reversibility and sensitivity to
perturbations of quantum evolutions. For weak perturbations its decay rate is
given by the width of the local density of states (LDOS). When the perturbation
is strong enough, it has been shown in chaotic systems that its decay is
dictated by the classical Lyapunov exponent. However, several recent studies
have shown an unexpected non-uniform decay rate as a function of the
perturbation strength instead of that Lyapunov decay. Here we study the
systematic behavior of this regime in perturbed cat maps. We show that some
perturbations produce coherent oscillations in the width of LDOS that imprint
clear signals of the perturbation in LE decay. We also show that if the
perturbation acts in a small region of phase space (local perturbation) the
effect is magnified and the decay is given by the width of the LDOS.Comment: 8 pages, 8 figure
Universal Response of Quantum Systems with Chaotic Dynamics
The prediction of the response of a closed system to external perturbations
is one of the central problems in quantum mechanics, and in this respect, the
local density of states (LDOS) provides an in- depth description of such a
response. The LDOS is the distribution of the overlaps squared connecting the
set of eigenfunctions with the perturbed one. Here, we show that in the case of
closed systems with classically chaotic dynamics, the LDOS is a Breit-Wigner
distribution under very general perturbations of arbitrary high intensity.
Consequently, we derive a semiclassical expression for the width of the LDOS
which is shown to be very accurate for paradigmatic systems of quantum chaos.
This Letter demonstrates the universal response of quantum systems with
classically chaotic dynamics.Comment: 4 pages, 3 figure
Quantum non-Markovian behavior at the chaos border
In this work we study the non-Markovian behaviour of a qubit coupled to an
environment in which the corresponding classical dynamics change from
integrable to chaotic. We show that in the transition region, where the
dynamics has both regular islands and chaotic areas, the average non-Markovian
behaviour is enhanced to values even larger than in the regular regime. This
effect can be related to the non-Markovian behaviour as a function of the the
initial state of the environment, where maxima are attained at the regions
dividing separate areas in classical phase space, particularly at the borders
between chaotic and regular regions. Moreover, we show that the fluctuations of
the fidelity of the environment -- which determine the non-Markovianity measure
-- give a precise image of the classical phase portrait.Comment: 23 pages, 9 figures (JPA style). Closest to published versio
Irreversibility in quantum maps with decoherence
The Bolztmann echo (BE) is a measure of irreversibility and sensitivity to
perturbations for non-isolated systems. Recently, different regimes of this
quantity were described for chaotic systems. There is a perturbative regime
where the BE decays with a rate given by the sum of a term depending on the
accuracy with which the system is time-reversed and a term depending on the
coupling between the system and the environment. In addition, a parameter
independent regime, characterised by the classical Lyapunov exponent, is
expected. In this paper we study the behaviour of the BE in hyperbolic maps
that are in contact with different environments. We analyse the emergence of
the different regimes and show that the behaviour of the decay rate of the BE
is strongly dependent on the type of environment.Comment: 13 pages, 3 figures
Relaxation of isolated quantum systems beyond chaos
In classical statistical mechanics there is a clear correlation between
relaxation to equilibrium and chaos. In contrast, for isolated quantum systems
this relation is -- to say the least -- fuzzy. In this work we try to unveil
the intricate relation between the relaxation process and the transition from
integrability to chaos. We study the approach to equilibrium in two different
many body quantum systems that can be parametrically tuned from regular to
chaotic. We show that a universal relation between relaxation and
delocalization of the initial state in the perturbed basis can be established
regardless of the chaotic nature of system.Comment: 4+ pages, 4 figs. Closest to published versio
Lyapunov decay in quantum irreversibility
The Loschmidt echo -- also known as fidelity -- is a very useful tool to
study irreversibility in quantum mechanics due to perturbations or
imperfections. Many different regimes, as a function of time and strength of
the perturbation, have been identified. For chaotic systems, there is a range
of perturbation strengths where the decay of the Loschmidt echo is perturbation
independent, and given by the classical Lyapunov exponent. But observation of
the Lyapunov decay depends strongly on the type of initial state upon which an
average is done. This dependence can be removed by averaging the fidelity over
the Haar measure, and the Lyapunov regime is recovered, as it was shown for
quantum maps. In this work we introduce an analogous quantity for systems with
infinite dimensional Hilbert space, in particular the quantum stadium billiard,
and we show clearly the universality of the Lyapunov regime.Comment: 8 pages, 6 figures. Accepted in Phil. Trans. R. Soc.
Out-of-time-order correlators and quantum chaos
Quantum Chaos has originally emerged as the field which studies how the
properties of classical chaotic systems arise in their quantum counterparts.
The growing interest in quantum many-body systems, with no obvious classical
meaning has led to consider time-dependent quantities that can help to
characterize and redefine Quantum Chaos. This article reviews the prominent
role that the out of time ordered correlator (OTOC) plays to achieve such goal.Comment: Article to be submitted to Scholarpedia. 21 pages, 11 figure