2,110 research outputs found
Quantum computation of multifractal exponents through the quantum wavelet transform
We study the use of the quantum wavelet transform to extract efficiently
information about the multifractal exponents for multifractal quantum states.
We show that, combined with quantum simulation algorithms, it enables to build
quantum algorithms for multifractal exponents with a polynomial gain compared
to classical simulations. Numerical results indicate that a rough estimate of
fractality could be obtained exponentially fast. Our findings are relevant e.g.
for quantum simulations of multifractal quantum maps and of the Anderson model
at the metal-insulator transition.Comment: 9 pages, 9 figure
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
Discrepancies between decoherence and the Loschmidt echo
The Loschmidt echo and the purity are two quantities that can provide
invaluable information about the evolution of a quantum system. While the
Loschmidt echo characterizes instability and sensitivity to perturbations,
purity measures the loss of coherence produced by an environment coupled to the
system. For classically chaotic systems both quantities display a number of --
supposedly universal -- regimes that can lead on to think of them as equivalent
quantities. We study the decay of the Loschmidt echo and the purity for systems
with finite dimensional Hilbert space and present numerical evidence of some
fundamental differences between them.Comment: 6 pages, 3 figures. Changed title. Added 1 figure. Published version
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
Multifractality of quantum wave packets
We study a version of the mathematical Ruijsenaars-Schneider model, and
reinterpret it physically in order to describe the spreading with time of
quantum wave packets in a system where multifractality can be tuned by varying
a parameter. We compare different methods to measure the multifractality of
wave packets, and identify the best one. We find the multifractality to
decrease with time until it reaches an asymptotic limit, different from the
mulifractality of eigenvectors, but related to it, as is the rate of the
decrease. Our results could guide the study of experimental situations where
multifractality is present in quantum systems.Comment: 6 pages, 4 figures, final version including a new figure (figure 1
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.
Semiclassical approach to the work distribution
Work in closed quantum systems is usually defined by a two-point measurement. This definition of work is compatible with quantum fluctuation theorems but it fundamentally differs from its classical counterpart. In this paper, we study the correspondence principle in quantum chaotic systems. We derive a semiclassical expression of the work distribution for chaotic systems undergoing a general, finite time, process. This semiclassical distribution converges to the classical distribution in the usual classical limit. We show numerically that, for a particle inside a chaotic cavity, the semiclassical distribution provides a good approximation to quantum distribution.Fil: Garcia-Mata, Ignacio. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - Mar del Plata. Instituto de Investigaciones FĂsicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Cs.exactas y Naturales. Instituto de Investigaciones FĂsicas de Mar del Plata; ArgentinaFil: Roncaglia, Augusto Jose. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Oficina de CoordinaciĂłn Administrativa Ciudad Universitaria. Instituto de FĂsica de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de FĂsica de Buenos Aires; ArgentinaFil: Wisniacki, Diego Ariel. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Oficina de CoordinaciĂłn Administrativa Ciudad Universitaria. Instituto de FĂsica de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de FĂsica de Buenos Aires; Argentin
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