arXiv subjects

Diego A. Wisniacki

Publications and source records attributed to Diego A. Wisniacki.

51 records · Page 3Linked to original sources

arXiv2012

Perturbations and chaos in quantum maps

The local density of states (LDOS) is a distribution that characterizes the effect of perturbations on quantum systems. Recently, it was proposed a semiclassical theory for the LDOS of chaotic billiards and maps. This theory predicts that the LDOS is a Breit-Wigner distribution independent of the perturbation strength and also gives a semiclassical expression for the LDOS witdth. Here, we test the validity of such an approximation in quantum maps varying the degree of chaoticity, the region in phase space where the perturbation is applying and the intensity of the perturbation. We show that for highly chaotic maps or strong perturbations the semiclassical theory of the LDOS is accurate to describe the quantum distribution. Moreover, the width of the LDOS is also well represented for its semiclassical expression in the case of mixed classical dynamics.

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arXiv2011

Semiclassical approach to fidelity amplitude

The fidelity amplitude is a quantity of paramount importance in echo type experiments. We use semiclassical theory to study the average fidelity amplitude for quantum chaotic systems under external perturbation. We explain analytically two extreme cases: the random dynamics limit --attained approximately by strongly chaotic systems-- and the random perturbation limit, which shows a Lyapunov decay. Numerical simulations help us bridge the gap between both extreme cases.

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arXiv2011

Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime

The Loschmidt echo is a measure of the stability and reversibility of quantum evolution under perturbations of the Hamiltonian. One of the expected and most relevant characteristics of this quantity for chaotic systems is an exponential decay with a perturbation independent decay rate given by the classical Lyapunov exponent. However, a non-uniform decay -- instead of the Lyapunov regime -- has been reported in several systems. In this work we find an analytical semiclassical expression for the averaged fidelity amplitude that can be related directly to the anomalous -- unexpected-- behaviour of the LE.

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arXiv2010

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.

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arXiv2010

Casimir force between integrable and chaotic pistons

We have computed numerically the Casimir force between two identical pistons inside a very long cylinder, considering different shapes for the pistons. The pistons can be considered as quantum billiards, whose spectrum determines the vacuum force. The smooth part of the spectrum fixes the force at short distances, and depends only on geometric quantities like the area or perimeter of the piston. However, correcting terms to the force, coming from the oscillating part of the spectrum which is related to the classical dynamics of the billiard, are qualitatively different for classically integrable or chaotic systems. We have performed a detailed numerical analysis of the corresponding Casimir force for pistons with regular and chaotic classical dynamics. For a family of stadium billiards, we have found that the correcting part of the Casimir force presents a sudden change in the transition from regular to chaotic geometries.

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arXiv2010

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.

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arXiv2009

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.

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arXiv2009

Distribution of resonances in the quantum open baker map

We study relevant features of the spectrum of the quantum open baker map. The opening consists of a cut along the momentum $p$ direction of the 2-torus phase space, modelling an open chaotic cavity. We study briefly the classical forward trapped set and analyze the corresponding quantum nonunitary evolution operator. The distribution of eigenvalues depends strongly on the location of the escape region with respect to the central discontinuity of this map. This introduces new ingredients to the association among the classical escape and quantum decay rates. Finally, we could verify that the validity of the fractal Weyl law holds in all cases.

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arXiv2008

Scaling laws in the quantum to classical transition in chaotic systems

We study the quantum to classical transition in a chaotic system surrounded by a diffusive environment. The emergence of classicality is monitored by the Renyi entropy, a measure of the entanglement of a system with its environment. We show that the Renyi entropy has a transition from quantum to classical behavior that scales with $\hbar^2_{\rm eff}/D$, where $\hbar_{\rm eff}$ is the effective Planck constant and $D$ is the strength of the noise. However, it was recently shown that a different scaling law controls the quantum to classical transition when it is measured comparing the corresponding phase space distributions. We discuss here the meaning of both scalings in the precise definition of a frontier between the classical and quantum behavior. We also show that there are quantum coherences that the Renyi entropy is unable to detect which questions its use in the studies of decoherence.

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arXiv2006

Quantum to classical transition in a system with a mixed classical dynamics

We study how decoherence rules the quantum-classical transition of the Kicked Harmonic Oscillator (KHO). When the amplitude of the kick is changed the system presents a classical dynamics that range from regular to a strong chaotic behavior. We show that for regular and mixed classical dynamics, and in the presence of noise, the distance between the classical and the quantum phase space distributions is proportional to a single parameter $χ\equiv K\hbar_{\rm eff}^2/4D^{3/2}$ which relates the effective Planck constant $\hbar_{\rm eff}$, the kick amplitude $K$ and the diffusion constant $D$. This is valid when $χ< 1$, a case that is always attainable in the semiclassical regime independently of the value of the strength of noise given by $D$. Our results extend a recent study performed in the chaotic regime.

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arXiv2005

Motion of vortices implies chaos in Bohmian mechanics

Bohmian mechanics is a causal interpretation of quantum mechanics in which particles describe trajectories guided by the wave function. The dynamics in the vicinity of nodes of the wave function, usually called vortices, is regular if they are at rest. However, vortices generically move during time evolution of the system. We show that this movement is the origin of chaotic behavior of quantum trajectories. As an example, our general result is illustrated numerically in the two-dimensional isotropic harmonic oscillator.

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arXiv2003

Short time decay of the Loschmidt echo

The Loschmidt echo measures the sensitivity to perturbations of quantum evolutions. We study its short time decay in classically chaotic systems. Using perturbation theory and throwing out all correlation imposed by the initial state and the perturbation, we show that the characteristic time of this regime is well described by the inverse of the width of the local density of states. This result is illustrated and discussed in a numerical study in a 2-dimensional chaotic billiard system perturbed by various contour deformations and using different types of initial conditions. Moreover, the influence to the short time decay of sub-Planck structures developed by time evolution is also investigated.

nlin.CD↗

arXiv2002

Quantum irreversibility, perturbation independent decay, and the parametric theory of the local density of states

The idea of perturbation independent decay (PID) has appeared in the context of survival-probability studies, and lately has emerged in the context of quantum irreversibility studies. In both cases the PID reflects the Lyapunov instability of the underlying semiclassical dynamics, and it can be distinguished from the Wigner-type decay that holds in the perturbative regime. The theory of the survival probability is manifestly related to the parametric theory of the local density of states (LDOS). In this Paper we demonstrate that in spite of the common "ideology", the physics of quantum irreversibility is {\em not} trivially related to the parametric theory of the LDOS. Rather, it is essential to take into account subtle cross correlations which are not captured by the LDOS alone.

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arXiv2002

Stadium Billiard with Moving Walls

We study the evolution of the energy distribution for a stadium with moving walls. We consider one period driving cycle, which is characterized by an amplitude $A$ and wall velocity $V$. This evolving energy distribution has both "parametric" and "stochastic" components. The latter are important for the theory of quantum irreversibility and dissipation in driven mesoscopic devices (eg in the context of quantum computation). For extremely slow wall velocity $V$ the spreading mechanism is dominated by transitions between neighboring levels, while for larger (non-adiabatic) velocities the spreading mechanism has both perturbative and non-perturbative features. We present, for the first time, a numerical study which is aimed in identifying the latter features. A procedure is developed for the determination of the various $V$ regimes. The possible implications on linear response theory are discussed.

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arXiv2002

Sensitivity to perturbations in a quantum chaotic billiard

The Loschmidt echo (LE) measures the ability of a system to return to the initial state after a forward quantum evolution followed by a backward perturbed one. It has been conjectured that the echo of a classically chaotic system decays exponentially, with a decay rate given by the minimum between the width $Γ$ of the local density of states and the Lyapunov exponent. As the perturbation strength is increased one obtains a cross-over between both regimes. These predictions are based on situations where the Fermi Golden Rule (FGR) is valid. By considering a paradigmatic fully chaotic system, the Bunimovich stadium billiard, with a perturbation in a regime for which the FGR manifestly does not work, we find a cross over from $Γ$ to Lyapunov decay. We find that, challenging the analytic interpretation, these conjetures are valid even beyond the expected range.

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