Decoherence and Loschmidt echoes: quantum against classical

We discuss the stability of quantum motion under system's perturbations in the light of the corresponding classical behavior. In particular we focus our attention on the so called "fidelity" or Loschmidt echo, its relation with the decay of correlations, and discuss the quantum-classical correspondence. We then report on the numerical simulation of the double-slit experiment, where the initial wave-packet is bounded inside a billiard domain with perfectly reflecting walls. If the shape of the billiard is such that the classical ray dynamics is regular, we obtain interference fringes whose visibility can be controlled by changing the parameters of the initial state. However, if we modify the shape of the billiard thus rendering classical (ray) dynamics fully chaotic, the interference fringes disappear and the intensity on the screen becomes the (classical) sum of intensities for the two corresponding one-slit experiments. Thus we show a clear and fundamental example in which transition to chaotic motion in a deterministic classical system, in absence of any external noise, leads to a profound modification in the quantum behavior.

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“…As it is discussed in more detail in contribution [27], the quantum fidelity (6) is expected to follow the classical fidelity (1) …”

Section: Stability Of Quantum Motion Under System's Perturbationsmentioning

confidence: 99%

Quantum chaos, dynamical stability and decoherence

Casati

Prosen

2005

Braz. J. Phys.

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“…The need is further stressed by the relevance of the LE to quantum computation [18,19,20], decoherence in open systems [21,22,23], and mesoscopic physics [24]. Indeed, the decay of the LE is related to the decay of quantum correlations and the quantum-classical correspondence, as can be shown using the Wigner function representation [22,25,26,27].…”

Section: Introductionmentioning

confidence: 99%

Decay of the Loschmidt echo in a time-dependent environment

2006

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We study the decay rate of the Loschmidt echo or fidelity in a chaotic system under a time-dependent perturbation V(q,t) with typical strength Planck's/tau(v) . The perturbation represents the action of an uncontrolled environment interacting with the system, and is characterized by a correlation length xi(0) and a correlation time tau(0). For small perturbation strengths or rapid fluctuating perturbations, the Loschmidt echo decays exponentially with a rate predicted by the Fermi "golden rule," 1/approximately tau =tau(c)/tau(v)(2), where tau(c) approximately min[tau(0), xi(0)/upsilon] and upsilon is the typical particle velocity. Whenever the rate 1/approximately tau is larger than the Lyapunov exponent of the system, a perturbation independent Lyapunov decay regime arises. We also find that by speeding up the fluctuations (while keeping the perturbation strength fixed) the fidelity decay becomes slower, and hence one can protect the system against decoherence.

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“…Over the last decade, fidelity decay has become a subject of immense interest in various fields including quantum information (as a measure of stability of quantum motion against perturbations), statistical physics (as Loschmidt echo) and quantum chaos [2]. Past studies of fidelity decay have focused on different aspects such as the connection between fidelity decay and the classical notion of Lyapunov exponents [3], characterization of quantum chaos [4,5], the effect of different kinds of perturbations and in different time regimes [6][7][8][9], conditions for anomalous slow decay or freeze of fidelity [10][11][12], perturbation independent fidelity decay [3], and connections to decoherence [13][14][15][16]. Many of these studies have focused on a particular type of perturbationchanges in a control parameter of the system.…”

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confidence: 99%

Stabilizing quantum dynamics through coupling to a quantized environment

Kumari,

Martin-Martinez,

Kempf

et al. 2017

Preprint

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We show that introducing a small uncertainty in the parameters of quantum systems can make the dynamics of these systems robust against perturbations. Concretely, for the case where a system is subject to perturbations due to an environment, we derive a lower bound on the fidelity decay, which increases with increasing uncertainty in the state of the environment. Remarkably, this robustness in fidelity can be achieved even in fragile chaotic systems. We show that non-Markovianity is necessary for attaining robustness in the fidelity.(1) Here U sys and U sys are the time evolution unitary op-

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Decoherence and Loschmidt echoes: quantum against classical

Cited by 3 publications

References 11 publications

Quantum chaos, dynamical stability and decoherence

Quantum chaos, dynamical stability and decoherence

Decay of the Loschmidt echo in a time-dependent environment

Stabilizing quantum dynamics through coupling to a quantized environment

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