A nuclear magnetic resonance answer to the Boltzmann–Loschmidt controversy?

Pastawski, Horacio M.; Levstein, Patricia R.; Usaj, Gonzalo; Raya, Jésus; Hirschinger, Jérôme

doi:10.1016/s0378-4371(00)00146-1

Cited by 120 publications

(148 citation statements)

References 7 publications

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“…These used mainly the interacting 1 H nuclei in organic crystals and liquid crystals in a number of configurations and settings [7,8,10]. As a whole, the experiments were consistent with the fact that the experimental T 3 never exceeds more than a few times T 2 .…”

Section: A Brief History Of Time Reversalsupporting

confidence: 56%

“…The relaxation time T 2 is directly related to the secular dipolar Hamiltonian and the same holds for T 3 . This is precisely the case that motivated the Central Hypothesis of Irreversibility [8], which essentially manifests that the many-body dynamics amplifies the effect of experimental imperfections and uncontrolled degrees of freedom. In an isolated molecule this would yield some characteristic time scale T Σ , but in a crystal presents a decoherence time T 3 , proportional to T 2 instead of T Σ .…”

Section: Implementations Of Time-reversal In Nuclear Magnetic Resonanmentioning

confidence: 93%

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Quantum dynamics of excitations and decoherence in many-spin systems detected with Loschmidt echoes: its relation to their spreading through the Hilbert space

Sánchez

Levstein

Buljubasich

et al. 2016

Phil. Trans. R. Soc. A.

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In this work, we overview time-reversal nuclear magnetic resonance (NMR) experiments in many-spin systems evolving under the dipolar Hamiltonian. The Loschmidt echo (LE) in NMR is the signal of excitations which, after evolving with a forward Hamiltonian, is recovered by means of a backward evolution. The presence of non-diagonal terms in the non-equilibrium density matrix of the many-body state is directly monitored experimentally by encoding the multiple quantum coherences. This enables a spin counting procedure, giving information on the spreading of an excitation through the Hilbert space and the formation of clusters of correlated spins. Two samples representing different spin systems with coupled networks were used in the experiments. Protons in polycrystalline ferrocene correspond to an ‘infinite’ network. By contrast, the liquid crystal N -(4-methoxybenzylidene)-4-butylaniline in the nematic mesophase represents a finite proton system with a hierarchical set of couplings. A close connection was established between the LE decay and the spin counting measurements, confirming the hypothesis that the complexity of the system is driven by the coherent dynamics.

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Section: A Brief History Of Time Reversalsupporting

confidence: 56%

Section: Implementations Of Time-reversal In Nuclear Magnetic Resonanmentioning

confidence: 93%

Quantum dynamics of excitations and decoherence in many-spin systems detected with Loschmidt echoes: its relation to their spreading through the Hilbert space

Sánchez

Levstein

Buljubasich

et al. 2016

Phil. Trans. R. Soc. A.

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“…A hypersensitivity of time reversal to perturbations was observed in recent NMR experiments on many-body spin systems [9] [10]. In essence, these experiments [11] [12] involve the creation of a local density excitation represented by a state |0 which evolves under a many-spin Hamiltonian H. The Loschmidt Echo (LE) is the probability to return to the initial state when a Hamiltonian evolution for a time t is followed by an identical period of imperfect reversal of that evolution, achieved by the transformation H → −(H + Σ), i.e.…”

mentioning

confidence: 85%

Decoherence as decay of the Loschmidt echo in a Lorentz gas

2002

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Classical chaotic dynamics is characterized by the exponential sensitivity to initial conditions. Quantum mechanics, however, does not show this feature. We consider instead the sensitivity of quantum evolution to perturbations in the Hamiltonian. This is observed as an atenuation of the Loschmidt Echo, M (t), i.e. the amount of the original state (wave packet of width σ) which is recovered after a time reversed evolution, in presence of a classically weak perturbation. By considering a Lorentz gas of size L, which for large L is a model for an unbounded classically chaotic system, we find numerical evidence that, if the perturbation is within a certain range, M (t) decays exponentially with a rate 1/τ φ determined by the Lyapunov exponent λ of the corresponding classical dynamics. This exponential decay extends much beyond the Eherenfest time tE and saturates at a time ts ≃ λ −1 ln( N ), where N ≃ (L/σ) 2 is the effective dimensionality of the Hilbert space. Since τ φ quantifies the increasing uncontrollability of the quantum phase (decoherence) its characterization and control has fundamental interest.

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“…In these systems, universal control has been achieved by implementing collective control together with suitable spin manipulation at the chain ends [20,21]. All these fine control attempts might be frustrated by decoherence [22,23,24]. Thus, the dependence of decoherence on nuclear spin network topology becomes an important issue.…”

Section: Introductionmentioning

confidence: 99%

Effective one-body dynamics in multiple-quantum NMR experiments

et al. 2009

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A suitable NMR experiment in a one-dimensional dipolar coupled spin system allows one to reduce the natural many-body dynamics into effective one-body dynamics. We verify this in a polycrystalline sample of hydroxyapatite (HAp) by monitoring the excitation of NMR many-body superposition states: the multiple-quantum coherences. The observed effective one-dimensionality of HAp relies on the quasi one-dimensional structure of the dipolar coupled network that, as we show here, is dynamically enhanced by the quantum Zeno effect. Decoherence is also probed through a Loschmidt echo experiment, where the time reversal is implemented on the double-quantum Hamiltonian, HDQ ∝ IWe contrast the decoherence of adamantane, a standard threedimensional system, with that of HAp. While the first shows an abrupt Fermi-type decay, HAp presents a smooth exponential law.

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A nuclear magnetic resonance answer to the Boltzmann–Loschmidt controversy?

Cited by 120 publications

References 7 publications

Quantum dynamics of excitations and decoherence in many-spin systems detected with Loschmidt echoes: its relation to their spreading through the Hilbert space

Quantum dynamics of excitations and decoherence in many-spin systems detected with Loschmidt echoes: its relation to their spreading through the Hilbert space

Decoherence as decay of the Loschmidt echo in a Lorentz gas

Effective one-body dynamics in multiple-quantum NMR experiments

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