Stability of quantum motion and correlation decay
Tomaz Prosen,Marko Znidaric +1 more
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TLDR
In this paper, the authors derived a relation between the fidelity of quantum motion, characterizing the stability of quantum dynamics with respect to arbitrary static perturbation of the unitary evolution propagator, and the integrated time auto-correlation function of the generator.Abstract:
We derive a simple and general relation between the fidelity of quantum motion, characterizing the stability of quantum dynamics with respect to arbitrary static perturbation of the unitary evolution propagator, and the integrated time auto-correlation function of the generator of perturbation. Surprisingly, this relation predicts the slower decay of fidelity the faster the decay of correlations. In particular, for non-ergodic and non-mixing dynamics, where asymptotic decay of correlations is absent, a qualitatively different and faster decay of fidelity is predicted on a timescale 1/δ as opposed to mixing dynamics where the fidelity is found to decay exponentially on a timescale 1/δ2, where δ is the strength of perturbation. A detailed discussion of a semiclassical regime of small effective values of Planck constant is given where classical correlation functions can be used to predict quantum fidelity decay. Note that the correct and intuitively expected classical stability behaviour is recovered in the classical limit → 0, as the two limits δ → 0 and → 0 do not commute. In addition, we also discuss non-trivial dependence on the number of degrees of freedom. All the theoretical results are clearly demonstrated numerically on the celebrated example of a quantized kicked top.read more
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Dynamics of Loschmidt echoes and fidelity decay
TL;DR: In this article, a review of different regimes for fidelity decay in quantum information processes is presented, and some important applications and experiments are discussed, using time correlation functions as a backbone for the discussion.
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Decoherence, entanglement and irreversibility in quantum dynamical systems with few degrees of freedom
Ph. Jacquod,Cyril Petitjean +1 more
TL;DR: In this paper, the authors summarize and amplify recent investigations of coupled quantum dynamical systems with few degrees of freedom in the short-wavelength, semiclassical limit, focusing on the correspondence between quantum and classical physics.
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Loschmidt Echo
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Eigenstate thermalization hypothesis and out of time order correlators.
Laura Foini,Jorge Kurchan +1 more
TL;DR: The eigenstate thermalization hypothesis (ETH) implies a form for the matrix elements of local operators between eigenstates of the Hamiltonian, expected to be valid for chaotic systems.
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Wave chaos in acoustics and elasticity
Gregor Tanner,Niels Søndergaard +1 more
TL;DR: In this paper, the authors provide an overview over basic concepts in this emerging field of wave chaos, which ranges from ray approximations of the Green function to periodic orbit trace formulae and random matrix theory and summarizes the state of the art in applying these ideas in acoustics.
References
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Book
Quantum Computation and Quantum Information
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Quantum Computation and Quantum Information
TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
Book
Quantum signatures of chaos
TL;DR: The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2, 3) as mentioned in this paper.
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Stability of quantum motion in chaotic and regular systems
TL;DR: In this paper, it is shown that if a quantum system has a classically chaotic analog, the overlap tends to a very small value, with small fluctuations, while if the classical analog is regular, it remains appreciable and its fluctuations are much larger.
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Environment-independent decoherence rate in classically chaotic systems.
TL;DR: An exponential decay for the Loschmidt echo is predicted with a (decoherence) rate which is asymptotically given by the mean Lyapunov exponent of the classical system, and therefore independent of the perturbation strength, within a given range of strengths.