Decoherence as decay of the Loschmidt echo in a Lorentz gas

Cucchietti, Fernando M.; Pastawski, Horacio M.; Wisniacki, Diego A.

doi:10.1103/physreve.65.045206

Cited by 68 publications

(81 citation statements)

References 32 publications

(33 reference statements)

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“…In order to understand how classical chaos emerges from quantum dynamics, we compute OTOC and the two-point correlator in the regime of eff → 0 at short time scales.Lyapunov Exponent and OTOC's growth rate (CGR).-To specify our quantum diagnostics for chaotic behavior in the QKR, we choose OTOC, C(t) [14,15], and two-point correlator, B(t), as:We point out that C(t) is closely related to the Loschmidt echo (also known as fidelity). In the previous works, fidelity has been used as a theoretical and experimental diagnostic of quantum chaos [16,[25][26][27][28][29][30][31][32]. Before carrying out quantum calculations, we consider the classical correspondence of C(t) [14,15].…”

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confidence: 99%

Lyapunov Exponent and Out-of-Time-Ordered Correlator’s Growth Rate in a Chaotic System

2017

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It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a useful characteristic of quantum-chaotic behavior, because in the semi-classical limit, → 0, its rate of exponential growth resembles the classical Lyapunov exponent. Here, we calculate the fourpoint correlator, C(t), for the classical and quantum kicked rotor -a textbook driven chaotic system -and compare its growth rate at initial times with the standard definition of the classical Lyapunov exponent. Using both quantum and classical arguments, we show that the OTOC's growth rate and the Lyapunov exponent are in general distinct quantities, corresponding to the logarithm of phase-space averaged divergence rate of classical trajectories and to the phase-space average of the logarithm, respectively. The difference appears to be more pronounced in the regime of low kicking strength K, where no classical chaos exists globally. In this case, the Lyapunov exponent quickly decreases as K → 0, while the OTOC's growth rate may decrease much slower showing higher sensitivity to small chaotic islands in the phase space. We also show that the quantum correlator as a function of time exhibits a clear singularity at the Ehrenfest time tE: transitioning from a time-independent value of t −1 ln C(t) at t < tE to its monotonous decrease with time at t > tE. We note that the underlying physics here is the same as in the theory of weak (dynamical) localization [Aleiner and Larkin, Phys. Rev. B 54, 14423 (1996); Tian, Kamenev, and Larkin, Phys. Rev. Lett. 93, 124101 (2004)] and is due to a delay in the onset of quantum interference effects, which occur sharply at a time of the order of the Ehrenfest time.Introduction. -One of the central goals in the study of quantum chaos is to establish a correspondence principle between classical and quantum dynamics of classically chaotic systems [1][2][3][4][5][6][7]. Several previous works [7][8][9][10][11] have attempted to recover fingerprints of classical chaos in quantum dynamics. In particular, Aleiner and Larkin [12] showed the existence of a semiclassical "quantum chaotic" regime attributed to the delay in the onset of quantum effects (due to weak localization) revealing the key measure of classical chaos -the Lyapunov exponent (LE). Recently, the subject of quantum chaos has been revived by the discovery of an unexpected conjecture that puts a bound on the growth rate of an outof-time-ordered four-point correlator (OTOC) [13,14]. OTOC was first introduced by Larkin and Ovchinnikov to quantify the regime of validity of quasi-classical methods in the theory of superconductivity [15]. The growth rate of OTOC appears to be closely related to LE. Recent works have proposed experimental protocols to probe OTOC in cold atom and cavity QED setups [16]. Several recent preprints have employed OTOC as a probe to characterize many-body-localized systems [17].

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confidence: 99%

Lyapunov Exponent and Out-of-Time-Ordered Correlator’s Growth Rate in a Chaotic System

2017

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“…Extending the algorithm for more than one dimension is also straightforward, as we can simply perform a decomposition of the Hamiltonian into five parts: the diagonal energies, and two terms for each dimension. Our implementation is based on the second order formulation of Equation 3.…”

Section: Trotter-suzuki Algorithm and Efficient Kernelsmentioning

confidence: 99%

“…For the case of a single particle in real space that we treat here, the algorithm discretizes the domain with a finite mesh and calculates the pairwise evolution between neighboring sites in the mesh. The Trotter-Suzuki algorithm has been successfully used [3,5,6]. Efficient kernels for contemporary multicore CPUs and GPUs have already been developed [1].…”

Section: Introductionmentioning

confidence: 99%

A second-order distributed Trotter–Suzuki solver with a hybrid CPU–GPU kernel

Wittek

Cucchietti

2013

Computer Physics Communications

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The Trotter-Suzuki approximation leads to an efficient algorithm for solving the timedependent Schrödinger equation. Using existing highly optimized CPU and GPU kernels, we developed a distributed version of the algorithm that runs efficiently on a cluster. Our implementation also improves single node performance, and is able to use multiple GPUs within a node. The scaling is close to linear using the CPU kernels, whereas the efficiency of GPU kernels improve with larger matrices. We also introduce a hybrid kernel that simultaneously uses multicore CPUs and GPUs in a distributed system. This kernel is shown to be efficient when the matrix size would not fit in the GPU memory. Larger quantum systems scale especially well with a high number nodes. The code is available under an open source license.

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“…The Suzuki-Trotter method has been used extensively in the field of statistical physics [28][29][30] and Monte Carlo simulations [25]. See also [31,32] This paper is organized as follows: in section 2, we will present the method and show how to apply it for factorizing an exponential operator.…”

Section: Introductionmentioning

confidence: 99%

Deposition of SrZrO₃ Thin Films Using Liquid Delivery Metal–Organic Chemical Vapor Deposition

Uchiyama

Sakairi

Shiosaki

et al. 2009

jjap

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There is a widespread belief in the quantum physical community, and textbooks used to teach quantum mechanics, that it is a difficult task to apply the time evolution operator e itĤ / h on an initial wavefunction. Because the Hamiltonian operator is, generally, the sum of two operators, then it is not possible to apply the time evolution operator on an initial wavefunction ψ(x, 0), for it implies using terms like (â +b) n . A possible solution is to factorize the time evolution operator and then apply successively the individual exponential operator on the initial wavefunction. However, the exponential operator does not directly factorize, i.e. eâ +b = eâeˆb. In this study we present a useful procedure for factorizing the time evolution operator when the argument of the exponential is a sum of two operators, which obey specific commutation relations. Then, we apply the exponential operator as an evolution operator for the case of elementary unidimensional potentials, like a particle subject to a constant force and a harmonic oscillator. Also, we discuss an apparent paradox concerning the time evolution operator and non-spreading wave packets addressed previously in the literature.

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Decoherence as decay of the Loschmidt echo in a Lorentz gas

Cited by 68 publications

References 32 publications

Lyapunov Exponent and Out-of-Time-Ordered Correlator’s Growth Rate in a Chaotic System

Lyapunov Exponent and Out-of-Time-Ordered Correlator’s Growth Rate in a Chaotic System

A second-order distributed Trotter–Suzuki solver with a hybrid CPU–GPU kernel

Deposition of SrZrO₃ Thin Films Using Liquid Delivery Metal–Organic Chemical Vapor Deposition

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Decoherence as decay of the Loschmidt echo in a Lorentz gas

Cited by 68 publications

References 32 publications

Lyapunov Exponent and Out-of-Time-Ordered Correlator’s Growth Rate in a Chaotic System

Lyapunov Exponent and Out-of-Time-Ordered Correlator’s Growth Rate in a Chaotic System

A second-order distributed Trotter–Suzuki solver with a hybrid CPU–GPU kernel

Deposition of SrZrO3 Thin Films Using Liquid Delivery Metal–Organic Chemical Vapor Deposition

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Deposition of SrZrO₃ Thin Films Using Liquid Delivery Metal–Organic Chemical Vapor Deposition