Quantum freeze of fidelity decay for a class of integrable dynamics

Abstract

We discuss quantum fidelity decay of classically regular dynamics, in particular for an important special case of a vanishing time averaged perturbation operator, i.e. vanishing expectation values of the perturbation in the eigenbasis of unperturbed dynamics. A complete semiclassical picture of this situation is derived in which we show that the quantum fidelity of individual coherent initial states exhibits three different regimes in time: (i) first it follows the corresponding classical fidelity up to time t1=hbar^(-1/2), (ii) then it freezes on a plateau of constant value, (iii) and after a time scale t_2=min[hbar^(1/2) delta^(-2),hbar^(-1/2) delta^(-1)] it exhibits fast ballistic decay as exp(-const. delta^4 t^2/hbar) where delta is a strength of perturbation. All the constants are computed in terms of classical dynamics for sufficiently small effective value hbar of the Planck constant. A similar picture is worked out also for general initial states, and specifically for random initial states, where t_1=1, and t_2=delta^(-1). This prolonged stability of quantum dynamics in the case of a vanishing time averaged perturbation could prove to be useful in designing quantum devices. Theoretical results are verified by numerical experiments on the quantized integrable top.

arXiv comment32 pages, 8 figures (1 color); minor typos corrected, published version; see also movies at http://chaos.fiz.uni-lj.si/papers/freeze

References in corpus (27)

• Environment-independent decoherence rate in classically chaotic systems
• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
• On general relation between quantum ergodicity and fidelity of quantum dynamics
• Sensitivity of Wave Field Evolution and Manifold Stability in Chaotic Systems
• Stability of quantum motion and correlation decay
• Fidelity Decay as an Efficient Indicator of Quantum Chaos
• Quantum Chaotic Environments, The Butterfly Effect, And Decoherence
• Attenuation of polarization echoes in NMR: A study of the emergence of dynamical irreversibility in many-body quantum systems
• Sensitivity of Quantum Motion for Classically Chaotic Systems
• Measuring the Lyapunov exponent using quantum mechanics
• Quantum Dynamical Echoes in the Spin 'Diffusion' in Mesoscopic Systems
• Echo spectroscopy and quantum stability of trapped atoms
• The Edge of Quantum Chaos
• Decay of the Loschmidt Echo for quantum states with sub-Planck scale structures
• Fidelity and Purity Decay in Weakly Coupled Composite Systems
• Can quantum chaos enhance stability of quantum computation?
• Quantum irreversibility, perturbation independent decay, and the parametric theory of the local density of states
• Simple strong glass forming models: mean-field solution with activation
• Short time decay of the Loschmidt echo
• Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics
• Anomalous power law of quantum reversibility for classically regular dynamics
• Sensitivity to perturbations in a quantum chaotic billiard
• Crossover of quantum Loschmidt echo from golden rule decay to perturbation-independent decay
• Echoes in classical dynamical systems
• On the stability of classical chaotic motion under system's perturbations
• Quantum Irreversibility of Energy Spreading
• Dynamical fidelity of a solid-state quantum computation

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• Dynamics of Loschmidt echoes and fidelity decay
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• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
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• Semiclassical time-evolution of the reduced density matrix and dynamically assisted generation of entanglement for bipartite quantum systems
• Universality of the Lyapunov regime for the Loschmidt echo
• Early-Time Exponential Instabilities in Non-Chaotic Quantum Systems
• Dephasing representation of quantum fidelity for general pure and mixed states
• Revivals of Coherence in Chaotic Atom-Optics Billiards
• Quantum freeze of fidelity decay for chaotic dynamics
• Quantum Fidelity Decay of Quasi-Integrable Systems
• Generation of entanglement in regular systems
• Pointer States via Engineered Dissipation
• Stability of quantum motion in regular systems: a uniform semiclassical approach
• Anomalous slow fidelity decay for symmetry breaking perturbations
• Loschmidt echoes in two-body random matrix ensembles
• The Effects of Symmetries on Quantum Fidelity Decay
• On the origin of the exponential decay of the Loschmidt echo in integrable systems
• Fidelity decay in interacting two-level boson systems: Freezing and revivals
• Stability of Fock states in a two-component Bose-Einstein condensate with a regular classical counterpart
• Decoherence in regular systems
• Sensitivity of Quantum Motion to Perturbation in Triangle Map
• Long-Time Coherence in Echo Spectroscopy with $\pi /2$--$\pi$--$\pi /2$ Pulse Sequence
• Probing two-particle exchange processes in two-mode Bose-Einstein condensates
• Dynamical stability for finite quantum spin chains against a time-periodic inhomogeneous perturbation