Quantum Reversibility and Echoes in Interacting Systems

Abstract

In Echo experiments, imperfect time-reversal operations are performed on a subset of the total number of degrees of freedom. To capture the physics of these experiments, we introduce a partial fidelity, the Boltzmann echo, where only part of the system's degrees of freedom can be time-reversed. We present a semiclassical calculation of the Boltzmann echo. We show that, as the time-reversal operation is performed more and more accurately, the decay rate of the Boltzmann echo saturates at a value given by the decoherence rate of the controlled degrees of freedom due to their coupling to uncontrolled ones. We connect these results with NMR spin echo experiments.

4 pages, one figure in .eps format

References in corpus (11)

• Environment-independent decoherence rate in classically chaotic systems
• Charge echo in a Cooper-pair box
• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
• Sensitivity of Wave Field Evolution and Manifold Stability in Chaotic Systems
• Stability of quantum motion and correlation decay
• Echo spectroscopy and quantum stability of trapped atoms
• Quantum Dynamical Echoes in the Spin 'Diffusion' in Mesoscopic Systems
• Semiclassical evaluation of quantum fidelity
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• Fidelity and Purity Decay in Weakly Coupled Composite Systems
• Wave Packet Echoes in the Motion of Trapped Atoms

Cited by in corpus (12)

• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• The Loschmidt Echo as a robust decoherence quantifier for many-body systems
• Loschmidt echo for local perturbations: non-monotonous cross-over from the Fermi-golden-rule to the escape-rate regime
• Quantum Corrections to Fidelity Decay in Chaotic Systems
• Proliferation of effective interactions: decoherence-induced equilibration in a closed many-body system
• The semiclassical propagator in Fock space: dynamical echo and many-body interference
• A single-world consistent interpretation of quantum mechanics from fundamental time and length uncertainties
• Fragility of superposition states evaluated by the Loschmidt Echo
• Mechanisms of irreversible decoherence in solids
• Irreversibility in quantum maps with decoherence
• Adiabatic quantum decoherence in many non-interacting subsystems induced by the coupling with a common boson bath
• Time Reversibility of Quantum Diffusion in Small-world Networks