Accuracy of the adiabatic-impulse approximation for closed and open quantum systems
arXiv:1712.04488 · doi:10.1103/PhysRevA.97.032121
Abstract
We study the adiabatic-impulse approximation (AIA) as a tool to approximate the time evolution of quantum states, when driven through a region of small gap. The AIA originates from the Kibble-Zurek theory applied to continuous quantum phase transitions. The Kibble-Zurek mechanism was developed to predict the power-law scaling of the defect density across a continuous quantum phase transition. Instead here, we quantify the accuracy of the AIA via the trace norm distance with respect to the exact evolved state. As expected, we find that for short times/fast protocols, the AIA outperforms the simple adiabatic approximation. However, for large times/slow protocols, the situation is actually reversed and the AIA provides a worse approximation. Nevertheless, we found a variation of the AIA that can perform better than the adiabatic one. This counter-intuitive modification consists in crossing twice the region of small gap. Our findings are illustrated by several examples of driven closed and open quantum systems.
16 pages, 9 figures
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Cited by in corpus (6)
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- Dynamical critical scaling of long-range interacting quantum magnets
- Kibble-Zurek mechanism in driven-dissipative systems crossing a non-equilibrium phase transition
- Dynamics and correlations at a quantum phase transition beyond Kibble-Zurek
- Locating quantum critical points with Kibble-Zurek quenches
- Universal Quench Dynamics of an Open Quantum System