.. _sphx_glr_api_gallery_semiclassical_ehrenfest:

The Ehrenfest time
----------------------

How long a quantum wavepacket in a chaotic system keeps following a
classical trajectory: the logarithmic Ehrenfest time of Berman and
Zaslavsky, measured on the quantum kicked rotor.


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    <div class="sphx-glr-thumbcontainer" tooltip="Ehrenfest&#x27;s theorem says a narrow wavepacket&#x27;s centre obeys Newton&#x27;s equations as long as the packet stays small compared with the scale on which the force varies. Berman and Zaslavsky (1978) asked how long that lasts when the classical motion is chaotic. A minimum-uncertainty packet starts with width of order \sqrt\hbar, and chaos stretches it by e^{\lambda t}, with \lambda the Lyapunov exponent. The packet reaches the size of the system, and stops following any single trajectory, after">

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  :doc:`/api/gallery/semiclassical/ehrenfest/plot_ehrenfest_time_kicked_rotor`

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   /api/gallery/semiclassical/ehrenfest/plot_ehrenfest_time_kicked_rotor