.. _sphx_glr_api_gallery_dynamics:

Dynamics
--------

Real-time wavepacket propagation: Bloch oscillations and the
Wannier-Stark ladder under a uniform lattice tilt.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="A uniform force on an electron in a periodic lattice does not produce uniform acceleration, the way it would in free space: Bloch&#x27;s 1929 argument (formalized by Wannier in 1960) shows the electron instead oscillates periodically in real space, with period T_B=2\pi/F (in units where \hbar=1). In real crystals scattering happens on a far shorter timescale than T_B, which is why the effect went unobserved for over 60 years -- it took artificial semiconductor superlattices (Waschke et al., 1993), with a far larger effective lattice constant, to see it directly. See /history for the full historical context.">

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  .. image:: /api/gallery/dynamics/images/thumb/sphx_glr_plot_bloch_oscillations_thumb.png
    :alt:

  :doc:`/api/gallery/dynamics/plot_bloch_oscillations`

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      <div class="sphx-glr-thumbnail-title">Bloch Oscillations and the Wannier-Stark Ladder</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/dynamics/plot_bloch_oscillations