.. _sphx_glr_api_gallery_classical_chains:

Coupled lattice chains
----------------------

One-dimensional lattices: the exactly-solvable harmonic chain, the
Fermi-Pasta-Ulam-Tsingou beta-lattice and its famous non-ergodic
recurrence, and the discrete sine-Gordon chain's topological solitons.


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


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

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="HarmonicChain models N identical point masses m, connected in a line by identical springs of constant k, with both ends clamped to fixed walls (q_0 = q_{N+1} = 0). Writing q_i and p_i for the displacement and momentum of mass i, the system is the separable Hamiltonian">

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  .. image:: /api/gallery/classical/chains/images/thumb/sphx_glr_plot_01_harmonic_chain_thumb.png
    :alt:

  :doc:`/api/gallery/classical/chains/plot_01_harmonic_chain`

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      <div class="sphx-glr-thumbnail-title">The harmonic chain: normal modes, exactly</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="FPUTChain is the classic Fermi-Pasta-Ulam-Tsingou \beta-lattice: N fixed-end masses m coupled by springs with an added quartic non-linearity, so the inter-site stretch r_i = q_{i+1} - q_i costs potential energy">

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  .. image:: /api/gallery/classical/chains/images/thumb/sphx_glr_plot_02_fput_recurrence_thumb.png
    :alt:

  :doc:`/api/gallery/classical/chains/plot_02_fput_recurrence`

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      <div class="sphx-glr-thumbnail-title">The Fermi-Pasta-Ulam-Tsingou recurrence</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="SineGordonChain is a discretized chain of N coupled pendulums (the Frenkel-Kontorova model) with free (Neumann-like) ends, so a topological kink can propagate off either end. The potential energy is">

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  .. image:: /api/gallery/classical/chains/images/thumb/sphx_glr_plot_03_sine_gordon_thumb.png
    :alt:

  :doc:`/api/gallery/classical/chains/plot_03_sine_gordon`

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      <div class="sphx-glr-thumbnail-title">Sine-Gordon solitons: kink propagation and a kink-antikink breather</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/classical/chains/plot_01_harmonic_chain
   /api/gallery/classical/chains/plot_02_fput_recurrence
   /api/gallery/classical/chains/plot_03_sine_gordon