.. _sphx_glr_api_gallery_non_hermitian:

Non-Hermitian lattices
----------------------

Lattices with balanced gain and loss: PT-symmetric spectra that stay
real up to a threshold, the exceptional points at which eigenvalues
*and* eigenvectors coalesce, the Petermann factor that measures how far
the eigenbasis has been skewed, and the selective amplification of a
topological edge mode.


.. raw:: html

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


.. raw:: html

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

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="A lattice with balanced gain and loss -- imaginary onsite energies \pm i\gamma on the two sublattices -- has a non-Hermitian Hamiltonian, but it commutes with the combined parity-time operation \mathcal{PT}. Bender and Boettcher&#x27;s 1998 observation was that such a Hamiltonian can still have an entirely real spectrum, up to a threshold in \gamma at which eigenvalues collide pairwise and split into complex-conjugate pairs.">

.. only:: html

  .. image:: /api/gallery/non_hermitian/images/thumb/sphx_glr_plot_pt_symmetry_thumb.png
    :alt:

  :doc:`/api/gallery/non_hermitian/plot_pt_symmetry`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">PT Symmetry, Exceptional Points, and a Selectively Amplified Edge Mode</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/non_hermitian/plot_pt_symmetry