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https://github.com/triqs/dft_tools
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73 lines
1.6 KiB
ReStructuredText
73 lines
1.6 KiB
ReStructuredText
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.. highlight:: c
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Meshes
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#######
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The linear meshes
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==================
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The mesh kind
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--------------
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This option is particularly important for the Matsubara Green functions in imaginary time.
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Briefly, if we want to describe a function on an interval:
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* ``full_bins`` includes both endpoints,
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* ``half_bins`` includes none of the endpoints
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* ``without_last`` includes only the first endpoint.
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We then have to be careful for example when we fourier transform the function (to not take twice the same point).
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The four basic meshes
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=====================
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Real time
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----------
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The domain is the set of real numbers.
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By default, the mesh kind is ``full_bins``.
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Be careful to the value of a function at a point in case of discontinuities: is its value equal to the limit from below ? To the limit from above ? By none of these limits ?
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Real frequency
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---------------
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The domain is the set of real numbers.
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By default, the mesh kind is ``full_bins``.
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Matsubara time
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---------------
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The domain is (approximatively) the set of real numbers between 0 and :math:`\beta`.
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In fact, other points are also in the domain, but the values at these points are given by the values on this restricted domain.
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:math:`G(\tau+\beta)=-G(\tau)` for fermions, :math:`G(\tau+\beta)=G(\tau)` for bosons.
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The limits from above or below at these both points can be different.
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Depending on what one needs, we can choose ``full_bins``, ``half_bins`` or ``without_last``.
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Matsubara frequency
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--------------------
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The domain is discrete. The Matsubara frequencies are :math:`\omega_n=\frac{(2n+1)\pi}{beta}` for fermions and :math:`\omega_n=\frac{2n\pi}{beta}` for bosons.
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