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**NOTE**: these are archival examples, and provided files may not be compatible with the present API of the W-SLDA Toolkit!
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[[_TOC_]]
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# Example 1: gas confined in a tube
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The solution of cold atomic gas in an external potential of the form of a tube. Gas with is in BCS regime with $`ak_F=-0.9`$. In the calculation, we assumed translation symmetry along z direction and `st-wslda-2d` was used. In the computation, `double` arithmetic is utilized.
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* [predefines.h](uploads/b0f9c475f5dbd44640310b713ecb5ea5/tube_predefines.h)
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* [problem-definition.h](uploads/cd9da4754c87bf4eabe4977246ba534b/tube_problem-definition.h)
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* [input.txt](uploads/df292f7036ca8ffd86d4986cb40c1449/tube_input.txt)
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* [output](uploads/799f6e104160a09fe4bf542d989cedcf/tube.out)
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The graph below shows density distribution (left) and the absolute value of delta (right) for the converged solution.
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# Example 2: vortex solution within BdG
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The solution representing a vortex confined in a tube. The conditions are the same as for *Example 1*. To speed up the convergence process we start from the state provided by *Example 1*. In the computation, `double complex` arithmetic is utilized.
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* [predefines.h](uploads/0a1ad93743c8f9544e59338ba8220563/vortex_predefines.h)
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* [problem-definition.h](uploads/215195b78623a61bc1f4df47c27e5d7a/vortex_problem-definition.h)
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* [input.txt](uploads/1e340d91f45dc57900152866a9a956ef/vortex_input.txt)
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* [output](uploads/633a07650caee1345b0a1fbdd9513d51/vortex.out)
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The graph below shows density distribution (left) and the absolute value of delta (right) for the converged solution. By arrows currents are plotted.
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# Example 3: mass imbalanced gas in a harmonic trap
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This example is motivated by work [arXiv:1909.03424](https://arxiv.org/abs/1909.03424).
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Namely, let us consider gas of:
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* component *a*: $`{}^{161}\textrm{Dy}`$,
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* component *b*: $`{}^{40}\textrm{K}`$,
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confined in harmonic trap:
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```math
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V_{a,b}(x)=\dfrac{m_a \omega_a^2 x^2}{2}
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```
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where traping frequencies of both components are different (in the example we use according to [arXiv:1909.03424](https://arxiv.org/abs/1909.03424) $`\omega_a/\omega_b=120/430`$). In addition $`N_{\textrm{Dy}} / N_{\textrm{K}} = 20000/8000`$. In the calculations BdG functional is used, with the scattering length exceeding other length scales (in the example $`a=100`$). In the calculation `st-wslda-1d` was used.
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* [predefines.h](uploads/8bed3548acc9dd04a2ccf54a35687ac7/DyK_predefines.h)
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* [problem-definition.h](uploads/475df575833b5d4e92acd77b30992930/DyK_problem-definition.h)
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* [logger.h](uploads/8ac2b1262a442fa45092727564919f94/DyK_logger.h)
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* [input.txt](uploads/287f965385d1da19e7d84f007ec26a0e/DyK_input.txt)
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* [DyK.out](uploads/8829e64cb15639be6a1dfb44e55c5314/DyK.out)
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The graph below shows density distribution along *x* axis of $`{}^{161}\textrm{Dy}`$ (red) and $`{}^{40}\textrm{K}`$ (blue). The phase separation phenomenon is visible.
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\ No newline at end of file |
