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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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# Example 1: Unitary Fermi Gas is confided in a 1D (smooth) squared well
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Target: generate solution in a 1D potential well $`V_{\textrm{ext}}(x,y,z)\rightarrow V_{\textrm{ext}}(x)`$, with bulk density corresponding $`k_F=1`$.
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Code: `st-wslda-1d`
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Settings:
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* [only-trap_predefines.h](uploads/5122091213e767bee5a89afbc45b7993/only-trap_predefines.h)
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* [only-trap_problem-definition.h](uploads/5a7357a2d602ec450520392fcdf2e84b/only-trap_problem-definition.h)
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* [only-trap_logger.h](uploads/750f361d4a09b1095d357cb3c6841043/only-trap_logger.h)
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* [only-trap_input.txt](uploads/f34247597824ab74800e9d3521577fdf/only-trap_input.txt)
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Output:
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* [only-trap.stdout](uploads/0aeeac20397398ee3e45ae7dbbf6fcde/only-trap.stdout)
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Simple plotting script:
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```python
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import numpy as np
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import matplotlib.pyplot as plt
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from wdata.io import WData, Var
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data = WData.load("only-trap.wtxt")
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fig, ax = plt.subplots()
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ax.plot(data.xyz[0], data.rho_a[-1]*2, color='red', label=r'density', lw=3.0) # plot last frame [-1]
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ax.set(xlabel='x', ylabel=r'$n(x)$')
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ax2 = ax.twinx() # instantiate a second axes that shares the same x-axis
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ax2.plot(data.xyz[0], np.angle(data.delta[-1])/np.pi, color='blue', label=r'arg. of phase', lw=2.0, ls="--") # plot last frame [-1]
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ax2.set(ylabel=r'$V_{ext}(x)$')
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fig.legend(loc="upper left", bbox_to_anchor=(0.3,0.3), bbox_transform=ax.transAxes)
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fig.savefig("only-trap.png")
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```
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# Example 2: Soliton in the unitary Fermi gas.
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Target: on top of the Example 1 imprint soliton.
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Code: `st-wslda-1d`
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Settings:
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* [soliton-x0_predefines.h](uploads/e3084b524d482bc515621352fadca83c/soliton-x0_predefines.h)
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* [soliton-x0_problem-definition.h](uploads/5ad3f678404f2c4514f25c6bd118924b/soliton-x0_problem-definition.h)
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* [soliton-x0_logger.h](uploads/d6d215b8ea32b8080f7458f1f9fb3883/soliton-x0_logger.h)
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* [soliton-x0_input.txt](uploads/1c6687fb205ee655eabb61e6d8b56a33/soliton-x0_input.txt)
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Output:
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* [soliton-x0.stdout](uploads/4e94c17ea973b427b4ffd7f990769a49/soliton-x0.stdout)
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Simple plotting script:
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```python
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import numpy as np
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import matplotlib.pyplot as plt
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from wdata.io import WData, Var
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data = WData.load("soliton-x0.wtxt")
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fig, ax = plt.subplots()
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ax.plot(data.xyz[0], data.rho_a[-1]*2, color='red', label=r'density', lw=3.0) # plot last frame [-1]
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ax.set(xlabel='x', ylabel=r'$n(x)$')
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ax2 = ax.twinx() # instantiate a second axes that shares the same x-axis
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ax2.plot(data.xyz[0], np.angle(data.delta[-1])/np.pi, color='blue', label=r'arg. of phase', lw=2.0, ls="--") # plot last frame [-1]
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ax2.set(ylabel=r'$Arg[\Delta](x)/\pi$')
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fig.legend(loc="upper left", bbox_to_anchor=(0.15,0.3), bbox_transform=ax.transAxes)
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fig.savefig("soliton-x0.png")
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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 |
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# Archival examples
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For other examples you can see [here](st-wslda examples archival). |
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\ No newline at end of file |
