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‎HierarchicalEOM.jl/SIAM.html‎

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<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
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<meta name="author" content="Yi-Te Huang">
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<title>Single-impurity Anderson model – Tutorials for Quantum Toolbox in Julia</title>
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<div class="quarto-title-meta-heading">Last Update</div>
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<p class="date">2025-10-06</p>
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<p class="date">2025-10-13</p>
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@@ -538,7 +538,7 @@ <h2 class="anchored" data-anchor-id="calculate-density-of-states-dos">Calculate
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<span id="cb12-2"><a href="#cb12-2"></a>dos <span class="op">=</span> <span class="fu">DensityOfStates</span>(M_odd, ados_s, d_up, ωlist)</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<pre><code>Calculating density of states in frequency domain...
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[DONE]</code></pre>
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Package information:
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====================================
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Julia Ver. 1.12.0
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HierarchicalEOM Ver. 2.7.0
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QuantumToolbox Ver. 0.36.0
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HierarchicalEOM Ver. 2.8.0
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QuantumToolbox Ver. 0.37.0
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SciMLOperators Ver. 1.9.0
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‎HierarchicalEOM.jl/SIAM.ipynb‎

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"# Single-impurity Anderson model\n",
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"\n",
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"Yi-Te Huang \n",
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"2025-10-06\n",
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"2025-10-13\n",
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"\n",
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"## Introduction\n",
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"\n",
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"[`QuantumToolbox.jl`](https://github.com/qutip/QuantumToolbox.jl) to\n",
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"construct the operators."
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],
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"- the chemical potential $\\mu$\n",
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"- the total number of exponentials for the reservoir $2(N + 1)$"
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],
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"id": "2c3bc793-8fb4-48df-ae02-769bb6207aaa"
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{
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"source": [
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"## Construct HEOMLS matrix"
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"id": "2221c24a-358e-41ad-8563-16f63a73278b"
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{
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"## Solve stationary state of ADOs"
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"id": "0b11e45d-fc23-420e-887c-8f72e548fd69"
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"source": [
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"## Calculate density of states (DOS)"
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"Calculating density of states in frequency domain...\n",
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"[DONE]"
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"source": [
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"plot the results"
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"## Version Information"
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"Systems.” *Communications Physics* 6 (1): 313.\n",
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"<https://doi.org/10.1038/s42005-023-01427-2>."
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],
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"id": "6fcddff6-4815-413e-8ce0-0f132222e49d"
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‎HierarchicalEOM.jl/cavityQED.html‎

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<p class="date">2025-10-06</p>
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<p class="date">2025-10-13</p>
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb9"><pre class="sourceCode numberSource julia number-lines code-with-copy"><code class="sourceCode julia"><span id="cb9-1"><a href="#cb9-1"></a>t_list <span class="op">=</span> <span class="fl">0</span><span class="op">:</span><span class="fl">1</span><span class="op">:</span><span class="fl">500</span></span>
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<span id="cb9-2"><a href="#cb9-2"></a>sol_H <span class="op">=</span> <span class="fu">HEOMsolve</span>(M_Heom, ψ<span class="fl">0</span>, t_list; e_ops <span class="op">=</span> [σz, a<span class="op">'</span> <span class="op">*</span> a])</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<pre><code>Calculating power spectrum in frequency domain...
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[DONE]</code></pre>
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====================================
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Julia Ver. 1.12.0
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QuantumToolbox Ver. 0.36.0
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