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‎HierarchicalEOM.jl/SIAM.html‎

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@@ -446,10 +446,10 @@ <h2 class="anchored" data-anchor-id="hamiltonian">Hamiltonian</h2>
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<div class="cell-output cell-output-stdout">
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<pre><span class="ansi-green-fg ansi-bold">Precompiling</span> packages...
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<span class="ansi-green-fg ansi-bold">Precompiling</span> packages...
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</pre>
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@@ -512,12 +512,19 @@ <h2 class="anchored" data-anchor-id="construct-heomls-matrix">Construct HEOMLS m
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<span id="cb6-2"><a href="#cb6-2"></a>M_even <span class="op">=</span> <span class="fu">M_Fermion</span>(Hsys, tier, bath_list)</span>
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<span id="cb6-3"><a href="#cb6-3"></a>M_odd <span class="op">=</span> <span class="fu">M_Fermion</span>(Hsys, tier, bath_list, ODD)</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<div class="cell-output cell-output-stdout">
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<pre><code>Preparing block matrices for HEOM Liouvillian superoperator (using 4 threads)...
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Progress: [==============================] 100.0% --- Elapsed Time: 0h 00m 00s (ETA: 0h 00m 00s)
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<div class="ansi-escaped-output">
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<pre>Preparing block matrices for HEOM Liouvillian superoperator (using 4 threads)...
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<span class="ansi-green-fg">[M_Fermion] 100%|█████████████████████████| Time: 0:00:01 ( 0.76 ms/it)</span>
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Constructing matrix...[DONE]
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Preparing block matrices for HEOM Liouvillian superoperator (using 4 threads)...
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Progress: [==============================] 100.0% --- Elapsed Time: 0h 00m 00s (ETA: 0h 00m 00s)
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Constructing matrix...[DONE]</code></pre>
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Constructing matrix...[DONE]
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</pre>
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</div>
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</div>
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<div class="cell-output cell-output-display" data-execution_count="1">
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<pre><code>Fermion type HEOMLS matrix acting on odd-parity ADOs
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<section id="solve-stationary-state-of-ados" class="level2">
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<h2 class="anchored" data-anchor-id="solve-stationary-state-of-ados">Solve stationary state of ADOs</h2>
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<div id="10" class="cell" data-execution_count="1">
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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>ados_s <span class="op">=</span> <span class="fu">steadystate</span>(M_even)</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb8"><pre class="sourceCode numberSource julia number-lines code-with-copy"><code class="sourceCode julia"><span id="cb8-1"><a href="#cb8-1"></a>ados_s <span class="op">=</span> <span class="fu">steadystate</span>(M_even)</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<div class="cell-output cell-output-stdout">
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<pre><code>Solving steady state for ADOs by linear-solve method...
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Calculating left preconditioner with ilu...[DONE]
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<section id="calculate-density-of-states-dos" class="level2">
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<h2 class="anchored" data-anchor-id="calculate-density-of-states-dos">Calculate density of states (DOS)</h2>
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<div id="12" class="cell" data-execution_count="1">
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb12"><pre class="sourceCode numberSource julia number-lines code-with-copy"><code class="sourceCode julia"><span id="cb12-1"><a href="#cb12-1"></a>ωlist <span class="op">=</span> <span class="op">-</span><span class="fl">10</span><span class="op">:</span><span class="fl">1</span><span class="op">:</span><span class="fl">10</span></span>
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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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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb11"><pre class="sourceCode numberSource julia number-lines code-with-copy"><code class="sourceCode julia"><span id="cb11-1"><a href="#cb11-1"></a>ωlist <span class="op">=</span> <span class="op">-</span><span class="fl">10</span><span class="op">:</span><span class="fl">1</span><span class="op">:</span><span class="fl">10</span></span>
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<span id="cb11-2"><a href="#cb11-2"></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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<div class="cell-output cell-output-stdout">
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<pre><code>Calculating density of states in frequency domain...
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[DONE]</code></pre>
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</pre>
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</div>
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<pre><code>21-element Vector{Float64}:
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<p>plot the results</p>
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<div id="14" class="cell" data-execution_count="1">
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<span id="cb15-2"><a href="#cb15-2"></a>ax <span class="op">=</span> <span class="fu">Axis</span>(fig[<span class="fl">1</span>, <span class="fl">1</span>], xlabel <span class="op">=</span> L<span class="st">"\omega"</span>)</span>
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<span id="cb15-4"><a href="#cb15-4"></a></span>
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<span id="cb15-5"><a href="#cb15-5"></a>fig</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb13"><pre class="sourceCode numberSource julia number-lines code-with-copy"><code class="sourceCode julia"><span id="cb13-1"><a href="#cb13-1"></a>fig <span class="op">=</span> <span class="fu">Figure</span>()</span>
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<span id="cb13-2"><a href="#cb13-2"></a>ax <span class="op">=</span> <span class="fu">Axis</span>(fig[<span class="fl">1</span>, <span class="fl">1</span>], xlabel <span class="op">=</span> L<span class="st">"\omega"</span>)</span>
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<span id="cb13-3"><a href="#cb13-3"></a><span class="fu">lines!</span>(ax, ωlist, dos)</span>
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<span id="cb13-4"><a href="#cb13-4"></a></span>
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<span id="cb13-5"><a href="#cb13-5"></a>fig</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<figure class="figure">
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<h2 class="anchored" data-anchor-id="version-information">Version Information</h2>
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb14"><pre class="sourceCode numberSource julia number-lines code-with-copy"><code class="sourceCode julia"><span id="cb14-1"><a href="#cb14-1"></a>HierarchicalEOM.<span class="fu">versioninfo</span>()</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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<pre><span style="font-weight:bold;color:rgb(0,135,0)"> __</span>
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Package information:
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====================================
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Julia Ver. 1.12.1
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HierarchicalEOM Ver. 2.8.0
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QuantumToolbox Ver. 0.37.0
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HierarchicalEOM Ver. 2.9.0
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QuantumToolbox Ver. 0.38.1
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SciMLOperators Ver. 1.9.0
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LinearSolve Ver. 3.28.0
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OrdinaryDiffEqCore Ver. 1.36.0

‎HierarchicalEOM.jl/SIAM.ipynb‎

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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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"id": "b3403bcd-eb4a-4fb6-9806-0d78e3a3e530"
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"id": "a2243f4d-c429-4ae6-8c2f-d09948e3ea67"
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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": "0b29a56d-348f-4160-a11f-9ddd8c8e9f97"
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"id": "4e959502-183d-4a02-bd9a-0fef172bf40f"
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"source": [
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"## Construct HEOMLS matrix"
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],
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"id": "c6764b48-5e73-49d7-b8c5-8e533532de7b"
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"id": "9a50fc55-87d0-428a-84b2-f2b9526582b3"
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},
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"outputs": [
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{
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"name": "stdout",
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"text": [
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"Preparing block matrices for HEOM Liouvillian superoperator (using 4 threads)...\n",
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"Progress: [==============================] 100.0% --- Elapsed Time: 0h 00m 00s (ETA: 0h 00m 00s)\n",
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"Constructing matrix...[DONE]\n",
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"Preparing block matrices for HEOM Liouvillian superoperator (using 4 threads)...\n",
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"Progress: [==============================] 100.0% --- Elapsed Time: 0h 00m 00s (ETA: 0h 00m 00s)\n",
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"Constructing matrix...[DONE]"
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]
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},
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],
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"id": "4654b67e-257c-457e-9196-b1b218c5481f"
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"id": "0b40c18d-ad1a-4457-a1be-4af85977c3b5"
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"## Calculate density of states (DOS)"
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],
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"id": "da8f6f3e-8034-4f0f-9375-f222b83435e6"
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"id": "da38e223-11dd-494f-92c5-5d354fd8effb"
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"outputs": [
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{
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"name": "stdout",
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"text": [
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"Calculating density of states in frequency domain...\n",
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"Progress: [== ] 9.5% --- Elapsed Time: 0h 00m 01s (ETA: 0h 00m 09s)Progress: [======= ] 23.8% --- Elapsed Time: 0h 00m 02s (ETA: 0h 00m 06s)Progress: [========== ] 33.3% --- Elapsed Time: 0h 00m 03s (ETA: 0h 00m 06s)Progress: [============ ] 42.9% --- Elapsed Time: 0h 00m 05s (ETA: 0h 00m 06s)Progress: [=============== ] 52.4% --- Elapsed Time: 0h 00m 06s (ETA: 0h 00m 05s)Progress: [================== ] 61.9% --- Elapsed Time: 0h 00m 07s (ETA: 0h 00m 04s)Progress: [===================== ] 71.4% --- Elapsed Time: 0h 00m 09s (ETA: 0h 00m 03s)Progress: [======================== ] 81.0% --- Elapsed Time: 0h 00m 10s (ETA: 0h 00m 02s)Progress: [============================ ] 95.2% --- Elapsed Time: 0h 00m 11s (ETA: 0h 00m 00s)Progress: [==============================] 100.0% --- Elapsed Time: 0h 00m 11s (ETA: 0h 00m 00s)\n",
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"[DONE]"
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]
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},
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"metadata": {},
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"plot the results"
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],
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"id": "ca09a2a4-2484-4a64-b611-bb55e86bd1f9"
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"id": "d7c1f994-0c23-4d45-98a3-6fab115015b3"
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"## Version Information"
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],
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"id": "ce84c689-a35f-44b3-8088-0e774499d21f"
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"id": "7cda9955-1188-4de0-b81c-43d3514e6e0c"
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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": "6bdaa4cc-78f2-4413-8f59-3da236d958a0"
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"id": "6c14fd07-9a66-41ce-a142-b32d076a91d6"
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}
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"nbformat": 4,

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