-
Notifications
You must be signed in to change notification settings - Fork 0
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
Documenter.jl
committed
Oct 29, 2023
1 parent
09180f7
commit 380edf1
Showing
3 changed files
with
9 additions
and
9 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -1 +1 @@ | ||
{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-29T09:14:34","documenter_version":"1.1.2"}} | ||
{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-29T15:25:37","documenter_version":"1.1.2"}} |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -1,2 +1,2 @@ | ||
<!DOCTYPE html> | ||
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · SpectralDensities.jl</title><meta name="title" content="Home · SpectralDensities.jl"/><meta property="og:title" content="Home · SpectralDensities.jl"/><meta property="twitter:title" content="Home · SpectralDensities.jl"/><meta name="description" content="Documentation for SpectralDensities.jl."/><meta property="og:description" content="Documentation for SpectralDensities.jl."/><meta property="twitter:description" content="Documentation for SpectralDensities.jl."/><meta property="og:url" content="https://quantum-exeter.github.io/SpectralDensities.jl/"/><meta property="twitter:url" content="https://quantum-exeter.github.io/SpectralDensities.jl/"/><link rel="canonical" href="https://quantum-exeter.github.io/SpectralDensities.jl/"/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="search_index.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>SpectralDensities.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#Features"><span>Features</span></a></li><li><a class="tocitem" href="#Quick-start"><span>Quick start</span></a></li><li><a class="tocitem" href="#Defining-custom-spectral-densities"><span>Defining custom spectral densities</span></a></li></ul></li><li><a class="tocitem" href="reference/">API Reference</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/quantum-exeter/SpectralDensities.jl/blob/main/docs/src/index.md#" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="SpectralDensities.jl"><a class="docs-heading-anchor" href="#SpectralDensities.jl">SpectralDensities.jl</a><a id="SpectralDensities.jl-1"></a><a class="docs-heading-anchor-permalink" href="#SpectralDensities.jl" title="Permalink"></a></h1><p>This package implements commonly used spectral densities for Open Quantum Systems and typical operations on them.</p><h2 id="Features"><a class="docs-heading-anchor" href="#Features">Features</a><a id="Features-1"></a><a class="docs-heading-anchor-permalink" href="#Features" title="Permalink"></a></h2><p>Features of SpectralDensities.jl include:</p><ul><li>Definition of most widely used spectral densities: Ohmic, Sub-Ohmic, Supra-Ohmic, Lorentzian (Underdamped), Debye (Overdamped)</li><li>Flexibility to choose desidred cutoff functions: hard cutoffs, exponential cutoff, gaussian cutoff.</li><li>Calculation of the correlation function of a given spectral density (with specialised methods for the pre-defined types)</li><li>Calculation of reorganisation energy of a given spectral density (with specialised methods for the pre-defined types)</li><li>Calculation of the memory kernel of a given spectral density, both in the time domain, and the imaginary part in the Fourier domain (with specialised methods for some of the pre-defined types)</li><li>Methods to compute the spectral density integrals that appear in the weak coupling (2nd order expansion), both for the dynamics (see e.g. H. Breuer, F. Petruccione, "The Theory of Open Quantum Systems"), and the equilibrium mean-force state (see e.g. J.D. Cresser, J. Anders, Phys. Rev. Lett. 127, 250601 (2021)).</li></ul><h2 id="Quick-start"><a class="docs-heading-anchor" href="#Quick-start">Quick start</a><a id="Quick-start-1"></a><a class="docs-heading-anchor-permalink" href="#Quick-start" title="Permalink"></a></h2><p>The desired spectral density can be constructed by simply passing the desired parameters to their respective constructor. For example, for an Ohmic spectral density <span>$J(\omega) = 3\omega$</span> we have</p><pre><code class="language-Julia hljs">Johmic = OhmicSD(3)</code></pre><p>To add a ctuoff to a base spectral density, one simply passes it to the cutoff constructor. For example, to add an exponential cutoff <span>$e^{-\omega/7}$</span> we can do</p><pre><code class="language-Julia hljs">Jc = ExponentialCutoffSD(Johmic, 7)</code></pre><h2 id="Defining-custom-spectral-densities"><a class="docs-heading-anchor" href="#Defining-custom-spectral-densities">Defining custom spectral densities</a><a id="Defining-custom-spectral-densities-1"></a><a class="docs-heading-anchor-permalink" href="#Defining-custom-spectral-densities" title="Permalink"></a></h2><p>The base <a href="reference/#SpectralDensities.AbstractSD"><code>AbstractSD</code></a> can be easily extended by the user. To do so, one must create a new sub-type for which <em>at least</em> one of the methods <a href="reference/#SpectralDensities.sd-Union{Tuple{T}, Tuple{T, Any}} where T<:AbstractSD"><code>sd</code></a> (the spectral density itself <span>$J(\omega)$</span>) or <a href="reference/#SpectralDensities.sdoverω-Union{Tuple{T}, Tuple{T, Any}} where T<:AbstractSD"><code>sdoverω</code></a> (the spectral density divided by frequency <span>$J(\omega)/\omega$</span>) must be defined. It is strongly recommended to define, if possible, <a href="reference/#SpectralDensities.sdoverω-Union{Tuple{T}, Tuple{T, Any}} where T<:AbstractSD"><code>sdoverω</code></a> since it typically makes it simpler to numerically handle potential singularities.</p><p>This is the only requirement, and all other methods will automatically work on the new subtype. Of course, as is typical of Julia's super flexible multiple-dispatch system, the user should consider providing custom functions on the new type for the reorganisation energy, etc.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="reference/">API Reference »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Sunday 29 October 2023 09:14">Sunday 29 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> | ||
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · SpectralDensities.jl</title><meta name="title" content="Home · SpectralDensities.jl"/><meta property="og:title" content="Home · SpectralDensities.jl"/><meta property="twitter:title" content="Home · SpectralDensities.jl"/><meta name="description" content="Documentation for SpectralDensities.jl."/><meta property="og:description" content="Documentation for SpectralDensities.jl."/><meta property="twitter:description" content="Documentation for SpectralDensities.jl."/><meta property="og:url" content="https://quantum-exeter.github.io/SpectralDensities.jl/"/><meta property="twitter:url" content="https://quantum-exeter.github.io/SpectralDensities.jl/"/><link rel="canonical" href="https://quantum-exeter.github.io/SpectralDensities.jl/"/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="search_index.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>SpectralDensities.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#Features"><span>Features</span></a></li><li><a class="tocitem" href="#Quick-start"><span>Quick start</span></a></li><li><a class="tocitem" href="#Defining-custom-spectral-densities"><span>Defining custom spectral densities</span></a></li></ul></li><li><a class="tocitem" href="reference/">API Reference</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/quantum-exeter/SpectralDensities.jl/blob/main/docs/src/index.md#" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="SpectralDensities.jl"><a class="docs-heading-anchor" href="#SpectralDensities.jl">SpectralDensities.jl</a><a id="SpectralDensities.jl-1"></a><a class="docs-heading-anchor-permalink" href="#SpectralDensities.jl" title="Permalink"></a></h1><p>This package implements commonly used spectral densities for Open Quantum Systems and typical operations on them.</p><h2 id="Features"><a class="docs-heading-anchor" href="#Features">Features</a><a id="Features-1"></a><a class="docs-heading-anchor-permalink" href="#Features" title="Permalink"></a></h2><p>Features of SpectralDensities.jl include:</p><ul><li>Definition of most widely used spectral densities: Ohmic, Sub-Ohmic, Supra-Ohmic, Lorentzian (Underdamped), Debye (Overdamped)</li><li>Flexibility to choose desidred cutoff functions: hard cutoffs, exponential cutoff, gaussian cutoff.</li><li>Calculation of the correlation function of a given spectral density (with specialised methods for the pre-defined types)</li><li>Calculation of reorganisation energy of a given spectral density (with specialised methods for the pre-defined types)</li><li>Calculation of the memory kernel of a given spectral density, both in the time domain, and the imaginary part in the Fourier domain (with specialised methods for some of the pre-defined types)</li><li>Methods to compute the spectral density integrals that appear in the weak coupling (2nd order expansion), both for the dynamics (see e.g. H. Breuer, F. Petruccione, "The Theory of Open Quantum Systems"), and the equilibrium mean-force state (see e.g. J.D. Cresser, J. Anders, Phys. Rev. Lett. 127, 250601 (2021)).</li></ul><h2 id="Quick-start"><a class="docs-heading-anchor" href="#Quick-start">Quick start</a><a id="Quick-start-1"></a><a class="docs-heading-anchor-permalink" href="#Quick-start" title="Permalink"></a></h2><p>The desired spectral density can be constructed by simply passing the desired parameters to their respective constructor. For example, for an Ohmic spectral density <span>$J(\omega) = 3\omega$</span> we have</p><pre><code class="language-Julia hljs">Johmic = OhmicSD(3)</code></pre><p>To add a ctuoff to a base spectral density, one simply passes it to the cutoff constructor. For example, to add an exponential cutoff <span>$e^{-\omega/7}$</span> we can do</p><pre><code class="language-Julia hljs">Jc = ExponentialCutoffSD(Johmic, 7)</code></pre><h2 id="Defining-custom-spectral-densities"><a class="docs-heading-anchor" href="#Defining-custom-spectral-densities">Defining custom spectral densities</a><a id="Defining-custom-spectral-densities-1"></a><a class="docs-heading-anchor-permalink" href="#Defining-custom-spectral-densities" title="Permalink"></a></h2><p>The base <a href="reference/#SpectralDensities.AbstractSD"><code>AbstractSD</code></a> can be easily extended by the user. To do so, one must create a new sub-type for which <em>at least</em> one of the methods <a href="reference/#SpectralDensities.sd-Union{Tuple{T}, Tuple{T, Any}} where T<:AbstractSD"><code>sd</code></a> (the spectral density itself <span>$J(\omega)$</span>) or <a href="reference/#SpectralDensities.sdoverω-Union{Tuple{T}, Tuple{T, Any}} where T<:AbstractSD"><code>sdoverω</code></a> (the spectral density divided by frequency <span>$J(\omega)/\omega$</span>) must be defined. It is strongly recommended to define, if possible, <a href="reference/#SpectralDensities.sdoverω-Union{Tuple{T}, Tuple{T, Any}} where T<:AbstractSD"><code>sdoverω</code></a> since it typically makes it simpler to numerically handle potential singularities.</p><p>This is the only requirement, and all other methods will automatically work on the new subtype. Of course, as is typical of Julia's super flexible multiple-dispatch system, the user should consider providing custom functions on the new type for the reorganisation energy, etc.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="reference/">API Reference »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Sunday 29 October 2023 15:25">Sunday 29 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> |
Oops, something went wrong.