{"id":245,"date":"2021-03-27T14:31:36","date_gmt":"2021-03-27T14:31:36","guid":{"rendered":"https:\/\/3189810918.blog.com.gr\/?p=245"},"modified":"2021-03-27T15:07:39","modified_gmt":"2021-03-27T15:07:39","slug":"the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye","status":"publish","type":"post","link":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/","title":{"rendered":"The distribution of energy states in liquids, 100 years after Einstein and Debye"},"content":{"rendered":"\n<p>In an article published in the journal PNAS by Matteo Baggioli, and Alessio Zaccone of University of Milano, the law which governs the distribution of vibrational energy states of liquids has been derived mathematically for the first time. The new mathematical theory by Zaccone &amp; Baggioli solved the problem of obtaining the distribution of these complex energy states by combining the so-called Zeldovich regularization for unstable quantum states with the mathematical theory of distributions by L. Schwartz. The final result provides an equation in closed form for the distribution of energy states in liquids, which goes linear in the frequency, as opposed to the Debye law for solids, which goes quadratic in frequency, and also correctly predicts its temperature dependence.<\/p>\n\n\n\n<p><a href=\"https:\/\/www.pnas.org\/content\/118\/5\/e2022303118\">Universal law for the vibrational density of states of liquids | PNAS<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"413\" src=\"https:\/\/www.www.www.theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1024x413.png\" alt=\"\" class=\"wp-image-249\" srcset=\"https:\/\/theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1024x413.png 1024w, https:\/\/theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-300x121.png 300w, https:\/\/theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-768x310.png 768w, https:\/\/theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1536x620.png 1536w, https:\/\/theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-2048x827.png 2048w, https:\/\/theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1200x484.png 1200w, https:\/\/theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1980x799.png 1980w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>In an article published in the journal PNAS by Matteo Baggioli, and Alessio Zaccone of University of Milano, the law which governs the distribution of vibrational energy states of liquids has been derived mathematically for the first time. The new mathematical theory by Zaccone &amp; Baggioli solved the problem of obtaining the distribution of these [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[3],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The distribution of energy states in liquids, 100 years after Einstein and Debye - TheoryLab<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The distribution of energy states in liquids, 100 years after Einstein and Debye - TheoryLab\" \/>\n<meta property=\"og:description\" content=\"In an article published in the journal PNAS by Matteo Baggioli, and Alessio Zaccone of University of Milano, the law which governs the distribution of vibrational energy states of liquids has been derived mathematically for the first time. The new mathematical theory by Zaccone &amp; Baggioli solved the problem of obtaining the distribution of these [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/\" \/>\n<meta property=\"og:site_name\" content=\"TheoryLab\" \/>\n<meta property=\"article:published_time\" content=\"2021-03-27T14:31:36+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-03-27T15:07:39+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.www.www.theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1024x413.png\" \/>\n<meta name=\"author\" content=\"Matteo Baggioli\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Matteo Baggioli\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/\"},\"author\":{\"name\":\"Matteo Baggioli\",\"@id\":\"https:\/\/theorylab-sjtu.com\/#\/schema\/person\/7614fab82233e5bf9dcc437cd0913eb9\"},\"headline\":\"The distribution of energy states in liquids, 100 years after Einstein and Debye\",\"datePublished\":\"2021-03-27T14:31:36+00:00\",\"dateModified\":\"2021-03-27T15:07:39+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/\"},\"wordCount\":143,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/theorylab-sjtu.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.www.www.theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1024x413.png\",\"articleSection\":[\"News\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/\",\"url\":\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/\",\"name\":\"The distribution of energy states in liquids, 100 years after Einstein and Debye - TheoryLab\",\"isPartOf\":{\"@id\":\"https:\/\/theorylab-sjtu.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.www.www.theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1024x413.png\",\"datePublished\":\"2021-03-27T14:31:36+00:00\",\"dateModified\":\"2021-03-27T15:07:39+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#primaryimage\",\"url\":\"https:\/\/www.www.www.theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1024x413.png\",\"contentUrl\":\"https:\/\/www.www.www.theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1024x413.png\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/theorylab-sjtu.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"The distribution of energy states in liquids, 100 years after Einstein and Debye\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/theorylab-sjtu.com\/#website\",\"url\":\"https:\/\/theorylab-sjtu.com\/\",\"name\":\"TheoryLab\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\/\/theorylab-sjtu.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/theorylab-sjtu.com\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/theorylab-sjtu.com\/#organization\",\"name\":\"TheoryLab\",\"url\":\"https:\/\/theorylab-sjtu.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/theorylab-sjtu.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/logo-1.png\",\"contentUrl\":\"https:\/\/theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/logo-1.png\",\"width\":1200,\"height\":1200,\"caption\":\"TheoryLab\"},\"image\":{\"@id\":\"https:\/\/theorylab-sjtu.com\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/theorylab-sjtu.com\/#\/schema\/person\/7614fab82233e5bf9dcc437cd0913eb9\",\"name\":\"Matteo Baggioli\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/theorylab-sjtu.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/b0bb45e66c21205b1caa3cd6b68cf885?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/b0bb45e66c21205b1caa3cd6b68cf885?s=96&d=mm&r=g\",\"caption\":\"Matteo Baggioli\"},\"url\":\"https:\/\/theorylab-sjtu.com\/index.php\/author\/mbaggioli\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"The distribution of energy states in liquids, 100 years after Einstein and Debye - TheoryLab","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/","og_locale":"en_US","og_type":"article","og_title":"The distribution of energy states in liquids, 100 years after Einstein and Debye - TheoryLab","og_description":"In an article published in the journal PNAS by Matteo Baggioli, and Alessio Zaccone of University of Milano, the law which governs the distribution of vibrational energy states of liquids has been derived mathematically for the first time. The new mathematical theory by Zaccone &amp; Baggioli solved the problem of obtaining the distribution of these [&hellip;]","og_url":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/","og_site_name":"TheoryLab","article_published_time":"2021-03-27T14:31:36+00:00","article_modified_time":"2021-03-27T15:07:39+00:00","og_image":[{"url":"https:\/\/www.www.www.theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1024x413.png"}],"author":"Matteo Baggioli","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Matteo Baggioli","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#article","isPartOf":{"@id":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/"},"author":{"name":"Matteo Baggioli","@id":"https:\/\/theorylab-sjtu.com\/#\/schema\/person\/7614fab82233e5bf9dcc437cd0913eb9"},"headline":"The distribution of energy states in liquids, 100 years after Einstein and Debye","datePublished":"2021-03-27T14:31:36+00:00","dateModified":"2021-03-27T15:07:39+00:00","mainEntityOfPage":{"@id":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/"},"wordCount":143,"commentCount":0,"publisher":{"@id":"https:\/\/theorylab-sjtu.com\/#organization"},"image":{"@id":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#primaryimage"},"thumbnailUrl":"https:\/\/www.www.www.theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1024x413.png","articleSection":["News"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/","url":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/","name":"The distribution of energy states in liquids, 100 years after Einstein and Debye - TheoryLab","isPartOf":{"@id":"https:\/\/theorylab-sjtu.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#primaryimage"},"image":{"@id":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#primaryimage"},"thumbnailUrl":"https:\/\/www.www.www.theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1024x413.png","datePublished":"2021-03-27T14:31:36+00:00","dateModified":"2021-03-27T15:07:39+00:00","breadcrumb":{"@id":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#primaryimage","url":"https:\/\/www.www.www.theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1024x413.png","contentUrl":"https:\/\/www.www.www.theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/Capture-2-1024x413.png"},{"@type":"BreadcrumbList","@id":"https:\/\/theorylab-sjtu.com\/index.php\/2021\/03\/27\/the-distribution-of-energy-states-in-liquids-100-years-after-einstein-and-debye\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/theorylab-sjtu.com\/"},{"@type":"ListItem","position":2,"name":"The distribution of energy states in liquids, 100 years after Einstein and Debye"}]},{"@type":"WebSite","@id":"https:\/\/theorylab-sjtu.com\/#website","url":"https:\/\/theorylab-sjtu.com\/","name":"TheoryLab","description":"","publisher":{"@id":"https:\/\/theorylab-sjtu.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/theorylab-sjtu.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/theorylab-sjtu.com\/#organization","name":"TheoryLab","url":"https:\/\/theorylab-sjtu.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/theorylab-sjtu.com\/#\/schema\/logo\/image\/","url":"https:\/\/theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/logo-1.png","contentUrl":"https:\/\/theorylab-sjtu.com\/wp-content\/uploads\/2021\/03\/logo-1.png","width":1200,"height":1200,"caption":"TheoryLab"},"image":{"@id":"https:\/\/theorylab-sjtu.com\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/theorylab-sjtu.com\/#\/schema\/person\/7614fab82233e5bf9dcc437cd0913eb9","name":"Matteo Baggioli","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/theorylab-sjtu.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/b0bb45e66c21205b1caa3cd6b68cf885?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/b0bb45e66c21205b1caa3cd6b68cf885?s=96&d=mm&r=g","caption":"Matteo Baggioli"},"url":"https:\/\/theorylab-sjtu.com\/index.php\/author\/mbaggioli\/"}]}},"_links":{"self":[{"href":"https:\/\/theorylab-sjtu.com\/index.php\/wp-json\/wp\/v2\/posts\/245"}],"collection":[{"href":"https:\/\/theorylab-sjtu.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theorylab-sjtu.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theorylab-sjtu.com\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/theorylab-sjtu.com\/index.php\/wp-json\/wp\/v2\/comments?post=245"}],"version-history":[{"count":3,"href":"https:\/\/theorylab-sjtu.com\/index.php\/wp-json\/wp\/v2\/posts\/245\/revisions"}],"predecessor-version":[{"id":251,"href":"https:\/\/theorylab-sjtu.com\/index.php\/wp-json\/wp\/v2\/posts\/245\/revisions\/251"}],"wp:attachment":[{"href":"https:\/\/theorylab-sjtu.com\/index.php\/wp-json\/wp\/v2\/media?parent=245"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theorylab-sjtu.com\/index.php\/wp-json\/wp\/v2\/categories?post=245"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theorylab-sjtu.com\/index.php\/wp-json\/wp\/v2\/tags?post=245"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}