{"id":10933,"date":"2026-10-22T22:05:26","date_gmt":"2026-10-22T22:05:26","guid":{"rendered":"https:\/\/vallico.net\/casinoqmc\/?page_id=10933"},"modified":"2026-10-22T22:05:31","modified_gmt":"2026-10-22T22:05:31","slug":"videos-and-simulations","status":"publish","type":"page","link":"https:\/\/vallico.net\/casinoqmc\/videos-and-simulations\/","title":{"rendered":"Videos and Simulations"},"content":{"rendered":"\n<!-- Videos and simulations: one Custom HTML block for the WordPress page.\n     No script, no outside resource. The films, posters, stills and the caffeine\n     page are under https:\/\/casinoqmc.net\/films\/; the beryllium page is under \/pilotfilm\/.\n     webfilms1, 22 October 2026. -->\n<style>\n  .vs figure{margin:0 0 0.6em}\n  .vs video{display:block;width:100%;height:auto;background:#060a13}\n  .vs figcaption{font-size:0.85em;line-height:1.5;margin-top:0.5em}\n  .vs p.vs-stills{font-size:0.85em;margin:0 0 2.2em}\n  .vs h3{margin:1.6em 0 0.5em}\n<\/style>\n<div class=\"vs\">\n\n<p>\n  These films are calculations made with CASINO. The pictures of particles are\n  drawn from the positions the calculations computed; the family tree is drawn\n  from the record of which walkers a calculation copied and removed. Most show diffusion Monte\n  Carlo, in which a population of walkers, each one copy of the positions of\n  all the particles, is carried by a random walk in imaginary time towards the\n  state of lowest energy; that walk is how the calculation finds the state, not\n  the motion of the particles. The last film shows something else: electrons\n  moved in real time along de Broglie&ndash;Bohm trajectories. Two of the\n  calculations can also be turned and played in the browser.\n<\/p>\n\n<h3>The living electron cloud: caffeine<\/h3>\n<figure>\n  <video controls playsinline preload=\"none\" width=\"1920\" height=\"1080\"\n         poster=\"https:\/\/casinoqmc.net\/films\/caffeine_dmc_1080p_credited_poster.jpg\">\n    <source src=\"https:\/\/casinoqmc.net\/films\/caffeine_dmc_1080p_credited.mp4\" type=\"video\/mp4\"\/>\n  <\/video>\n  <figcaption>\n    Caffeine&rsquo;s 74 outer electrons as a diffusion Monte Carlo calculation\n    with CASINO v3.1.1134 found them on 20 October 2026, every coloured point a\n    computed position, from 128 preparatory random walks to about 2000 walkers,\n    a copy drawn as a brief flare and a removal as a fade, ending in a long\n    exposure of 840 steps that builds up the density of the outer electrons;\n    what moves is the calculation&rsquo;s random walk, which runs in imaginary\n    time to find the molecule&rsquo;s state of lowest energy, not the electrons.\n    Film by Mike Towler.\n  <\/figcaption>\n<\/figure>\n<p class=\"vs-stills\">\n  <a href=\"https:\/\/casinoqmc.net\/films\/caffeine_still_2_population_screen_credited.jpg\">One step of the walk<\/a>,\n  every electron of about 2000 walkers; and\n  <a href=\"https:\/\/casinoqmc.net\/films\/caffeine_poster_a2_screen_credited.png\">the poster<\/a>,\n  the long exposure: the density of the outer electrons summed over 840 steps;\n  the walk runs in imaginary time and is not the electrons&rsquo; motion. The same calculation&rsquo;s walkers can be turned in the browser, below.\n<\/p>\n\n<h3>The walkers&rsquo; family tree<\/h3>\n<figure>\n  <video controls playsinline preload=\"none\" width=\"1920\" height=\"1080\"\n         poster=\"https:\/\/casinoqmc.net\/films\/caffeine_tree_1080p_credited_poster.jpg\">\n    <source src=\"https:\/\/casinoqmc.net\/films\/caffeine_tree_1080p_credited.mp4\" type=\"video\/mp4\"\/>\n  <\/video>\n  <figcaption>\n    Every one of the 2072 walkers alive at the last of 2000 steps of a\n    diffusion Monte Carlo calculation of caffeine with CASINO v3.1.1134 on 20\n    October 2026, each walker one set of positions for all 74 outer electrons,\n    traced back through the calculation&rsquo;s copies to the 89 of the 2000\n    starting walkers from which all of them descend, the branches with no\n    descendant at the last step drawn faintly; the tree records copying and\n    removal in imaginary time, the calculation&rsquo;s way of finding the\n    molecule&rsquo;s state of lowest energy, and nothing the electrons do.\n    Film by Mike Towler.\n  <\/figcaption>\n<\/figure>\n<p class=\"vs-stills\">\n  <a href=\"https:\/\/casinoqmc.net\/films\/caffeine_tree_still_1_whole_screen_credited.jpg\">The whole tree<\/a>,\n  the first step at the centre and the last at the rim; and\n  <a href=\"https:\/\/casinoqmc.net\/films\/caffeine_tree_still_2_family_screen_credited.jpg\">one family<\/a>,\n  the 154 walkers alive at the last step that descend from one walker of the\n  first; the tree records copying and removal in the calculation&rsquo;s walk in\n  imaginary time, not anything the electrons do.\n<\/p>\n\n<h3>C<sub>60<\/sub><\/h3>\n<figure>\n  <video controls playsinline preload=\"none\" width=\"1920\" height=\"1080\"\n         poster=\"https:\/\/casinoqmc.net\/films\/c60_dmc_1080p_credited_poster.jpg\">\n    <source src=\"https:\/\/casinoqmc.net\/films\/c60_dmc_1080p_credited.mp4\" type=\"video\/mp4\"\/>\n  <\/video>\n  <figcaption>\n    The 240 outer electrons of C<sub>60<\/sub>, sixty carbon atoms in the shape\n    of a football, as a diffusion Monte Carlo calculation with CASINO v3.1.1157\n    found them on 21 October 2026, every coloured point a computed position,\n    from 128 preparatory random walks that settle from a random start to about\n    1000 walkers, a copy drawn as a brief flare and a removal as a fade, ending\n    in a long exposure of 840 steps that builds up the density of the outer\n    electrons into a cage, seen along a fivefold and then a threefold axis;\n    what moves is the calculation&rsquo;s random walk, which runs in imaginary\n    time to find the molecule&rsquo;s state of lowest energy, not the electrons.\n    Film by Mike Towler.\n  <\/figcaption>\n<\/figure>\n<p class=\"vs-stills\">\n  <a href=\"https:\/\/casinoqmc.net\/films\/c60_still_1_exposure_screen_credited.jpg\">The long exposure<\/a>,\n  every electron of every walker summed over 1800 steps, seen through a\n  pentagon; and\n  <a href=\"https:\/\/casinoqmc.net\/films\/c60_still_2_population_screen_credited.jpg\">one step of the walk<\/a>,\n  1000 walkers seen through a hexagon; the walk runs in imaginary time and is\n  not the electrons&rsquo; motion.\n<\/p>\n\n<h3>Quantum nuclei<\/h3>\n<figure>\n  <video controls playsinline preload=\"none\" width=\"1920\" height=\"1080\"\n         poster=\"https:\/\/casinoqmc.net\/films\/nuclei_dmc_1080p_credited_poster.jpg\">\n    <source src=\"https:\/\/casinoqmc.net\/films\/nuclei_dmc_1080p_credited.mp4\" type=\"video\/mp4\"\/>\n  <\/video>\n  <figcaption>\n    Four small molecules in which the nuclei, too, are treated as quantum\n    particles (the hydrogen molecular ion, the hydrogen molecule with heavy\n    hydrogen beside it, and the muonic molecular ion, two protons bound by a\n    negative muon), as diffusion Monte Carlo calculations with CASINO v3.1.1188\n    found them on 22 October 2026, after 512 preparatory random walks that\n    spread the hydrogen molecular ion&rsquo;s protons from one line over a\n    shell: every point a computed position of a nucleus, an electron or the\n    muon, in 20,000 walkers for each molecule (a walker is a copy of the\n    positions of all its particles), each drawn about its own centre of mass\n    and then turned so that its two nuclei lie on one line, a drawing\n    convention, and each molecule at its own scale; neither the preparatory\n    walks nor the diffusion Monte Carlo walk, which runs in imaginary time as a\n    way of finding each molecule&rsquo;s state of lowest energy, is the\n    particles&rsquo; motion.\n    Film by Mike Towler.\n  <\/figcaption>\n<\/figure>\n<p class=\"vs-stills\">\n  Two stills from the same calculations:\n  <a href=\"https:\/\/casinoqmc.net\/films\/nuclei_still_1_h2plus_screen_credited.jpg\">the hydrogen molecular ion<\/a>,\n  each walker about its own centre of mass, the protons on a shell; and\n  <a href=\"https:\/\/casinoqmc.net\/films\/nuclei_still_2_h2_screen_credited.jpg\">the hydrogen molecule<\/a>,\n  each walker turned so that its protons lie on one line; the walks run in\n  imaginary time and are not the particles&rsquo; motion.\n<\/p>\n\n<h3>Electrons freezing<\/h3>\n<figure>\n  <video controls playsinline preload=\"none\" width=\"1920\" height=\"1080\"\n         poster=\"https:\/\/casinoqmc.net\/films\/wigner_1080p_credited_poster.jpg\">\n    <source src=\"https:\/\/casinoqmc.net\/films\/wigner_1080p_credited.mp4\" type=\"video\/mp4\"\/>\n  <\/video>\n  <figcaption>\n    Forty-two electrons in a flat cell that repeats without end, computed with\n    CASINO v3.1.1188 on 22 October 2026 at nine densities from\n    r<sub>s<\/sub>&nbsp;=&nbsp;1 to 150, each density a diffusion Monte Carlo\n    calculation of its own, so that the dial stepping through them is not a\n    clock: one walker&rsquo;s electrons step by step, every point a computed\n    position, the rows that form at low density lying in a direction set not\n    by any freezing but by the cell, which is cut to hold a triangular lattice;\n    the density of the other electrons as seen from one, where alone a fluid\n    trial function&rsquo;s freezing shows, since it keeps the density itself\n    even, first averaged over direction, a hole that grows into rings as the\n    density falls, then with each view turned so that its nearest neighbour\n    lies on a line, a way of drawing under which, at the lowest density, the\n    rings break into six peaks sixty degrees apart; then the density of a\n    crystal trial function, its lattice put there by its choice of sites, and a\n    small graph on which the crystal&rsquo;s energy falls below the\n    fluid&rsquo;s between r<sub>s<\/sub>&nbsp;=&nbsp;30 and 60; the walk runs in\n    imaginary time to find the state of lowest energy and is not the motion of\n    the electrons.\n    Film by Mike Towler.\n  <\/figcaption>\n<\/figure>\n<p class=\"vs-stills\">\n  Two stills:\n  <a href=\"https:\/\/casinoqmc.net\/films\/wigner_still_A_nine_densities_screen_credited.jpg\">nine densities<\/a>,\n  the density of the other electrons seen from one, each view turned, as a\n  way of drawing, so that its nearest neighbour lies on the line; and\n  <a href=\"https:\/\/casinoqmc.net\/films\/wigner_still_B_two_orders_screen_credited.jpg\">two kinds of order<\/a>\n  at r<sub>s<\/sub>&nbsp;=&nbsp;150, the fluid&rsquo;s turned pair density\n  above the crystal trial function&rsquo;s density, whose lattice is put there\n  by its choice of sites; the walk runs in imaginary time and is not the\n  electrons&rsquo; motion.\n<\/p>\n\n<h3>Octane<\/h3>\n<figure>\n  <video controls loop playsinline preload=\"none\" width=\"1200\" height=\"472\"\n         poster=\"https:\/\/casinoqmc.net\/films\/octane_dmc_walkers_1200x472_credited_poster.jpg\">\n    <source src=\"https:\/\/casinoqmc.net\/films\/octane_dmc_walkers_1200x472_credited.mp4\" type=\"video\/mp4\"\/>\n  <\/video>\n  <figcaption>\n    The loop on CASINO&rsquo;s home page: the electrons of n-octane as the\n    walkers of a diffusion Monte Carlo calculation with CASINO v3.1.1055, every\n    electron of every walker a point of light, amber spin up and azure spin\n    down, about 180 walkers after each of 240 steps of 0.01 a.u., each frame\n    one step with the three before it fading behind, the last 30 steps laid\n    over the first 30 so that the loop has no seam; the walk runs in imaginary\n    time to find the molecule&rsquo;s state of lowest energy and is not the\n    motion of the electrons.\n    Film by Mike Towler.\n  <\/figcaption>\n<\/figure>\n<p class=\"vs-stills\">\n  <a href=\"https:\/\/casinoqmc.net\/films\/octane_dmc_exposure_1200x472_credited.png\">The same walk as a long exposure<\/a>,\n  about 180 walkers at each of 241 steps on one picture; the walk runs in\n  imaginary time and is not the electrons&rsquo; motion.\n<\/p>\n\n<h3>Towards quantum equilibrium: beryllium<\/h3>\n<figure>\n  <video controls playsinline preload=\"none\" width=\"1920\" height=\"1080\"\n         poster=\"https:\/\/casinoqmc.net\/films\/pilotfilm_beryllium_1080p_credited_poster.jpg\">\n    <source src=\"https:\/\/casinoqmc.net\/films\/pilotfilm_beryllium_1080p_credited.mp4\" type=\"video\/mp4\"\/>\n  <\/video>\n  <figcaption>\n    The beryllium atom in a superposition of twelve of its states, its four\n    electrons moved in real time by the de Broglie&ndash;Bohm guidance\n    equation, computed with CASINO v3.1.851: on the left, 4000 atoms started\n    from the distribution of the ground state alone, out of equilibrium with\n    the wave; on the right, 2000 started in equilibrium; beneath, for both, H, a\n    coarse-grained measure of the distance from equilibrium: on the left it\n    falls overall, rises again between 80 and 120 atomic units of time, and is\n    still above zero at 200 (4.8 femtoseconds). Each point of light is a\n    computed position of one electron, amber spin up and blue spin down; the\n    trails join successive computed positions by straight segments.\n    Film by Mike Towler.\n  <\/figcaption>\n<\/figure>\n<p class=\"vs-stills\">\n  <a href=\"https:\/\/casinoqmc.net\/films\/poster_t115_4k_credited.png\">The poster<\/a>,\n  the scene at 115 atomic units of time. The same scene can be turned in the\n  browser, below.\n<\/p>\n\n<h3>Simulations to turn in the browser<\/h3>\n<p>\n  <a href=\"https:\/\/casinoqmc.net\/films\/caffeine_dmc_walkers_credited.html\">Caffeine&rsquo;s walkers<\/a>:\n  steps 401 to 660 of the same calculation as the first film, one walker in\n  twenty, on a page made by CASINO&rsquo;s walkerfilm utility that plays in a\n  browser and turns under a finger; the walk runs in imaginary time to find\n  the molecule&rsquo;s state of lowest energy and is not the electrons&rsquo;\n  motion. One file of 17 MB.\n<\/p>\n<p>\n  <a href=\"https:\/\/casinoqmc.net\/pilotfilm\/pilotfilm_beryllium.html\">Towards quantum equilibrium<\/a>:\n  the beryllium scene of the last film, drawn live in the browser: drag to\n  turn the atoms, pinch or scroll to zoom, play and pause, with the same\n  explanation under &ldquo;About this picture&rdquo;. One file of 15 MB.\n<\/p>\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>These films are calculations made with CASINO. The pictures of particles are drawn from the positions the calculations computed; the family tree is drawn from the record of which walkers a calculation copied and removed. Most show diffusion Monte Carlo, in which a population of walkers, each one copy of the positions of all the &hellip; <a href=\"https:\/\/vallico.net\/casinoqmc\/videos-and-simulations\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Videos and Simulations<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-10933","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Videos and Simulations - Quantum Monte Carlo<\/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:\/\/vallico.net\/casinoqmc\/videos-and-simulations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Videos and Simulations - Quantum Monte Carlo\" \/>\n<meta property=\"og:description\" content=\"These films are calculations made with CASINO. 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