{"id":234477,"date":"2026-04-02T06:33:42","date_gmt":"2026-04-02T11:33:42","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2026\/04\/extending-the-adiabatic-theorem"},"modified":"2026-04-02T06:33:42","modified_gmt":"2026-04-02T11:33:42","slug":"extending-the-adiabatic-theorem","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2026\/04\/extending-the-adiabatic-theorem","title":{"rendered":"Extending the Adiabatic Theorem"},"content":{"rendered":"<p style=\"padding-right: 20px\"><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/extending-the-adiabatic-theorem.jpg\"><\/a><\/p>\n<p>Jerk the support from which a swinging pendulum hangs, and you will change the pendulum\u2019s motion. But move the support very gradually, and the system will adapt so that the pendulum\u2019s motion relative to its support remains unchanged. A similar principle holds true for quantum systems. The quantum adiabatic theorem says that a system, when perturbed sufficiently slowly, remains in its instantaneous ground state. Sarah Damerow and Stefan Kehrein of the University of G\u00f6ttingen in Germany now show that aspects of this principle remain true even for the opposite limit: The ground state remains the single most likely state even for a quantum system subjected to an instantaneous perturbation [<a href=\"https:\/\/physics.aps.org\/articles\/v19\/s43#c1\">1<\/a>].<\/p>\n<p>Formally, the quantum adiabatic theorem describes how a perturbed system\u2019s Hamiltonian evolves in time. It shows that, for a slow perturbation, the system transitions from its initial ground state to the time-evolved Hamiltonian\u2019s ground state with a probability greater than the combined probabilities of all the excited states.<\/p>\n<p>Damerow and Kehrein used analytical and numerical tools to examine a quantum system undergoing rapid perturbation. They considered a quantum Ising model\u2014a lattice of interacting magnetic spins\u2014subjected to a rapidly changing external field. They found that the system was more likely to evolve from its initial ground state to the time-evolved Hamiltonian\u2019s ground state than to any given excited state\u2014provided that the lattice was in the same magnetic phase (paramagnetic or ferromagnetic) in both ground states.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Jerk the support from which a swinging pendulum hangs, and you will change the pendulum\u2019s motion. But move the support very gradually, and the system will adapt so that the pendulum\u2019s motion relative to its support remains unchanged. A similar principle holds true for quantum systems. The quantum adiabatic theorem says that a system, when [\u2026]<\/p>\n","protected":false},"author":427,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1617],"tags":[],"class_list":["post-234477","post","type-post","status-publish","format-standard","hentry","category-quantum-physics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/234477","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/427"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=234477"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/234477\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=234477"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=234477"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=234477"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}