{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:04:49Z","timestamp":1760238289484,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,7,31]],"date-time":"2020-07-31T00:00:00Z","timestamp":1596153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["108-2112-M-003-006-MY2"],"award-info":[{"award-number":["108-2112-M-003-006-MY2"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We propose a possible scheme to study the thermalization in a quantum harmonic oscillator with random disorder. Our numerical simulation shows that through the effect of random disorder, the system can undergo a transition from an initial nonequilibrium state to a equilibrium state. Unlike the classical damped harmonic oscillator where total energy is dissipated, total energy of the disordered quantum harmonic oscillator is conserved. In particular, at equilibrium the initial mechanical energy is transformed to the thermodynamic energy in which kinetic and potential energies are evenly distributed. Shannon entropy in different bases are shown to yield consistent results during the thermalization.<\/jats:p>","DOI":"10.3390\/e22080855","type":"journal-article","created":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T03:16:46Z","timestamp":1596424606000},"page":"855","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Thermalization in a Quantum Harmonic Oscillator with Random Disorder"],"prefix":"10.3390","volume":"22","author":[{"given":"Ya-Wei","family":"Hsueh","sequence":"first","affiliation":[{"name":"Department of Physics, National Central University, Jhong-li 32001, Taiwan"}]},{"given":"Che-Hsiu","family":"Hsueh","sequence":"additional","affiliation":[{"name":"Department of Physics, National Taiwan Normal University, Taipei 11677, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1682-2389","authenticated-orcid":false,"given":"Wen-Chin","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Physics, National Taiwan Normal University, Taipei 11677, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1103\/RevModPhys.83.863","article-title":"Colloquium: Nonequilibrium dynamics of closed interacting quantum systems","volume":"83","author":"Polkovnikov","year":"2011","journal-title":"Rev. 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