{"title":"从克雷洛夫复杂性看自相关函数的普遍假设","authors":"Ren Zhang, Hui Zhai","doi":"10.1007/s44214-024-00054-4","DOIUrl":null,"url":null,"abstract":"<p>In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the autocorrelation function. In particular, we focus on a particular kind of operator complexity called the Krylov complexity. We find that a set of Lanczos coefficients <span>\\(\\{b_{n}\\}\\)</span> computed for determining the Krylov complexity can reveal the universal behaviors of autocorrelations, which are otherwise impossible. When the time axis is scaled by <span>\\(b_{1}\\)</span>, different autocorrelation functions obey a universal function form at short time. We further propose a characteristic parameter deduced from <span>\\(\\{b_{n}\\}\\)</span> that can largely determine the behavior of autocorrelations at the intermediate time. This parameter can also largely determine whether the autocorrelation function oscillates or monotonically decays in time. We present numerical evidences and physical intuitions to support these universal hypotheses of autocorrelations. We emphasize that these universal behaviors are held across different operators and different physical systems.</p>","PeriodicalId":501227,"journal":{"name":"Quantum Frontiers","volume":"48 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Universal hypothesis of autocorrelation function from Krylov complexity\",\"authors\":\"Ren Zhang, Hui Zhai\",\"doi\":\"10.1007/s44214-024-00054-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the autocorrelation function. In particular, we focus on a particular kind of operator complexity called the Krylov complexity. We find that a set of Lanczos coefficients <span>\\\\(\\\\{b_{n}\\\\}\\\\)</span> computed for determining the Krylov complexity can reveal the universal behaviors of autocorrelations, which are otherwise impossible. When the time axis is scaled by <span>\\\\(b_{1}\\\\)</span>, different autocorrelation functions obey a universal function form at short time. We further propose a characteristic parameter deduced from <span>\\\\(\\\\{b_{n}\\\\}\\\\)</span> that can largely determine the behavior of autocorrelations at the intermediate time. This parameter can also largely determine whether the autocorrelation function oscillates or monotonically decays in time. We present numerical evidences and physical intuitions to support these universal hypotheses of autocorrelations. We emphasize that these universal behaviors are held across different operators and different physical systems.</p>\",\"PeriodicalId\":501227,\"journal\":{\"name\":\"Quantum Frontiers\",\"volume\":\"48 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Frontiers\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s44214-024-00054-4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Frontiers","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s44214-024-00054-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Universal hypothesis of autocorrelation function from Krylov complexity
In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the autocorrelation function. In particular, we focus on a particular kind of operator complexity called the Krylov complexity. We find that a set of Lanczos coefficients \(\{b_{n}\}\) computed for determining the Krylov complexity can reveal the universal behaviors of autocorrelations, which are otherwise impossible. When the time axis is scaled by \(b_{1}\), different autocorrelation functions obey a universal function form at short time. We further propose a characteristic parameter deduced from \(\{b_{n}\}\) that can largely determine the behavior of autocorrelations at the intermediate time. This parameter can also largely determine whether the autocorrelation function oscillates or monotonically decays in time. We present numerical evidences and physical intuitions to support these universal hypotheses of autocorrelations. We emphasize that these universal behaviors are held across different operators and different physical systems.