{"title":"规则晶格上量子扩散的波动和持续性。","authors":"Cheng Ma, Omar Malik, G Korniss","doi":"10.1103/PhysRevE.111.024126","DOIUrl":null,"url":null,"abstract":"<p><p>We investigate quantum persistence by analyzing amplitude and phase fluctuations of the wave function governed by the time-dependent free-particle Schrödinger equation. The quantum system is initialized with local random uncorrelated Gaussian amplitude and phase fluctuations. In analogy with classical diffusion, the persistence probability is defined as the probability that the local (amplitude or phase) fluctuations have not changed sign up to time t. Our results show that the persistence probability in quantum diffusion exhibits exponential-like tails. More specifically, in d=1 the persistence probability decays in a stretched exponential fashion, while in d=2 and d=3 as an exponential. We also provide some insights by analyzing the two-point spatial and temporal correlation functions in the limit of small fluctuations. In particular, in the long-time asymptotic limit, the temporal correlation functions for both local amplitude and phase fluctuations become time-homogeneous. Hence, the zero-crossing events correspond to those governed by a stationary Gaussian process, with an autocorrelation-function power-law tail decaying sufficiently fast to imply an exponential-like tail of the persistence probabilities.</p>","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"111 2-1","pages":"024126"},"PeriodicalIF":2.2000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fluctuations and persistence in quantum diffusion on regular lattices.\",\"authors\":\"Cheng Ma, Omar Malik, G Korniss\",\"doi\":\"10.1103/PhysRevE.111.024126\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>We investigate quantum persistence by analyzing amplitude and phase fluctuations of the wave function governed by the time-dependent free-particle Schrödinger equation. The quantum system is initialized with local random uncorrelated Gaussian amplitude and phase fluctuations. In analogy with classical diffusion, the persistence probability is defined as the probability that the local (amplitude or phase) fluctuations have not changed sign up to time t. Our results show that the persistence probability in quantum diffusion exhibits exponential-like tails. More specifically, in d=1 the persistence probability decays in a stretched exponential fashion, while in d=2 and d=3 as an exponential. We also provide some insights by analyzing the two-point spatial and temporal correlation functions in the limit of small fluctuations. In particular, in the long-time asymptotic limit, the temporal correlation functions for both local amplitude and phase fluctuations become time-homogeneous. Hence, the zero-crossing events correspond to those governed by a stationary Gaussian process, with an autocorrelation-function power-law tail decaying sufficiently fast to imply an exponential-like tail of the persistence probabilities.</p>\",\"PeriodicalId\":48698,\"journal\":{\"name\":\"Physical Review E\",\"volume\":\"111 2-1\",\"pages\":\"024126\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2025-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review E\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/PhysRevE.111.024126\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, FLUIDS & PLASMAS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevE.111.024126","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, FLUIDS & PLASMAS","Score":null,"Total":0}
Fluctuations and persistence in quantum diffusion on regular lattices.
We investigate quantum persistence by analyzing amplitude and phase fluctuations of the wave function governed by the time-dependent free-particle Schrödinger equation. The quantum system is initialized with local random uncorrelated Gaussian amplitude and phase fluctuations. In analogy with classical diffusion, the persistence probability is defined as the probability that the local (amplitude or phase) fluctuations have not changed sign up to time t. Our results show that the persistence probability in quantum diffusion exhibits exponential-like tails. More specifically, in d=1 the persistence probability decays in a stretched exponential fashion, while in d=2 and d=3 as an exponential. We also provide some insights by analyzing the two-point spatial and temporal correlation functions in the limit of small fluctuations. In particular, in the long-time asymptotic limit, the temporal correlation functions for both local amplitude and phase fluctuations become time-homogeneous. Hence, the zero-crossing events correspond to those governed by a stationary Gaussian process, with an autocorrelation-function power-law tail decaying sufficiently fast to imply an exponential-like tail of the persistence probabilities.
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.