{"title":"经典和量子洛伦兹模型中的扩散、长尾和定位:统一的流体力学方法","authors":"T. R. Kirkpatrick, D. Belitz","doi":"arxiv-2409.08123","DOIUrl":null,"url":null,"abstract":"Long-time tails, or algebraic decay of time-correlation functions, have long\nbeen known to exist both in many-body systems and in models of non-interacting\nparticles in the presence of quenched disorder that are often referred to as\nLorentz models. In the latter, they have been studied extensively by a wide\nvariety of methods, the best known example being what is known as\nweak-localization effects in disordered systems of non-interacting electrons.\nThis paper provides a unifying, and very simple, approach to all of these\neffects. We show that simple modifications of the diffusion equation due to\neither a random diffusion coefficient, or a random scattering potential,\naccounts for both the decay exponents and the prefactors of the leading\nlong-time tails in the velocity autocorrelation functions of both classical and\nquantum Lorentz models.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"432 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Diffusion, Long-Time Tails, and Localization in Classical and Quantum Lorentz Models: A Unifying Hydrodynamic Approach\",\"authors\":\"T. R. Kirkpatrick, D. Belitz\",\"doi\":\"arxiv-2409.08123\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Long-time tails, or algebraic decay of time-correlation functions, have long\\nbeen known to exist both in many-body systems and in models of non-interacting\\nparticles in the presence of quenched disorder that are often referred to as\\nLorentz models. In the latter, they have been studied extensively by a wide\\nvariety of methods, the best known example being what is known as\\nweak-localization effects in disordered systems of non-interacting electrons.\\nThis paper provides a unifying, and very simple, approach to all of these\\neffects. We show that simple modifications of the diffusion equation due to\\neither a random diffusion coefficient, or a random scattering potential,\\naccounts for both the decay exponents and the prefactors of the leading\\nlong-time tails in the velocity autocorrelation functions of both classical and\\nquantum Lorentz models.\",\"PeriodicalId\":501066,\"journal\":{\"name\":\"arXiv - PHYS - Disordered Systems and Neural Networks\",\"volume\":\"432 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Disordered Systems and Neural Networks\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.08123\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Disordered Systems and Neural Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08123","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Diffusion, Long-Time Tails, and Localization in Classical and Quantum Lorentz Models: A Unifying Hydrodynamic Approach
Long-time tails, or algebraic decay of time-correlation functions, have long
been known to exist both in many-body systems and in models of non-interacting
particles in the presence of quenched disorder that are often referred to as
Lorentz models. In the latter, they have been studied extensively by a wide
variety of methods, the best known example being what is known as
weak-localization effects in disordered systems of non-interacting electrons.
This paper provides a unifying, and very simple, approach to all of these
effects. We show that simple modifications of the diffusion equation due to
either a random diffusion coefficient, or a random scattering potential,
accounts for both the decay exponents and the prefactors of the leading
long-time tails in the velocity autocorrelation functions of both classical and
quantum Lorentz models.