{"title":"无序系统普遍关系的 \"琐碎性","authors":"V. Pastukhov","doi":"arxiv-2409.01271","DOIUrl":null,"url":null,"abstract":"The universal relations for spin-$1/2$ fermions with contact interaction in\nthe presence of quenched disorder are discussed. The disorder is modeled by a\nrandom external potential with the Gaussian distribution and $\\delta$-like\ntwo-point correlation function. Utilizing simple scaling arguments, the\nrenormalizability of the theory, and the Hellmann-Feynman theorem we identified\nthe large-momentum tail of particle distribution and analog of Tan's energy\nrelation for many-fermion systems with disorder in arbitrary dimension $d\\ge\n2$. It is shown that the energy-pressure relation manifests a kind of scale\nanomaly in two and three dimensions.","PeriodicalId":501521,"journal":{"name":"arXiv - PHYS - Quantum Gases","volume":"41 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"`Triviality' of universal relations for disordered systems\",\"authors\":\"V. Pastukhov\",\"doi\":\"arxiv-2409.01271\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The universal relations for spin-$1/2$ fermions with contact interaction in\\nthe presence of quenched disorder are discussed. The disorder is modeled by a\\nrandom external potential with the Gaussian distribution and $\\\\delta$-like\\ntwo-point correlation function. Utilizing simple scaling arguments, the\\nrenormalizability of the theory, and the Hellmann-Feynman theorem we identified\\nthe large-momentum tail of particle distribution and analog of Tan's energy\\nrelation for many-fermion systems with disorder in arbitrary dimension $d\\\\ge\\n2$. It is shown that the energy-pressure relation manifests a kind of scale\\nanomaly in two and three dimensions.\",\"PeriodicalId\":501521,\"journal\":{\"name\":\"arXiv - PHYS - Quantum Gases\",\"volume\":\"41 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Quantum Gases\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.01271\",\"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 - Quantum Gases","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.01271","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
`Triviality' of universal relations for disordered systems
The universal relations for spin-$1/2$ fermions with contact interaction in
the presence of quenched disorder are discussed. The disorder is modeled by a
random external potential with the Gaussian distribution and $\delta$-like
two-point correlation function. Utilizing simple scaling arguments, the
renormalizability of the theory, and the Hellmann-Feynman theorem we identified
the large-momentum tail of particle distribution and analog of Tan's energy
relation for many-fermion systems with disorder in arbitrary dimension $d\ge
2$. It is shown that the energy-pressure relation manifests a kind of scale
anomaly in two and three dimensions.