{"extern":1,"type":"journal_article","date_updated":"2021-01-12T06:59:15Z","publist_id":"4175","volume":303,"intvolume":"       303","quality_controlled":0,"title":"Quantum diffusion and eigenfunction delocalization in a random band matrix model","_id":"2717","doi":"10.1007/s00220-011-1204-2","author":[{"full_name":"László Erdös","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Antti","full_name":"Knowles, Antti","last_name":"Knowles"}],"abstract":[{"lang":"eng","text":"We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions. The matrix elements H xy, indexed by, are independent, uniformly distributed random variables if {pipe}x-y{pipe} is less than the band width W, and zero otherwise. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales. We also show that the localization length of the eigenvectors of H is larger than a factor W d/6 times the band width. All results are uniform in the size of the matrix. "}],"issue":"2","publication_status":"published","publication":"Communications in Mathematical Physics","month":"04","date_created":"2018-12-11T11:59:14Z","citation":{"ista":"Erdös L, Knowles A. 2011. Quantum diffusion and eigenfunction delocalization in a random band matrix model. Communications in Mathematical Physics. 303(2), 509–554.","chicago":"Erdös, László, and Antti Knowles. “Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model.” <i>Communications in Mathematical Physics</i>. Springer, 2011. <a href=\"https://doi.org/10.1007/s00220-011-1204-2\">https://doi.org/10.1007/s00220-011-1204-2</a>.","apa":"Erdös, L., &#38; Knowles, A. (2011). Quantum diffusion and eigenfunction delocalization in a random band matrix model. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-011-1204-2\">https://doi.org/10.1007/s00220-011-1204-2</a>","short":"L. Erdös, A. Knowles, Communications in Mathematical Physics 303 (2011) 509–554.","ama":"Erdös L, Knowles A. Quantum diffusion and eigenfunction delocalization in a random band matrix model. <i>Communications in Mathematical Physics</i>. 2011;303(2):509-554. doi:<a href=\"https://doi.org/10.1007/s00220-011-1204-2\">10.1007/s00220-011-1204-2</a>","mla":"Erdös, László, and Antti Knowles. “Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model.” <i>Communications in Mathematical Physics</i>, vol. 303, no. 2, Springer, 2011, pp. 509–54, doi:<a href=\"https://doi.org/10.1007/s00220-011-1204-2\">10.1007/s00220-011-1204-2</a>.","ieee":"L. Erdös and A. Knowles, “Quantum diffusion and eigenfunction delocalization in a random band matrix model,” <i>Communications in Mathematical Physics</i>, vol. 303, no. 2. Springer, pp. 509–554, 2011."},"day":"01","publisher":"Springer","status":"public","year":"2011","page":"509 - 554","date_published":"2011-04-01T00:00:00Z"}