Stochastic integral representation for the dynamics of disordered systems

authored by: Ivana Kurečić, Tobias J. Osborne
Abstract: The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Itô stochastic calculus is obtained. The stochastic integral representation affords many advantages, including amenability to analytic approximation, potential applicability to interacting systems, and compatibility with tensor network methods. The integral may be expanded to produce a series of approximations, the first of which already includes all diffusive corrections and, further, is manifestly completely positive. The addition of fluctuations leads to a convergent series of systematic corrections. As examples, expressions for the density of states and spectral form factor for the Anderson model are obtained.
Organisation(s): Institute of Theoretical Physics
CRC 1227 Designed Quantum States of Matter (DQ-mat)
External Organisation(s): Max Planck Institute of Quantum Optics (MPQ)
Munich Center for Quantum Science and Technology (MCQST)
Type: Article
Journal: Physical Review A
Volume: 107
ISSN: 2469-9926
Publication date: 17.04.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Atomic and Molecular Physics, and Optics
Electronic version(s): http://arxiv.org/abs/1809.04341v1 (Access: Open)
https://doi.org/10.1103/PhysRevA.107.042213 (Access: Closed)

BibTeX

@article{c1a2686364324dd59edb85d32a61be24,
title = "Stochastic integral representation for the dynamics of disordered systems",
abstract = "The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via It{\^o} stochastic calculus is obtained. The stochastic integral representation affords many advantages, including amenability to analytic approximation, potential applicability to interacting systems, and compatibility with tensor network methods. The integral may be expanded to produce a series of approximations, the first of which already includes all diffusive corrections and, further, is manifestly completely positive. The addition of fluctuations leads to a convergent series of systematic corrections. As examples, expressions for the density of states and spectral form factor for the Anderson model are obtained.",
keywords = "quant-ph, cond-mat.dis-nn, hep-th",
author = "Ivana Kure{\v c}i{\'c} and Osborne, {Tobias J.}",
note = "Funding Information: This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through SFB 1227 (DQ-mat) and Germany's Excellence Strategy–EXC-2111–Grant No. 390814868, as well as the RTG 1991 and the EU through the ERC (European Research Council) Starting Grant WASCOSYS (Grant No. 636201).",
year = "2023",
month = apr,
day = "17",
doi = "10.1103/PhysRevA.107.042213",
language = "English",
volume = "107",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "4",
}