Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning
Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face ser...
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IOP Publishing
2025-01-01
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| Series: | Machine Learning: Science and Technology |
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| Online Access: | https://doi.org/10.1088/2632-2153/ada99d |
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| author | Yuanran Zhu Jia Yin Cian C Reeves Chao Yang Vojtěch Vlček |
| author_facet | Yuanran Zhu Jia Yin Cian C Reeves Chao Yang Vojtěch Vlček |
| author_sort | Yuanran Zhu |
| collection | DOAJ |
| description | Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green’s function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff–Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on recurrent neural networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green’s functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green’s functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$ where N _t is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications. |
| format | Article |
| id | doaj-art-5aba28e5577346459ffbbe227ba9066b |
| institution | Kabale University |
| issn | 2632-2153 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj-art-5aba28e5577346459ffbbe227ba9066b2025-02-04T14:17:33ZengIOP PublishingMachine Learning: Science and Technology2632-21532025-01-016101502710.1088/2632-2153/ada99dPredicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learningYuanran Zhu0https://orcid.org/0000-0001-6851-4161Jia Yin1Cian C Reeves2Chao Yang3https://orcid.org/0000-0001-7172-7539Vojtěch Vlček4https://orcid.org/0000-0002-2836-7619Applied Mathematics and Computational Research Division, Lawerence Berkeley National Laboratory , Berkeley, CA 94720, United States of AmericaSchool of Mathematical Sciences, Fudan University , Shanghai 200437, People’s Republic of ChinaDepartment of Physics, University of California , Santa Barbara, Santa Barbara, CA 93117, United States of AmericaApplied Mathematics and Computational Research Division, Lawerence Berkeley National Laboratory , Berkeley, CA 94720, United States of AmericaDepartment of Chemistry and Biochemistry, University of California , Santa Barbara, Santa Barbara, CA 93117, United States of America; Department of Materials, University of California , Santa Barbara, Santa Barbara, CA 93117, United States of AmericaUnderstanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green’s function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff–Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on recurrent neural networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green’s functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green’s functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$ where N _t is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.https://doi.org/10.1088/2632-2153/ada99doperator-learningnonequilibrium quantum many-body theorynonlinear integro-differential equationdynamics reduction |
| spellingShingle | Yuanran Zhu Jia Yin Cian C Reeves Chao Yang Vojtěch Vlček Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning Machine Learning: Science and Technology operator-learning nonequilibrium quantum many-body theory nonlinear integro-differential equation dynamics reduction |
| title | Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning |
| title_full | Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning |
| title_fullStr | Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning |
| title_full_unstemmed | Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning |
| title_short | Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning |
| title_sort | predicting nonequilibrium green s function dynamics and photoemission spectra via nonlinear integral operator learning |
| topic | operator-learning nonequilibrium quantum many-body theory nonlinear integro-differential equation dynamics reduction |
| url | https://doi.org/10.1088/2632-2153/ada99d |
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