Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation
We propose an algorithm that combines the inchworm method and the frozen Gaussian approximation to simulate the Caldeira-Leggett model in which a quantum particle is coupled with thermal harmonic baths. In particular, we are interested in the real-time dynamics of the reduced density operator. In ou...
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| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-03-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-03-24-1667/pdf/ |
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| author | Geshuo Wang Siyao Yang Zhenning Cai |
| author_facet | Geshuo Wang Siyao Yang Zhenning Cai |
| author_sort | Geshuo Wang |
| collection | DOAJ |
| description | We propose an algorithm that combines the inchworm method and the frozen Gaussian approximation to simulate the Caldeira-Leggett model in which a quantum particle is coupled with thermal harmonic baths. In particular, we are interested in the real-time dynamics of the reduced density operator. In our algorithm, we use frozen Gaussian approximation to approximate the wave function as a wave packet in integral form. The desired reduced density operator is then written as a Dyson series, which is the series expression of path integrals in quantum mechanics of interacting systems. To compute the Dyson series, we further approximate each term in the series using Gaussian wave packets, and then employ the idea of the inchworm method to accelerate the convergence of the series. The inchworm method formulates the series as an integro-differential equation of “full propagators'', and rewrites the infinite series on the right-hand side using these full propagators, so that the number of terms in the sum can be significantly reduced, and faster convergence can be achieved. The performance of our algorithm is verified numerically by various experiments. |
| format | Article |
| id | doaj-art-e27062efd19f4899abba7b00c6f599bb |
| institution | DOAJ |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-e27062efd19f4899abba7b00c6f599bb2025-08-20T02:40:32ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-03-019166710.22331/q-2025-03-24-166710.22331/q-2025-03-24-1667Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian ApproximationGeshuo WangSiyao YangZhenning CaiWe propose an algorithm that combines the inchworm method and the frozen Gaussian approximation to simulate the Caldeira-Leggett model in which a quantum particle is coupled with thermal harmonic baths. In particular, we are interested in the real-time dynamics of the reduced density operator. In our algorithm, we use frozen Gaussian approximation to approximate the wave function as a wave packet in integral form. The desired reduced density operator is then written as a Dyson series, which is the series expression of path integrals in quantum mechanics of interacting systems. To compute the Dyson series, we further approximate each term in the series using Gaussian wave packets, and then employ the idea of the inchworm method to accelerate the convergence of the series. The inchworm method formulates the series as an integro-differential equation of “full propagators'', and rewrites the infinite series on the right-hand side using these full propagators, so that the number of terms in the sum can be significantly reduced, and faster convergence can be achieved. The performance of our algorithm is verified numerically by various experiments.https://quantum-journal.org/papers/q-2025-03-24-1667/pdf/ |
| spellingShingle | Geshuo Wang Siyao Yang Zhenning Cai Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation Quantum |
| title | Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation |
| title_full | Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation |
| title_fullStr | Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation |
| title_full_unstemmed | Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation |
| title_short | Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation |
| title_sort | solving caldeira leggett model by inchworm method with frozen gaussian approximation |
| url | https://quantum-journal.org/papers/q-2025-03-24-1667/pdf/ |
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