Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum Baths
This paper reviews methods that aim at simulating nuclear quantum effects (NQEs) using generalized thermal baths. Generalized (or quantum) baths simulate statistical quantum features, and in particular zero-point energy effects, through non-Markovian stochastic dynamics. They make use of generalized...
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MDPI AG
2022-05-01
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| Online Access: | https://www.mdpi.com/2076-3417/12/9/4756 |
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| author | Simon Huppert Thomas Plé Sara Bonella Philippe Depondt Fabio Finocchi |
| author_facet | Simon Huppert Thomas Plé Sara Bonella Philippe Depondt Fabio Finocchi |
| author_sort | Simon Huppert |
| collection | DOAJ |
| description | This paper reviews methods that aim at simulating nuclear quantum effects (NQEs) using generalized thermal baths. Generalized (or quantum) baths simulate statistical quantum features, and in particular zero-point energy effects, through non-Markovian stochastic dynamics. They make use of generalized Langevin Equations (GLEs), in which the quantum Bose–Einstein energy distribution is enforced by tuning the random and friction forces, while the system degrees of freedom remain classical. Although these baths have been formally justified only for harmonic oscillators, they perform well for several systems, while keeping the cost of the simulations comparable to the classical ones. We review the formal properties and main characteristics of classical and quantum GLEs, in relation with the fluctuation–dissipation theorems. Then, we describe the quantum thermostat and quantum thermal bath, the two generalized baths currently most used, providing several examples of applications for condensed matter systems, including the calculation of vibrational spectra. The most important drawback of these methods, zero-point energy leakage, is discussed in detail with the help of model systems, and a recently proposed scheme to monitor and mitigate or eliminate it—the adaptive quantum thermal bath—is summarised. This approach considerably extends the domain of application of generalized baths, leading, for instance, to the successful simulation of liquid water, where a subtle interplay of NQEs is at play. The paper concludes by overviewing further development opportunities and open challenges of generalized baths. |
| first_indexed | 2024-03-10T04:18:37Z |
| format | Article |
| id | doaj.art-0f74304464e949e497997c45709028e8 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T04:18:37Z |
| publishDate | 2022-05-01 |
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| spelling | doaj.art-0f74304464e949e497997c45709028e82023-11-23T07:53:27ZengMDPI AGApplied Sciences2076-34172022-05-01129475610.3390/app12094756Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum BathsSimon Huppert0Thomas Plé1Sara Bonella2Philippe Depondt3Fabio Finocchi4Institut des Nanosciences de Paris (INSP), CNRS UMR 7588, Sorbonne Université, 4 Place Jussieu, 75005 Paris, FranceInstitut des Nanosciences de Paris (INSP), CNRS UMR 7588, Sorbonne Université, 4 Place Jussieu, 75005 Paris, FranceCentre Européen de Calcul Atomique et Moléculaire (CECAM), Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, SwitzerlandInstitut des Nanosciences de Paris (INSP), CNRS UMR 7588, Sorbonne Université, 4 Place Jussieu, 75005 Paris, FranceInstitut des Nanosciences de Paris (INSP), CNRS UMR 7588, Sorbonne Université, 4 Place Jussieu, 75005 Paris, FranceThis paper reviews methods that aim at simulating nuclear quantum effects (NQEs) using generalized thermal baths. Generalized (or quantum) baths simulate statistical quantum features, and in particular zero-point energy effects, through non-Markovian stochastic dynamics. They make use of generalized Langevin Equations (GLEs), in which the quantum Bose–Einstein energy distribution is enforced by tuning the random and friction forces, while the system degrees of freedom remain classical. Although these baths have been formally justified only for harmonic oscillators, they perform well for several systems, while keeping the cost of the simulations comparable to the classical ones. We review the formal properties and main characteristics of classical and quantum GLEs, in relation with the fluctuation–dissipation theorems. Then, we describe the quantum thermostat and quantum thermal bath, the two generalized baths currently most used, providing several examples of applications for condensed matter systems, including the calculation of vibrational spectra. The most important drawback of these methods, zero-point energy leakage, is discussed in detail with the help of model systems, and a recently proposed scheme to monitor and mitigate or eliminate it—the adaptive quantum thermal bath—is summarised. This approach considerably extends the domain of application of generalized baths, leading, for instance, to the successful simulation of liquid water, where a subtle interplay of NQEs is at play. The paper concludes by overviewing further development opportunities and open challenges of generalized baths.https://www.mdpi.com/2076-3417/12/9/4756generalized Langevin equationnuclear quantum effectsquasi-classical simulationsfluctuation–dissipation theorem |
| spellingShingle | Simon Huppert Thomas Plé Sara Bonella Philippe Depondt Fabio Finocchi Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum Baths Applied Sciences generalized Langevin equation nuclear quantum effects quasi-classical simulations fluctuation–dissipation theorem |
| title | Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum Baths |
| title_full | Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum Baths |
| title_fullStr | Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum Baths |
| title_full_unstemmed | Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum Baths |
| title_short | Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum Baths |
| title_sort | simulation of nuclear quantum effects in condensed matter systems via quantum baths |
| topic | generalized Langevin equation nuclear quantum effects quasi-classical simulations fluctuation–dissipation theorem |
| url | https://www.mdpi.com/2076-3417/12/9/4756 |
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