Numerical approximation of the time-ordered exponential for spin dynamic simulation
| Název práce v češtině: | Numerická aproximace time-ordered exponenciály pro dynamické simulace spinu |
|---|---|
| Název v anglickém jazyce: | Numerical approximation of the time-ordered exponential for spin dynamic simulation |
| Klíčová slova: | Time-ordered exponential|$\star$ - product|Magnus expansion|Geometrical numerical integrators|MAS NMR |
| Klíčová slova anglicky: | Time-ordered exponential|$\star$ - product|Magnus expansion|Geometrical numerical integrators|MAS NMR |
| Akademický rok vypsání: | 2021/2022 |
| Typ práce: | diplomová práce |
| Jazyk práce: | angličtina |
| Ústav: | Katedra numerické matematiky (32-KNM) |
| Vedoucí / školitel: | Stefano Pozza, Dr., Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 30.01.2022 |
| Datum zadání: | 31.01.2022 |
| Datum potvrzení stud. oddělením: | 16.05.2023 |
| Datum a čas obhajoby: | 09.06.2023 09:00 |
| Datum odevzdání elektronické podoby: | 04.05.2023 |
| Datum odevzdání tištěné podoby: | 09.05.2023 |
| Datum proběhlé obhajoby: | 09.06.2023 |
| Oponenti: | Scott Congreve, Ph.D. |
| Zásady pro vypracování |
| The work will require testing and adapting codes for spin dynamics simulation. The project aims to understand which methods reach a good accuracy in the fastest way on the data provided by the Laboratoire de Chimie de la matière condensée de Paris (Sorbonne University). The main programming languages will be Julia and MatLab. The work also requires to do a review of the literature on this topic.
The project offers the possibility to collaborate with the international members of the *-Lanczos (www.starlanczos.cz) and the MAGICA project (https://anr.fr/Project-ANR-20-CE29-0007). |
| Seznam odborné literatury |
| - Bak, M., Rasmussen, J. T., & Nielsen, N. C. (2011). SIMPSON: a general simulation program for solid-state NMR spectroscopy. Journal of magnetic resonance, 213(2), 366-400.
- Blanes, S., Casas, F.: A Concise Introduction to Geometric Numerical Integration. CRC Press, Bocan Raton, FL (2017) - Blanes, S., Casas, F., & Thalhammer, M. (2017). High-order commutator-free quasi-Magnus exponential integrators for non-autonomous linear evolution equations. Computer Physics Communications, 220, 243-262. - Giscard, P. L., & Bonhomme, C. (2020). Dynamics of quantum systems driven by time-varying Hamiltonians: Solution for the Bloch-Siegert Hamiltonian and applications to NMR. Physical Review Research, 2(2), 023081. - Giscard, P. L., & Pozza, S. (2021). Tridiagonalization of systems of coupled linear differential equations with variable coefficients by a Lanczos-like method. Linear Algebra and its Applications, 624, 153-173. - Gomez Pueyo, A., Marques, M. A., Rubio, A., & Castro, A. (2018). Propagators for the time-dependent Kohn–Sham equations: Multistep, Runge–Kutta, exponential Runge–Kutta, and commutator free Magnus methods. Journal of chemical theory and computation, 14(6), 3040-3052. - Gomez Pueyo, A., Blanes, S., & Castro, A. (2020). Propagators for quantum-classical models: Commutator-free Magnus methods. Journal of chemical theory and computation, 16(3), 1420-1430. |
| Předběžná náplň práce |
| Solving systems of linear ordinary differential equations with variable coefficients remains a challenge that can be expressed using the so-called time-ordered exponential (TOE). Many numerical methods for TOE approximation are found in literature based on different approaches such as exponential propagators, Magnus expansion, integration schemes. Recently, new approaches based on the so-called *-products have been tested successfully.
This project aims to test and compare state-of-the-art methods for TOE approximation on problems coming from the simulation of spin dynamics provided by the Laboratoire de Chimie de la matière condensée de Paris, Sorbonne University. If possible, a particular focus will be given to test the *-Lanczos algorithm. |
| Předběžná náplň práce v anglickém jazyce |
| Solving systems of linear ordinary differential equations with variable coefficients remains a challenge that can be expressed using the so-called time-ordered exponential (TOE). Many numerical methods for TOE approximation are found in literature based on different approaches such as exponential propagators, Magnus expansion, integration schemes. Recently, new approaches based on the so-called *-products have been tested successfully.
This project aims to test and compare state-of-the-art methods for TOE approximation on problems coming from the simulation of spin dynamics provided by the Laboratoire de Chimie de la matière condensée de Paris, Sorbonne University. If possible, a particular focus will be given to test the *-Lanczos algorithm. |