Sergio Blanes 
WPI, OMP 1, Seminar Room 08.135 
Mon, 26. Feb 24, 10:00 
Splitting methods with complex coefficients for the numerical integration of quantum systems 
The evolution of most quantum systems is modeled by differential
equation in the complex space. However, in general, the equations are
numerically solved using integrators with real coefficients. To
consider complex coefficients usually does not make the schemes
computationally more costly and can provide more accurate results. In
this talk, we explore the applicability of splitting methods involving
complex coefficients to solve numerically the timedependent
SchrÃ¶dinger equation. There are pros (high accuracy and not to
increase the cost) and cons (instability and loose of qualitative
properties) when using complex coefficients. However, there is a class
of methods with complex coefficients with a particular symmetry that
keep most pros while avoid most cons. This class of integrators are
stable and are conjugate to unitary methods for sufficiently small
step sizes. These are promising methods that we will explore: we build
new methods and we analyse their performance on several examples.
This is joint work with Joakim Bernier, Fernando Casas and Alejandro
Escorihuela. 
 Thematic program: Quantum Mechanics (2023/2024)
 Event: Workshop on "Complex operator splitting methods for GinzburgLandau equations and related problems" (2024)
