5 papers
Time-Dependent Logarithmic Perturbation Theory for Quantum Dynamics: Formulation and Applications
Juan Carlos del Valle, Paul Bergold, Karolina Kropielnicka
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schrödinger equation, in which the logarithm of the w…
Fourth-order compact exponential splittings for unbounded operators
Juan Carlos Del Valle, Arieh Iserles, Karolina Kropielnicka
We present a derivation and error bound for the family of fourth order splittings, originally introduced by Chin and Chen, where one of the operators is unbounded and the second on…
Correlations and signaling in the Schrödinger-Newton model
Jacek Aleksander Gruca, Ankit Kumar, Ray Ganardi +3
The Schrödinger--Newton model is a semi-classical theory in which, in addition to mutual attraction, massive quantum particles interact with their own gravitational fields. While…
Computation of some dispersive equations through their iterated linearisation
Guannan Chen, Arieh Iserles, Karolina Kropielnicka +1
It is often the case that, while the numerical solution of the non-linear dispersive equation represents a formidable challenge,…
Second-order exponential splittings in the presence of unbounded and time-dependent operators: construction and convergence
Karolina Kropielnicka, Juan Carlos del Valle
For linear differential equations of the form , , with a possibly unbounded operator , we construct and deduce error bounds for two families of se…