@article{SchuergerEngel2023,
  author    = {Sch{\"u}rger, Peter and Engel, Volker},
  title     = {On the relation between nodal structures in quantum wave functions and particle correlation},
  series = {AIP Advances},
  volume    = {13},
  journal   = {AIP Advances},
  number    = {12},
  doi       = {10.1063/5.0180004},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-350361},
  year      = {2023},
  abstract  = {We study the influence of nodal structures in two-dimensional quantum mechanical densities on wave packet entanglement. This is motivated by our recent study [Entropy, 25, 970 (2023)], which showed that the mutual information derived from the momentum-space probability density of a coupled two-particle system exhibits an unusual time dependence, which is not encountered if the position-space density is employed in the calculation. In studying a model density, here, we identify cases where the mutual information increases with the number of nodes in the wave function and approaches a finite value, whereas in this limit, the linear correlation vanishes. The results of the analytical model are then applied to interpret the correlation measures for coupled electron-nuclear dynamics, which are treated by numerically solving the time-dependent Schr{\"o}dinger equation.},
  language  = {en}
}
@phdthesis{Schuerger2024,
  author    = {Sch{\"u}rger, Peter},
  title     = {Information-Theoretical Studies on Time-Dependent Quantum Systems},
  doi       = {10.25972/OPUS-35221},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-352215},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2024},
  abstract  = {In this thesis, we apply the information-theoretic approach in the context of quantum dynamics and wave packet motion: Information-theoretic measures are calculated from position and momentum densities, which are obtained from time-dependent quantum wave functions. The aim of this thesis is to benchmark, analyze and interpret these quantities and relate their features to the wave packet dynamics. Firstly, this is done for the harmonic oscillator (HO) with and without static disorder. In the unperturbed HO, the analytical study of coherent and squeezed states reveals time-dependent entropy expressions related to the localization of the wave function. In the disordered HO, entropies from classical and quantum dynamics are compared for short and long times. In the quantum case, imprints of wave packet revivals are found in the entropy. Then, the energy dependence of the entropy for very long times is discussed. Secondly, this is donefor correlated electron-nuclear motion. Here, entropies derived from the total, electronic and nuclear density, respectively, are calculated in position and momentum space for weak and strong adiabatic electronic coupling. The correlation between electron and nucleus is investigated using different correlation measures, where some of these functions are sensitive to the nodal structure of the wave function. An analytic ansatz to interpret the information-theoretical quantities is applied as well.},
  subject      = {St{\"o}rungstheorie},
  language  = {en}
}
@article{SchuergerEngel2023,
  author    = {Sch{\"u}rger, Peter and Engel, Volker},
  title     = {Differential Shannon entropies characterizing electron-nuclear dynamics and correlation: momentum-space versus coordinate-space wave packet motion},
  series = {Entropy},
  volume    = {25},
  journal   = {Entropy},
  number    = {7},
  issn      = {1099-4300},
  doi       = {10.3390/e25070970},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-362670},
  year      = {2023},
  abstract  = {We calculate differential Shannon entropies derived from time-dependent coordinate-space and momentum-space probability densities. This is performed for a prototype system of a coupled electron-nuclear motion. Two situations are considered, where one is a Born-Oppenheimer adiabatic dynamics, and the other is a diabatic motion involving strong non-adiabatic transitions. The information about coordinate- and momentum-space dynamics derived from the total and single-particle entropies is discussed and interpreted with the help of analytical models. From the entropies, we derive mutual information, which is a measure for the electron-nuclear correlation. In the adiabatic case, it is found that such correlations are manifested differently in coordinate- and momentum space. For the diabatic dynamics, we show that it is possible to decompose the entropies into state-specific contributions.},
  language  = {en}
}