Schedule Aug 24, 2006
Analysis and Optimal Control of Electron Dynamics
Prof. Hardy Gross, Freie Univ, ITP & KITP

Two topics will be covered in this lecture: (i) The visualization and analysis of electronic motion by means of the so-called electron localization function (ELF), and (ii) optimal control theory of electronic dynamics. The ELF provides a way to visualize chemical bonds. It is derived from the conditional probability of finding an electron in the vicinity of a point r if one knows with certainty that there is another electron with the same spin at r. The shape of the ELF (as function of r) allows a topological classification of the different types of chemical bonds [1]. Here we generalize the ELF to the time-dependent case [2]. Two movies of the time-dependent ELF will be presented, one that shows the formation and breaking of chemical bonds in a proton-ethylene scattering process and another one that visualizes a laser-induced π-π* transition in acetylene in a time-resolved fashion.

In the context of optimal control we first present two generalizations of the standard formulation [3] of optimal-control theory: The first generalization [4] allows the calculation of optimized pulses with

Gross.jpg

frequency constraints. The second generalization [5] achieves the optimization of time-dependent control targets. The latter allows one to drag the density of the system along a given trajectory, as shown in the figure above. Finally, some aspects of marrying optimal control theory with time-dependent density functional theory will be discussed.


[1] A. Savin et al, Angew. Chem. 36, 1808 (1997).
[2] T. Burnus, M.A.L. Marques, E.K.U. Gross, Phys. Rev. A (Rapid Comm.) 71, 010501 (2005).
[3] W. Zhu, J. Botina, H. Rabitz, J. Chem. Phys. 108, 1953 (1998).
[4] J. Werschnik, E.K.U.Gross, J. Opt. B 7, S300 (2005).
[5] I Serban, J. Werschnik, E.K.U.Gross Phys. Rev. A 71, 053810 (2005).

Other video options

To begin viewing slides, click on the first slide below. (Or, view as pdf.)


[01] [02] [03] [04] [05] [06] [07] [08] [09] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69]

Author entry (protected)