A COKOSNUT code for the control of the time-dependent Kohn-Sham model. (English) Zbl 1376.93047

Summary: Optimal control of multi-electron systems is considered in the framework of the time-dependent density functional theory. For this purpose, the MATLAB package COKOSNUT is presented that aims at solving optimal quantum control problems governed by the Kohn-Sham equation. This package includes a robust globalized nonlinear conjugate gradient scheme and an efficient splitting procedure for the numerical integration of the nonlinear Kohn-Sham equations in two dimensions. Results of numerical experiments demonstrate the ability of the COKOSNUT code in computing accurate optimal controls.


93C20 Control/observation systems governed by partial differential equations
49N90 Applications of optimal control and differential games
81V70 Many-body theory; quantum Hall effect


Full Text: DOI


[1] Marques, M. A.L.; Oliveira, M. J.T.; Burnus, T., Comput. Phys. Commun., 183, 10, 2272-2281, (2012)
[2] Hohenberg, P.; Kohn, W., Phys. Rev., 136, B864-B871, (1964)
[3] Runge, E.; Gross, E. K.U., Phys. Rev. Lett., 52, 997-1000, (1984)
[4] Kohn, W.; Sham, L. J., Phys. Rev., 140, A1133-A1138, (1965)
[5] Marques, M. A.L.; Ullrich, C. A.; Nogueira, F.; Rubio, A.; Burke, K.; Gross, E. K.U., Time-dependent density functional theory, (Lecture Notes in Physics, vol. 706, (2006), Springer-Verlag, Berlin Heidelberg) · Zbl 1110.81002
[6] Jerome, J. W., J. Math. Anal. Appl., 429, 2, 995-1006, (2015)
[7] Ruggenthaler, M.; Penz, M.; van Leeuwen, R., J. Phys.: Condens. Matter., 27, 20, 203202, (2015)
[8] M. Sprengel, G. Ciaramella, A. Borzí, A theoretical investigation of time-dependent Kohn-Sham equations. arXiv:1701.02124 · Zbl 1365.35132
[9] Castro, A., ChemPhysChem, 14, 1488-1495, (2013)
[10] Castro, A.; Werschnik, J.; Gross, E. K.U., Phys. Rev. Lett., 109, 153-603, (2012)
[11] Werschnik, J., Quantum Optimal Control Theory: Filter Techniques, Time-Dependent Targets, and Time-Dependent Density-Functional Theory, (2006), Freie Universitt Berlin, (Ph.D. thesis)
[12] M. Sprengel, G. Ciaramella, A. Borzí, Investigation of optimal control problems governed by a time-dependent Kohn-Sham model. arXiv:1701.02679 · Zbl 1365.35132
[13] Castro, A.; Appel, H.; Oliveira, M.; Rozzi, C. A.; Andrade, X.; Lorenzen, F.; Marques, M. A.L.; Gross, E. K.U.; Rubio, A., Phys. Status Solidi b, 243, 11, 2465-2488, (2006)
[14] Constantin, L. A., Phys. Rev. B, 78, 155106, (2008)
[15] Parr, R. G.; Yang, W., Density-functional theory of atoms and molecules, (1989), Oxford University Press, Oxford
[16] Engel, E.; Dreizler, R. M., Density functional theory, an advanced course, (2011), Springer Heidelberg · Zbl 1216.81004
[17] Borzí, A., Nanoscale Syst. Math. Model. Theory Appl., 1, 93, (2012)
[18] Borzí, A.; Schulz, V., Computational optimization of systems governed by partial differential equations, (2012), Society for Industrial and Applied Mathematics, Philadelphia, USA · Zbl 1240.90001
[19] Tröltzsch, F., Optimal control of partial differential equations, (2010), American Mathematical Society, Providence, Rhode Island
[20] von Winckel, G.; Borzí, A., Inverse Probl., 24, 3, 034007, 23, (2008)
[21] von Winckel, G.; Borzì, A., Comput. Phys. Commun., 181, 12, 2158-2163, (2010)
[22] von Winckel, G.; Borzí, A.; Volkwein, S., SIAM J. Sci. Comput., 31, 6, 4176-4203, (2010)
[23] Ciaramella, G.; Borzí, A., Comput. Phys. Commun., 200, 312-323, (2016)
[24] Hager, W.; Zhang, H., SIAM J. Optim., 16, 1, 170-192, (2005)
[25] Faou, E.; Ostermann, A.; Schratz, K., IMA J. Numer. Anal., 35, 1, 161-178, (2015)
[26] Bao, W.; Jin, S.; Markowich, P. A., J. Comput. Phys., 175, 2, 487-524, (2002)
[27] Castro, A.; Räsänen, E.; Rozzi, C. A., Phys. Rev. B, 80, 033102, (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.