Welcome to the controllability calculator
This web pages implement a controllability calculator for bilinear quantum systems, as described in the paper V.Ramakrishna & al. "Controllability of molecular systems", Phys. Rev. A 51 (2) 1995, pp960-966. Please look at that paper for details. You can also take a look at my Ph.D. thesis and HDR here.
The calculator can be found on the next page. You can input your given system and output the result of the computation. The computation is done online on this server. For this reason the dimension of the systems that can be thus tested is limited to 10. An unrestricted version of the code (C++) can be obtained free of charge from the author. Write me at Gabriel.Turinici_AT_dauphine.fr .
Technical notes on input can be found on the next page. Please note that the result of computation should be interpreted as follows:
- if the result is "YES", then the system is controllable;
- ifnot, the system do not comply with the criterion mentionned above. However, as this "criterion" gives only sufficient conditions, the system may still be controllable. One remarkable case of when this may happen is when studying the controllability of a set of independent quantum systems. Please write directly to me Gabriel.Turinici_AT_dauphine.fr as in this case theoretical and numerical results are also available (cf. B. Li, G. Turinici, V. Ramakhrishna, and H. Rabitz. "Optimal dynamic discrimination of similar molecules through quantum learning control." Journal of Physical Chemistry B, 106(33):8125--8131, 2002.).
And now, go to the next page.
(c) Copyright Gabriel Turinici, 2001-2005. All rights reserved. Notice: This page is work in progress intended to be released with public academic licence. As a developpement version, its content may NOT be copied or distributed in any way without prior permission of the author(s) and of ALL other copyright owners.