I have a Hamiltonian which is time dependent but possesses periodic symmetry: $H(t+t_0)=H(t)$. Is there any clever techniques to exploit this? Edit: In particular, I would like a practical method to simulate the dynamics of such a system (as opposed to naive time-slicing).
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asked Jan 25, 2012 at 17:25
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1$\begingroup$ Do you want dynamics or average ground state? $\endgroup$– Joe FitzsimonsCommented Jan 25, 2012 at 19:04
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$\begingroup$ @JoeFitzsimons -- good question. This was an example question I used at a StackExchange participation drive, so I unfortunately didn't give it much thought. I will make it clearer now. $\endgroup$– Chris FerrieCommented Jan 26, 2012 at 0:36
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1$\begingroup$ qols.ph.ic.ac.uk/~sbuhmann/docs/lectures/AnalyticalMethods3.pdf Barring some typos, a lucid introduction. $\endgroup$– user34530Commented Nov 23, 2013 at 12:02
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I would suggest looking at the formalism of Floquet space. The basic idea is that one uses a time-independent but infinite dimensional Hamiltonian to simulate evolution under a time-dependent but finite dimensional Hamiltonian by using a new index to label terms in a Fourier series.
A good, short introduction can be found in Levante et al. For more details, Leskes et al provides a very through review. Finally, a simple example of an application of Floquet theory is given by Bain and Dumont.
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$\begingroup$ Chris, can you add some comments about truncating the series in order to implement this method? $\endgroup$ Commented Jan 26, 2012 at 0:40
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1$\begingroup$ @ChrisFerrie Another paper about Floquet theory: Shirley JH. Solutions of the Schrodinger equation with a Hamiltonian periodic in time. Phys Rev 1965; 138:B979-B987. $\endgroup$– user6048Commented Apr 2, 2013 at 22:51