Will anyone help me to find out the analytic expression(adsbygoogle = window.adsbygoogle || []).push({});

of the following [tex]2^N\times2^N[/tex] exponential?

[tex]exp[t(X\otimes X\otimes I\ldots\otimes I+I\otimes X\otimes X\otimes I\ldots\otimes I+\ldots+I\otimes I\otimes\ldots I \otimes X \otimes X+X\otimes I\ldots I\otimes X)][/tex],

where

[tex]

I= \left[\begin{array}{cc}

1 & 0 \\

0 & 1 \end{array}\right] [/tex]

and

[tex]

X=\left[\begin{array}{cc}

0 & 1 \\

1 & 0 \end{array}\right]

[/tex].

[Note that the parenthesis in the `exponential' contains sum of N+1 terms each of which is a tensor product of 2 Xs and (N-2) of Is in some order.]

I've evaluated (via Mathematica) for N=3,4,5,6. But I need an analytic expression for it.

Thanks and Regards.

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# Exponential of a Matrix

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