Find in Library

When two operators <i>A</i> and <i>B</i> do not commute, the calculation of the exponential operator <inline-formula> <math display="inline"> <semantics> <msup> <mi mathvariant="normal">e</mi> <mrow> <mi>A</mi> <mo>+</mo> <mi>B</mi> </mrow> </msup> </semantics> </math> </inline-formula> is a difficult and crucial problem. The applications are vast and diversified: to name but a few examples, quantum evolutions, product formulas, quantum control, Zeno effect. The latter are of great interest in quantum applications and quantum technologies. We present here a historical survey of results and techniques, and discuss differences and similarities. We also highlight the link with the strong coupling regime, via the adiabatic theorem, and contend that the &#8220;pulsed&#8221; and &#8220;continuous&#8221; formulations differ only in the order by which two limits are taken, and are but two faces of the same coin.