Floquet theory - 2024 ACF Regionals @ Ohio State

Question

The eigenvalues of this method’s namesake Hamiltonian are called the “quasi-energies.” For 10 points each:

[10h] Name this method that decomposes the time-evolution operator into the product of the exponential of a “stroboscopic kick operator” and the exponential of a namesake Hamiltonian. This method is used to analyze discrete time crystals.

ANSWER: Floquet theory [or Floquet analysis or Floquet time crystals]

[10e] Floquet theory treats quantum systems whose Hamiltonians have this property with respect to time, due to external driving. Functions with this property repeat at regular intervals.

ANSWER: periodic [or cyclic functions]

[10m] Floquet analysis is analogous to this theorem, which gives the form of solutions to Schrodinger’s equation in spatially periodic potentials. This theorem is used to obtain the electronic band structure of crystals.

ANSWER: Bloch’s theorem

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Summary


2024 ACF Regionals @ Cornell	01/27/2024	Y	1	10.00	100%	0%	0%
2024 ACF Regionals @ JMU	01/27/2024	Y	1	10.00	100%	0%	0%
2024 ACF Regionals @ Minnesota	01/27/2024	Y	1	20.00	100%	100%	0%
2024 ACF Regionals @ Nebraska	01/27/2024	Y	1	10.00	100%	0%	0%
2024 ACF Regionals @ Rutgers	01/27/2024	Y	1	20.00	100%	100%	0%
2024 ACF Regionals @ Imperial	01/27/2024	Y	1	20.00	100%	100%	0%
2024 ACF Regionals @ Vanderbilt	01/27/2024	Y	1	10.00	100%	0%	0%

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