Time Dependent Floquet Theory and Absence of an Adiabatic Limit

Details Time Dependent Floquet Theory and Absence of an Adiabatic Limit Time Dependent Floquet Theory and Absence of an Adiabatic Limit

1997-06-17

arxiv.org/abs/cond-mat/9706182v1

Phys. Rev. A 56, 4045 (1997)

Physics

Condensed Matter

13 pages, Latex, plus 2 Postscript figures

Scientific paper

10.1103/PhysRevA.56.4045

Quantum systems subject to time periodic fields of finite amplitude, lambda, have conventionally been handled either by low order perturbation theory, for lambda not too large, or by exact diagonalization within a finite basis of N states. An adiabatic limit, as lambda is switched on arbitrarily slowly, has been assumed. But the validity of these procedures seems questionable in view of the fact that, as N goes to infinity, the quasienergy spectrum becomes dense, and numerical calculations show an increasing number of weakly avoided crossings (related in perturbation theory to high order resonances). This paper deals with the highly non-trivial behavior of the solutions in this limit. The Floquet states, and the associated quasienergies, become highly irregular functions of the amplitude, lambda. The mathematical radii of convergence of perturbation theory in lambda approach zero. There is no adiabatic limit of the wave functions when lambda is turned on arbitrarily slowly. However, the quasienergy becomes independent of time in this limit. We introduce a modification of the adiabatic theorem. We explain why, in spite of the pervasive pathologies of the Floquet states in the limit N goes to infinity, the conventional approaches are appropriate in almost all physically interesting situations.

Affiliated with

Also associated with

No associations

Rating

Time Dependent Floquet Theory and Absence of an Adiabatic Limit does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Time Dependent Floquet Theory and Absence of an Adiabatic Limit, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Time Dependent Floquet Theory and Absence of an Adiabatic Limit will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-516707