1 - Sociedade Brasileira de Física

particle states are quasi-periodic (as 4n Bloch's or
Floquet's theorem)
-10 -
- la(t + r)> e a lo(t)>
Call 0 a = A a r ; A a is a quasi-energy.
We have to look for the,kind of periodic solution which
agrees with the kind of collective motion wears interested
in. It turns out that there Joe continuous ran of energy,
with w(W), where W is the expectation of H for TCHF solutia,
which is time-independent. Fig. 1 shows an example of
the function w(W) for a Lipkin model.
1.2
3 .4
wpm mooa
L0.11
w
w(W)
The reference state in quasi-periodic
-18
l'o (t T) ' e ° I .o (t)>
= - A T
o A t%
A o
A A
(A: occupied state)
The periodic part of the'states can be defined:
. .
t
le(t)› = e a W(t)'
p
/00(t) › e 1.0(t)›
aP andd
o
are periodic
20
0