Thinking in terms of the quantum adiabatic theorem (QAT), maybe it's possible to do this under some restriction on the eigenvalues of the matrix A(t).
Anyway it's known that the solutions, i.e. the elements of the matrix \Phi, are bounded in time if the eigenvalues of A(t) are always imaginary...
Hello everybody,
I'm trying to understand if is possible to say something about the Floquet exponents, in the limit of a very slow changing on time. I try to explain. Given the differential equation
$$
\dot{\vec{v}}(t) = A(t) \vec{v}(t)
$$
with
$$
A(t+T)=A(t)
$$
a monodromy matrix is given...
ok I solve it. I have calculated analytically the inner product and I see that it is zero. In fact, I had made a mistake in the numerical calculation.
Hi you all. I have to diagonalize a hermitian operator (hamiltonian), that has both discrete and continuous spectrum. If ψ is an eigenvector with eigenvalue in the continuous spectrum, and χ is an eigenvector with eigenvalue in the discrete spectrum, is correct to say that ψ and χ are always...
reading some articles I had confused ideas... rightly a quantumdot can be approximated with a two-states system in case it is in resonance with an electromagnetic field. hence the oscillations of rabi.
sorry for the question that I did in a moment of panic ;) thanks for the reply.
summarizing, I find from invariance of e.m. Lagrangian , with the help of Noether th, that the e.m. field has an intrinsic angular momentum. Quantizing in Coulomb gauge, I express this spin of e.m. field as
\vec{S} = \int d^{3}k i \vec{k}/k (a^{+}_{2}(\vec{k})...
sorry, I make an error, the \vec{k} comes from \vec{\epsilon}_{1}(\vec{k}) \times \vec{\epsilon}_{2}(\vec{k}) , so it is a versor! So I must write \vec{k}/k in place of \vec{k}...
andrien maybe you are my salvation! I don't have the book, can you get a little more detail? thanks to all
hi guys, I'm very stubborn so I quantized the spin
in gauge of coulomb with A^{0}=0 , and , after some calculations and observations on the polarization vectors , I find
\vec{S} = \int d^{3}k i \vec{k} (a^{+}_{2}(\vec{k}) a_{1}(\vec{k})-a^{+}_{1}(\vec{k}) a_{2}(\vec{k})) = \int...
hi, I try to use the Noether theorem to determinate the angular momentum of the electromagnetic field described by the Lagrangian density
L=-FαβFαβ/4
After some calculation I find a charge Jαβ that is the angular momentum tensor. So the generator of rotations are
(J^{23},J^{31},J^{12}) =...
yes, what you say is correct, in fact, the bare interaction Lagrangian density will not have to depend on the parameter μ (in the limit D=4) ... so if we express the lagrangian in terms of physical quantity (renormalizated charge, mass , ... ) then these physical parameters must transform...
... I think it's more correct to say that they are connected to form factors, in fact, using the identity of gordon we find that only a part of the finite term \Lambda(2)μ contributes to the form factor F2 , and so to the magnetic moment of the electron... anyway thanks to all for your answers, bye
ok now I understand. I calculate Λ(1)μ : the finite term in it is proportional to the matrix γμ, so it doesn't give any contribution to the magentic moment of the electron ( it contributes only to the form factor F1 )
certain that the ryder could write instead of "finite" in the expression...
thanks . however the \Lambdaμ is the vertex correction... when the ryder regularize it, whit the dimensional method, he writes it as the sum of two terms: \Lambda(2)μ that is convergent, and \Lambda(1)μ that contains the divergent term plus a finite term. Then he calculates the quantity...