Population of the initial density matrix

[DocMaly]

Is there a defined variable in SpinEvolution for the temperature to
control the initial population of the density matrix?

Thorsten

[Mikhail Veshtort]

Hi Thorsten,

There is no such variable. The program is assuming the high
temperature approximation for the density matrix and does not keep the
unit operator term in the matrix. In this situation, the inverse
temperature is just a constant proportionality factor in front of the
(remaining) density matrix, so this factor is also thrown away. Eq. 38
of the SpinEvolution JMR paper gives the exact form of the assumed
*equilibrium* density matrix. But the equilibrium density matrix is
relevant only if you are using T1 relaxation in the simulation. The
*initial* density is given explicitly by the user and may include any
factors you want. So why a variable to control the population and what
exactly would it do?

Mikhail

[DocMaly]

The reason why I'm asking is, for a spin 1 system such as 2H one would
expect different amplitudes for the transitions -1 ---> 0 and 0 --->
+1. Especially if you got to very low temperatures. Therefore I was
wondering if SpinEvolution can account for that.

Thorsten

[Mikhail Veshtort]

I never thought about it. Do you mean that under certain
circumstances, the quadrupolar term has to be accounted for in the
computation of the equilibrium density matrix (so that the matrix is
longer proportional to Iz)?
At this point, there is no way to automatically generate such a
matrix. But you still can do this manually. You just need to figure
out the correct expression for your initial density matrix that
includes the quadrupolar term, and specify it in the input file as
usual (at the rho0 line). You would have to use the bra-ket notation
for this though, because I did not implement any matrix algebra in the
interpreter of the rho0 expression (so, for example, I1z^2 will not be
understood by the program).

[DocMaly]

Yes, that's what I meant. If you calculate the initial population for
a spin 1 at lets say 5 mK, the spin is highly polarized. Now, I don't
know how many NMR experiments are performed at 5 mK, but if you think
about the spin-temperature this high degree of polarization can easily
be generated for example by DNP. Hence the question. However, I will
try to use a manually generated input matrix.
Thanks, Thorsten

[DocMaly]

Can I first calculate the initial density matrix in the variable
section and store it in a variable to use it as the input for rho0 ?

[Mikhail Veshtort]

I am afraid, no. The initial density matrix has to be given explicitly
(by a a symbolic expression) either the rho0 line, or in a separate
file referenced from the rho0 line. It may be helpful if have the
program print the Hamiltonian and the initial density matrix to the
terminal (see the -dump options) to make sure that you have set up
everything correctly.