The most boring quantum quench (looking for a textbook/paper)

[extranjero]

Hi,

usually, when we talk about quantum quench dynamics we assume situation when Hamiltonian of a system has a sudden change from $H_0$ to $H_1$. System was initially in the ground state (or more generally - eigenstate) of $H_0$. The interesting dynamics appears when the commutator $[H_0, H_1]\neq 0$. However, due to the some reasons I am looking for a textbook or a paper where non-interesting case $H_1 = a H_0$ is discussed, where $a$ is a number ($a>1$ for example). If you know such a book, please, give me a reference.

Thanks.

 

[DrClaude]

I don't know if you'll find this specific topic treated in a book, because it appears to be quite trivial, since $H_1$ and $H_0$ differ only by a choice of energy scale. The eigenstates of $H_0$ and $H_1$ are the same, so nothing happens to the state itself, only the time evolution will be affected, and then only by a trivial scaling factor.

 

[extranjero]

I know it, but in the anyway, it will be good to find this quite simple thing literally printed in a book (there is an old debate about this problem with my friend and he ask a proof in a book).

 

[DrClaude]

I know it, but in the anyway, it will be good to find this quite simple thing literally printed in a book (there is an old debate about this problem with my friend and he ask a proof in a book).

I don't see much interest in this. Would I write a textbook on QM, I don't think this would even make an interesting exercise.

May I ask what the debate is about?

 

[extranjero]

I am asking you to include this example into a future book, because some people (not even a student, but scientist who published in PRB) has a big difficulties with this.

You can see the 2 year debates and arguments on this problem here: https://www.researchgate.net/post/Is_my_solution_of_time-dependent_Schrodinger_equation_right

 

[DrClaude]

I am asking you to include this example into a future book, because some people (not even a student, but scientist who published in PRB) has a big difficulties with this.

You can see the 2 year debates and arguments on this problem here: https://www.researchgate.net/post/Is_my_solution_of_time-dependent_Schrodinger_equation_right

I don't think any textbook would help save that debate. One of the "debaters" seems to be stuck on the fact that it is a step function. It is easy to replace with a nicer "turn-on" function that will play essentially the same role.