Timeline for In fiber bundle picture of Berry connection, what is the vertical basis if the horizontal basis is the underlying parameter space?
Current License: CC BY-SA 4.0
8 events
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| Dec 16, 2020 at 18:56 | comment | added | TribalChief | @b-mera, I just posted another question on this, if you have the time to have a look: physics.stackexchange.com/q/601077/110719 . Thanks! | |
| Nov 26, 2020 at 23:48 | comment | added | TribalChief | @B-Mera, thanks for clarifying. | |
| Nov 26, 2020 at 11:44 | comment | added | B. Mera | You are welcome! Yes, it is the dynamical phase. I've considered this special case to illustrate the point. This is the kind of situation you expect when topology is not relevant and the dominant contribution comes from the energy of the configuration. | |
| Nov 26, 2020 at 4:34 | comment | added | TribalChief | @B-Mera, Thanks, it somewhat makes sense, but I am still a bit confused. Is the phase in your comment essentially the dynamical phase (phase due to E)? Or is it separate from that? | |
| Nov 25, 2020 at 23:07 | comment | added | B. Mera | You can have a curve which is purely vertical, but that essentially is something that doesn't change the state as I said before. Something like this occurs when you take a Hamiltonian depending on some parameters, say $x\in M$ where $M$ is some smooth manifold, but, for some reason, one eigenstate is $x$ independent but it's energy is $x$ dependent. Then, the adiabatic theorem would give you an evolution of the form $|\psi(t)\rangle =e^{-i\int_{0}^t E_0(x(s))ds} |\psi_0\rangle$, where $|\psi_0\rangle$, independent of $x$, satisfies $H(x)|\psi_0\rangle=E_0(x)|\psi_0\rangle$, for $x\in M$. | |
| Nov 25, 2020 at 21:43 | comment | added | TribalChief | Thanks for the answer. However, now I wonder, what would it mean in the fiber bundle picture if the final result was somehow $\langle m | \partial_\theta m\rangle$ and not $\langle m | \partial_X m\rangle$? That is, only the quantity in the vertical direction survives. Does this mean that it is some form of gauge-dependent velocity/transport? Or can it depend on base manifold coordinates as well (because the covariant derivative depends on the base manifold too)? I know there won't be parallel transport in this case, but I am making sure I understand correctly. | |
| Nov 25, 2020 at 21:05 | vote | accept | TribalChief | ||
| Nov 25, 2020 at 20:42 | history | answered | B. Mera | CC BY-SA 4.0 |