In the 1D case, the forward and backward journey in a closed path has to happen along the same path. So, whatever changed between states A to B, gets cancelled for the path from B to A. But in any higher dimensional system, we have the option to get back to the initial state without traversing the same route back. Consequently, we have the possibility of a non-zero geometric phase in a closed loop. It was nice to understand the above. :D
berry phase difference depends on the magnetic flux, but the cross-sectional area of the solenoid (through which the magnetic field is finite) is much smaller than the area spanned by the path we move the box along. do we use the solenoid area for the magnetic flux? what happens if we change the size and shape of the close path? what if the box made multiple revolutions?
We see that there is an analog between geometric phase and vector potential. In the aharonov-bohm examples, they are equal. are there experiments where we don't use magnetic flux/vector potential, but still see a phase difference? what kinds of parameters can R(t) take?
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Very well done! In fact this and the previous video were better than many others on the same topic. I appreciate it!
Thanks
one of the most clear lectures i've seen on the topic
Thank you
In the 1D case, the forward and backward journey in a closed path has to happen along the same path. So, whatever changed between states A to B, gets cancelled for the path from B to A. But in any higher dimensional system, we have the option to get back to the initial state without traversing the same route back. Consequently, we have the possibility of a non-zero geometric phase in a closed loop.
It was nice to understand the above. :D
Thanks for watching!
Really intuitive... thank you!
happy you found it useful.
Great video Sir.
Thank you, I am glad you enjoyed it.
berry phase difference depends on the magnetic flux, but the cross-sectional area of the solenoid (through which the magnetic field is finite) is much smaller than the area spanned by the path we move the box along. do we use the solenoid area for the magnetic flux? what happens if we change the size and shape of the close path? what if the box made multiple revolutions?
Multiple revolutions add more phase, however the exact path is unimportant. It is the fact that you go around the entire enclosed flux that counts.
Personal timestamps for note taking
1:39 5:00
Great lecture,very clear.
Many thanks!
Excuse me, at 1:58, shouldn't it be phi_n (0) at the very end of Phi(t)???
We see that there is an analog between geometric phase and vector potential. In the aharonov-bohm examples, they are equal. are there experiments where we don't use magnetic flux/vector potential, but still see a phase difference? what kinds of parameters can R(t) take?
Frankly, I have not thought about it too much, sorry.
Very Nice lecture
Thanks for liking
Griffith book ???????
Yes, indeed