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--- advanced_tools:geometric_phase [2018/04/09 08:11]
lushikatome [Concrete]
+++ advanced_tools:geometric_phase [2019/02/09 10:02] (current)
129.13.36.189 [Concrete]
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-====== Berry Phase ======
+====== Geometric Phase ======
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 A famous example is a Foucault pendulum. Such a pendulum is expected to return to its original position after a full rotation of the earth in 24 hrs. However, it doesn’t. It picks up an angle, called Hannay’s angle.
+[{{ :advanced_tools:geometricphase.png?nolink |Source: https://edoc.ub.uni-muenchen.de/17735/1/Atala_Marcos.pdf}}]
 ----
   * A nice laymen explanation of Berry phases is [[https://gravityandlevity.wordpress.com/2015/09/10/guest-post-if-you-walk-in-a-closed-loop-do-you-end-up-where-you-started/|If You Walk in A Closed Loop, Do You End Up Where You Started?]] by Anshul Kogar
-  * https://michaelberryphysics.files.wordpress.com/2013/07/berry178.pdf and
+  * Another great non-technical introduction is "[[https://michaelberryphysics.files.wordpress.com/2013/07/berry178.pdf|The Geometric Phase]]" by Michael Berry.
   * https://courses.cit.cornell.edu/ece5390/7_berry_phase.pdf
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+Before Berry reinterpreted geometric phases it was already known that if the parameters of quantum system change slowly the state of the system stays the same but it picks up a phase. This is known as adiabatic theorem. However, people believed that this phase was of no physical significance since it can have any arbitrary value.
+Berry suggested that the parameters should be varied in such a way that they end up at the values they started with. The phase that a system picks up after performing such a loop in parameter space is now called Berry's phase. This phase that the system picks up after a full cycle is non-arbitrary and has profound physical implications.
+----
   * For a nice introduction, see [[http://inspirehep.net/record/284501/|Quantum Phases And Angles]] by R. Jackiw
-  * For a discussion of Hannays angle, see Section 4.6.3 [[http://www.damtp.cam.ac.uk/user/tong/dynamics/clas.pdf|here]].
+  * A nice textbook that discusses Berry's phase is Griffith "Introduction to Quantum Mechanics", especially chapter 10.
+  * Geometric phases also exist in classical mechanics, like for example Hannay's angle. For a discussion of Hannay's angle, see Section 4.6.3 [[http://www.damtp.cam.ac.uk/user/tong/dynamics/clas.pdf|here]] and also [[http://cmt.nbi.ku.dk/student_projects/bachelor_theses/BachelorThesisMortenIbMunk-Nielsen.pdf|Geometric phases in classical mechanics]] by  Morten Ib Munk-Nielsen
+  * The standard reference is "Geometric Phases in Physics" edited by Alfred Shapere and Frank Wilczek
+  * A great discussion of the Hannay angle can be found in Spivak's Physics for Mathematicians.

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