advanced_tools:geometric_phase
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advanced_tools:geometric_phase [2017/07/03 17:12] jakobadmin created |
advanced_tools:geometric_phase [2019/02/09 10:02] (current) 129.13.36.189 [Concrete] |
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| - | ====== Berry Phase ====== | + | ====== Geometric Phase ====== |
| - | <tabbox Why is it interesting?> | ||
| - | Berry phases are, in some sense, the common origin of all anomaly effects. | ||
| - | This is stated, for example in http://www.sciencedirect.com/science/article/pii/0550321388902556?via%3Dihub | + | <tabbox Intuitive> |
| - | <tabbox Layman> | + | When a system moves once around a close loop, like for example a pendulum once around its suspension, we expect that it returns to exactly the same state that it started in. |
| - | https://michaelberryphysics.files.wordpress.com/2013/07/berry178.pdf and https://courses.cit.cornell.edu/ece5390/7_berry_phase.pdf | + | However, this is not always the case. System can pick up a pick up a phase while moving once around a closed loop. |
| - | + | ||
| - | <tabbox Student> | + | |
| - | For a nice introduction, see [[http://inspirehep.net/record/284501/|Quantum Phases And Angles]] by R. Jackiw | + | 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. |
| - | + | ||
| - | <tabbox Researcher> | + | |
| - | <note tip> | + | [{{ :advanced_tools:geometricphase.png?nolink |Source: https://edoc.ub.uni-muenchen.de/17735/1/Atala_Marcos.pdf}}] |
| - | The motto in this section is: //the higher the level of abstraction, the better//. | + | |
| - | </note> | + | |
| - | --> Common Question 1# | + | ---- |
| - | + | * 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 | |
| - | <-- | + | * 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 | ||
| + | |||
| + | <tabbox Concrete> | ||
| + | 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. | ||
| - | --> Common Question 2# | + | 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. |
| - | + | ---- | |
| - | <-- | + | |
| - | + | ||
| - | <tabbox Examples> | + | |
| - | --> Example1# | + | * For a nice introduction, see [[http://inspirehep.net/record/284501/|Quantum Phases And Angles]] by R. Jackiw |
| + | * 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. | ||
| - | <-- | + | <tabbox Abstract> |
| - | --> Example2:# | + | <note tip> |
| + | The motto in this section is: //the higher the level of abstraction, the better//. | ||
| + | </note> | ||
| - | + | <tabbox Why is it interesting?> | |
| - | <-- | + | |
| - | + | Berry phases are, in some sense, the common origin of all [[advanced_notions:quantum_field_theory:anomalies|anomaly effects]]. | |
| - | <tabbox History> | + | |
| + | This is stated, for example in [[http://www.sciencedirect.com/science/article/pii/0550321388902556?via%3Dihub|Berry's phase, commutators, and the Dirac sea]] by Michael Stone and William E. Goff | ||
| </tabbox> | </tabbox> | ||
advanced_tools/geometric_phase.1499094726.txt.gz · Last modified: 2017/12/04 08:01 (external edit)
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