advanced_tools:geometric_phase
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advanced_tools:geometric_phase [2018/04/09 08:17] 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. | 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. | ||
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| + | [{{ :advanced_tools:geometricphase.png?nolink |Source: https://edoc.ub.uni-muenchen.de/17735/1/Atala_Marcos.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. | + | 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. |
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| - | 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. | + | |
| + | 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. | ||
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| * For a nice introduction, see [[http://inspirehep.net/record/284501/|Quantum Phases And Angles]] by R. Jackiw | * For a nice introduction, see [[http://inspirehep.net/record/284501/|Quantum Phases And Angles]] by R. Jackiw | ||
| - | * Geometric phases also exist in classical mechanics, like for example Hannay's angle. | + | * A nice textbook that discusses Berry's phase is Griffith "Introduction to Quantum Mechanics", especially chapter 10. |
| - | 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 | + | * 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. | ||
advanced_tools/geometric_phase.1523254656.txt.gz · Last modified: 2018/04/09 06:17 (external edit)
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