Toroidal precession as a geometric phase

Burby, J. W.; Qin, Hong

doi:10.1063/1.4789377

Cited by 7 publications

(23 citation statements)

References 25 publications

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“…A standard example for where a Berry phase arises is the adiabatic evolution of a quantum mechanical wavefunction. Berry or geometrical phases have also found numerous applications in plasma physics (Littlejohn 1988; Liu & Qin 2011, 2012; Brizard & de Guillebon 2012; Burby & Qin 2013; Rax & Gueroult 2019). To discuss Berry phase in a general way, our setting is a Hilbert space, and we use bra-ket notation, where the Hermitian product of two vectors and is denoted by .…”

Section: Mathematical Backgroundmentioning

confidence: 99%

“…The concepts described in the previous section are illustrated with specific examples. The first example, in § 3.1, comes from the shallow-water equations of geophysical fluid dynamics (Delplace et al 2017). This example, although not directly related to plasma physics, is discussed in detail for its analytic transparency, minimal complexity and clear physical manifestation of the bulk-boundary correspondence principle.…”

Section: Examplesmentioning

confidence: 99%

“…Following Delplace et al (2017), the non-dimensionalized, linearized fluid equations of motion of the shallow-water system are…”

Section: Shallow-water Equations and Equatorial Wavesmentioning

confidence: 99%

“…In an infinite continuum medium, the wave vector space extends to infinity. An important breakthrough was that of Delplace, Marston & Venaille (2017), who demonstrated that a model in geophysical fluid dynamics can be understood through topological phase and bulk-boundary correspondence. Other topological phenomena in fluid and continuum electromagnetic media have also been discovered (Silveirinha 2015;Perrot, Delplace & Venaille 2019;Souslov et al 2019;Marciani & Delplace 2020).…”

Section: Introductionmentioning

confidence: 99%

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Topological phase in plasma physics

Parker

2021

J. Plasma Phys.

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Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological phase can also be fruitfully applied to plasmas. Here, the theory of topological phase is introduced, including a discussion of Berry phase, Berry connection, Berry curvature and Chern number. One of the clear physical manifestations of topological phase is the bulk-boundary correspondence, the existence of localized unidirectional modes at the interface between topologically distinct phases. These concepts are illustrated through examples, including the simple magnetized cold plasma. An outlook is provided for future theoretical developments and possible applications.

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Section: Mathematical Backgroundmentioning

confidence: 99%

Section: Examplesmentioning

confidence: 99%

“…Following Delplace et al (2017), the non-dimensionalized, linearized fluid equations of motion of the shallow-water system are…”

Section: Shallow-water Equations and Equatorial Wavesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Topological phase in plasma physics

Parker

2021

J. Plasma Phys.

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“…Geometric phase effects are well documented in charged particle physics 32,33 . They have, for instance, been studied for the cyclotron motion 34,35 , wave propagation and Faraday effects 36 and the bounce motion of trapped particles 37 .…”

Section: Introductionmentioning

confidence: 99%

Geometric phase in Brillouin flows

Rax

Gueroult

2019

Physics of Plasmas

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A geometric phase is found to arise from the cyclic adiabatic variation of the crossed magnetic and electric fields which sustain the Brillouin rotation of a plasma column. The expression of the gauge field associated with this geometric phase accumulation is explicited. The physical origin of this phase is shown to be the uncompensated inductive electric field drift that stems from magnetic field cyclic variations. Building on this result, the effect of a weak, periodic and adiabatic modulation of the axial magnetic field on the particle guiding center drift motion is demonstrated to be equivalent to that of a perpendicular electric field, allowing to study the gauge induced Brillouin flow through a geometrically equivalent linear radial electric field. This finding opens new perspectives to drive plasma rotation and hints at possible applications of this basic effect.

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On the correspondence between classical geometric phase of gyro-motion and quantum Berry phase

Zhu

Qin

2017

Physics of Plasmas

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We show that the geometric phase of the gyro-motion of a classical charged particle in a uniform time-dependent magnetic field described by Newton's equation can be derived from a coherent Berry phase for the coherent states of the Schrödinger equation or the Dirac equation. This correspondence is established by constructing coherent states for a particle using the energy eigenstates on the Landau levels and proving that the coherent states can maintain their status of coherent states during the slow varying of the magnetic field. It is discovered that orbital Berry phases of the eigenstates interfere coherently to produce an observable effect (which we termed "coherent Berry phase"), which is exactly the geometric phase of the classical gyro-motion. This technique works for particles with and without spin. For particles with spin, on each of the eigenstates that makes up the coherent states, the Berry phase consists of two parts that can be identified as those due to the orbital and the spin motion. It is the orbital Berry phases that interfere coherently to produce a coherent Berry phase corresponding to the classical geometric phase of the gyro-motion.The spin Berry phases of the eigenstates, on the other hand, remain to be quantum phase factors for the coherent states and have no classical counterpart.

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Toroidal precession as a geometric phase

Cited by 7 publications

References 25 publications

Topological phase in plasma physics

Topological phase in plasma physics

Geometric phase in Brillouin flows

On the correspondence between classical geometric phase of gyro-motion and quantum Berry phase

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