Topological phase in classical mechanics

Malykin, G. B.; Kharlamov, Sergei A.

doi:10.3367/ufnr.0173.200309e.0985

Cited by 13 publications

(4 citation statements)

References 30 publications

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“…The non-integrable phase that the eigenvectors of the Hermitian Hamiltonian possess is called Berry phase or the geometric (topological) phase. Today this phenomenon is well studied theoretically and repeatedly observed experimentally (see, for example, [9][10][11][12][13][14][15] and references therein). It turns out that the non-trivial connection Â occurs in the parameter space due to the presence of the points of degeneracy (term intersections) of the eigenvalues of the Hamiltonian in question.…”

Section: Hermitian Hamiltonian On the Parameter Space And Berry Phasementioning

confidence: 98%

Spin gauge fields: From Berry phase to topological spin transport and Hall effects

Bliokh

2005

Annals of Physics

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Section: Hermitian Hamiltonian On the Parameter Space And Berry Phasementioning

confidence: 98%

Spin gauge fields: From Berry phase to topological spin transport and Hall effects

Bliokh

2005

Annals of Physics

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“…Therefore, because the change in the pitch of the helicoidal winding of the SMF was produced in Ref. [27] by shifting only one of the two ends of the lightguide coil, one of the angles, a 1 or a 2 (to be specific, we assume that a 1 a Ryt ), changes in expression (18) for I full because of the changing magnitude of the Rytov effect. Figure 12 plots the light intensity I full as a function of the rotation angle a 1 as calculated in accordance with Eqn (18).…”

Section: Analysis Of Experimental Resultsmentioning

confidence: 99%

“…[27] by shifting only one of the two ends of the lightguide coil, one of the angles, a 1 or a 2 (to be specific, we assume that a 1 a Ryt ), changes in expression (18) for I full because of the changing magnitude of the Rytov effect. Figure 12 plots the light intensity I full as a function of the rotation angle a 1 as calculated in accordance with Eqn (18). The calculations assumed the polarizer coefficient in the FRI circuit e 1, and the value of ellipticity of Ginzburg's screw polarization modes for the equivalent uniform SMF of the contour was R 0Y pa14Y pa4.…”

Section: Analysis Of Experimental Resultsmentioning

confidence: 99%

Geometric phases in singlemode fiber lightguides and fiber ring interferometers

Malykin¹,

Pozdnyakova²

2004

Phys.-Usp.

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We consider various geometric phases (GPs) in singlemode fiber lightguides (SMFs) and in fiber ring interferometers (FRIs): the Pancharatnam phase stemming from the cyclic evolution of the polarization state of radiation (RP state) in SMF, the Rytov ± Vladimirski|¯phase (RV phase) stemming from the Rytov effect (specifically, rotation of the polarization plane due to noncoplanar winding of SMFs), as well as the nonreciprocal phase difference of counterpropagating waves (NPDCW) and nonreciprocal geometric phase of counterpropagating waves (NGPCW), which are caused by polarization nonreciprocity (PN) in FRIs. We show that in the general case, the Pancharatnam phase for an arbitrary RP state is inconsistent with the real phase change of light fluctuations in media that possess not only circular but also linear birefringence. We show that the RV phase, having a geometric origin, can in principle be considered as a dynamic phase (DP). We also show that the NGPCW can be considered as an effect of the evolution of the RP state mapped on the PoincareÂ sphere in Ginzburg's orthogonal screw polarization modes (GSPMs) of SMFs in the FRI contour. We analyze a number of experiments in which geometric phases were detected in FRIs: changing the RV phase and Rytov's angle (RA) in response to change of the pitch of helicoidal winding of SMFs. Contents 4.1 Kinematic phase in SMFs; 4.2 Linear birefringence of SMFs induced by bending; 4.3 Circular birefringence in SMFs induced by twisting. Ginzburg's screw polarization modes 5. The Rytov effect and Rytov ± Vladimirski|¯phase in SMFs and FRIs in the case of noncoplanar winding 297 5.1 The Rytov effect in a singlemode fiber lightguide of FRIs; 5.2 Similarities between the Rytov effect in polarization optics and the Ishlinski|¯effect in classical mechanics. Parallel vector translation. Noncommutativity of finite rotations; 5.3 The Rytov ± Vladimirski|¯phase and the Pancharatnam phase of the second kind in SMFs with noncoplanar winding 6. Polarization nonreciprocity in FRIs and the nonreciprocal geometric phase of counterpropagating waves 300 6.1 Polarization nonreciprocity in FRIs; 6.2 Nonreciprocal geometric phase of counterpropagating waves in FRIs 7. Analysis of experiments on recording the geometric phase in FRIs 303 7.1 Parameters of fiber ring interferometers on which measurements were conducted; 7.2 Analysis of experimental results 8. Unfounded hypotheses related to geometric phases in FRIs 305 9. Conclusion 305 References 306

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“…Introduction. After the discovery of the geometric phases in coherent quantum systems [1,2] (see also [3] on geometric phases in earlier work), it was natural to ask, whether these phases can be observed in quantum systems coupled to an environment. In particular, since the environment typically has a continuous spectrum, the gap in the spectrum of the system+environment vanishes, which blocks manipulations at frequencies below the gap.…”

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confidence: 99%

Geometric phase via adiabatic manipulations of the environment

Syzranov,

Makhlin

2008

Preprint

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We show that geometric phases may be generated in a quantum system subject to noise by adiabatic manipulations of the fluctuating fields, e.g., by variation of the system-environment coupling. For a two-state quantum system we express this phase in terms of the geometry of the path, traversed by the slowly varying direction and amplitude of the fluctuations. We discuss the origin of this phase and possibilities to separate it from the known environment-induced modification of the Berry phase.

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Topological phase in classical mechanics

Cited by 13 publications

References 30 publications

Spin gauge fields: From Berry phase to topological spin transport and Hall effects

Spin gauge fields: From Berry phase to topological spin transport and Hall effects

Geometric phases in singlemode fiber lightguides and fiber ring interferometers

Geometric phase via adiabatic manipulations of the environment

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