Berry phases in the reconstructed KdV equation
Copyright policy )Berry phases in the reconstructed KdV equation
We consider the KdV equation on a circle and its Lie–Poisson reconstruction, which is reminiscent of an equation of motion for fluid particles. For periodic waves, the stroboscopic reconstructed motion is governed by an iterated map whose Poincaré rotation number yields the drift velocity. We show that this number has a geometric origin: it is the sum of a dynamical phase, a Berry phase, and an “anomalous phase.” The last two quantities are universal: they are solely due to the underlying Virasoro group structure. The Berry phase, in particular, was previously described by Oblak [J. High Energy Phys. 10, 114 (2017)] for two-dimensional conformal field theories and follows from adiabatic deformations produced by the propagating wave. We illustrate these general results with cnoidal waves, for which all phases can be evaluated in closed form thanks to a uniformizing map that we derive. Along the way, we encounter “orbital bifurcations” occurring when a wave becomes non-uniformizable: there exists a resonance wedge, in the cnoidal parameter space, where particle motion is locked to the wave, while no such locking occurs outside of the wedge.
High Energy Physics - Theory, groupes de lie, Théorie des groupes, [PHYS.PHYS.PHYS-GEN-PH] Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], Berry phase, General Physics and Astronomy, FOS: Physical sciences, Topologie générale, groupes topologiques, groupes de lie, Poincare, Korteweg-de Vries equation, FOS: Mathematics, parameter space, circle, Mathematical Physics, intégrale, fluid, Physique théorique et mathématique, Géométrie riemannienne, intégrale, symplectique et de poisson, Nonlinear Sciences - Exactly Solvable and Integrable Systems, groupes topologiques, Applied Mathematics, Fluid Dynamics (physics.flu-dyn), Statistical and Nonlinear Physics, symplectique et de poisson, Physics - Fluid Dynamics, Mathematical Physics (math-ph), [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph], Géométrie riemannienne, Topologie générale, geometry: symplectic, group: Virasoro, KdV equations (Korteweg-de Vries equations), High Energy Physics - Theory (hep-th), Mathematics - Symplectic Geometry, bifurcation, Mécanique des milieux continus, Symplectic Geometry (math.SG), [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], Exactly Solvable and Integrable Systems (nlin.SI), Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
High Energy Physics - Theory, groupes de lie, Théorie des groupes, [PHYS.PHYS.PHYS-GEN-PH] Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], Berry phase, General Physics and Astronomy, FOS: Physical sciences, Topologie générale, groupes topologiques, groupes de lie, Poincare, Korteweg-de Vries equation, FOS: Mathematics, parameter space, circle, Mathematical Physics, intégrale, fluid, Physique théorique et mathématique, Géométrie riemannienne, intégrale, symplectique et de poisson, Nonlinear Sciences - Exactly Solvable and Integrable Systems, groupes topologiques, Applied Mathematics, Fluid Dynamics (physics.flu-dyn), Statistical and Nonlinear Physics, symplectique et de poisson, Physics - Fluid Dynamics, Mathematical Physics (math-ph), [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph], Géométrie riemannienne, Topologie générale, geometry: symplectic, group: Virasoro, KdV equations (Korteweg-de Vries equations), High Energy Physics - Theory (hep-th), Mathematics - Symplectic Geometry, bifurcation, Mécanique des milieux continus, Symplectic Geometry (math.SG), [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], Exactly Solvable and Integrable Systems (nlin.SI), Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).10 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!