Probing Wigner rotations for any group

Oblak, Blagoje

doi:10.1016/j.geomphys.2018.03.008

Cited by 3 publications

(10 citation statements)

References 68 publications

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“…These results are consistent with their AdS 3 analogues [13], of which they are a limit, although the tools [15] needed for BMS 3 differ sharply from their Virasoro counterparts. Note also that (39) coincides with the kinetic action functional recently derived in [16], so that gravitational Berry phases can be seen as symplectic fluxes on the space of boundary gravitons.…”

Section: Flat Limit Of Virasoro Berry Phasessupporting

confidence: 80%

“…We also show that they are flat limits of analogous Virasoro Berry phases affecting dressed particles in AdS 3 [13]. Our approach relies on various technical tools relevant to representations of semi-direct products; they are described in greater detail in [15].…”

Section: Berry Phases and Thomas Precession For Bmsmentioning

confidence: 94%

“…To apply eq. (15) to BMS 3 particles, one must first understand how it works for generic semi-direct product groups [15].…”

Section: Berry Phases Of One-particle Statesmentioning

confidence: 99%

“…is the (left) Maurer-Cartan form of G. (We write L f for left multiplication by f ∈ G.) To apply eq. ( 15) to BMS 3 particles, one must first understand how it works for generic semi-direct product groups [15].…”

Section: Berry Phases Of One-particle Statesmentioning

confidence: 99%

“…In fact, as in the AdS 3 case of [13], we will derive a general formula for Berry phases [14] associated with closed curves in the space of all asymptotic symmetries (including supertranslations). The computation will rely on certain technical tools developed in [15] and will reproduce the 'geometric action functionals' of BMS 3 [16]. For superrotations this will provide a gravitational, spin-dependent extension of Thomas precession (eq.…”

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confidence: 99%

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Thomas precession for dressed particles

Oblak

2018

Class. Quantum Grav.

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We consider a particle dressed with boundary gravitons in three-dimensional Minkowski space. The existence of BMS transformations implies that the particle's wavefunction picks up a Berry phase when subjected to changes of reference frames that trace a closed path in the asymptotic symmetry group. We evaluate this phase and show that, for BMS superrotations, it provides a gravitational generalization of Thomas precession. In principle, such phases are observable signatures of asymptotic symmetries.

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Section: Flat Limit Of Virasoro Berry Phasessupporting

confidence: 80%

Section: Berry Phases and Thomas Precession For Bmsmentioning

confidence: 94%

“…To apply eq. (15) to BMS 3 particles, one must first understand how it works for generic semi-direct product groups [15].…”

Section: Berry Phases Of One-particle Statesmentioning

confidence: 99%

Section: Berry Phases Of One-particle Statesmentioning

confidence: 99%

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confidence: 99%

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Thomas precession for dressed particles

Oblak

2018

Class. Quantum Grav.

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Berry phases in the reconstructed KdV equation

Oblak

Kozyreff

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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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.

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Adiabatic deformations of quantum Hall droplets

Oblak,

Estienne

2023

SciPost Phys.

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We consider area-preserving deformations of the plane, acting on electronic wave functions through “quantomorphisms” that change both the underlying metric and the confining potential. We show that adiabatic sequences of such transformations produce Berry phases that can be written in closed form in terms of the many-body current and density, even in the presence of interactions. For a large class of deformations that generalize squeezing and shearing, the leading piece of the phase is a super-extensive Aharonov-Bohm term (\propto N^2∝N2 for NN electrons) in the thermodynamic limit. Its gauge-invariant subleading partner only measures the current, whose dominant contribution to the phase stems from a jump at the edge in the limit of strong magnetic fields. This results in a finite Berry curvature per unit area, reminiscent of the Hall viscosity. We show that the latter is in fact included in our formalism, bypassing its standard derivation on a torus and suggesting realistic experimental setups for its observation in quantum simulators.

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Probing Wigner rotations for any group

Cited by 3 publications

References 68 publications

Thomas precession for dressed particles

Thomas precession for dressed particles

Berry phases in the reconstructed KdV equation

Adiabatic deformations of quantum Hall droplets

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