Exposing local symmetries in distorted driven lattices via time-averaged invariants

Wulf, Thomas; Morfonios, Christian V.; Diakonos, F. K.; Schmelcher, Peter

doi:10.1103/physreve.93.052215

Cited by 8 publications

(26 citation statements)

References 37 publications

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“…quantum systems with local symmetries. It is only recently that it has been shown [11][12][13][14][15][16][17][18][19][20] that the unique feature of the presence of local symmetries are the existence of invariant two-point correlator currents. However, all of these works address the case of one-dimensional stationary and non-interacting wave mechanical setups ranging from acoustics, optics to quantum mechanics and make no statement how a more general concept of local symmetries could look like, in particular in the case of dynamically interacting quantum systems.…”

Section: Discussionmentioning

confidence: 99%

“…The ITPC are the key quantities characterizing local discrete symmetries in one spatial dimension as has been shown in several works [13][14][15][16][17][18][19][20]. Applications to photonic multilayers have demonstrated that perfectly transmitting resonances can be completely classified according to sum rules imposed on the ITPC [14].…”

Section: Introductionmentioning

confidence: 90%

“…Reducing to a single particle in one dimension which is the case previously treated extensively [11][12][13][14][15][16][17][18][19][20] we obtain…”

Section: Non-interacting Particle Systemsmentioning

confidence: 99%

“…Recently several steps in the direction of a theory of local symmetries have been performed indeed [11][12][13][14][15][16][17][18][19][20]. The focus was hereby on the case of non-interacting stationary one-dimensional single particle or wave mechanical (acoustics, optics) problems which are described by the corresponding Schrödinger or Helmholtz equation Ψ ′′ (x) + S(x)Ψ(x) = 0 where the prime denotes differentiation with respect to the spatial variable x.…”

Section: Introductionmentioning

confidence: 99%

“…Very recently a local basis approach has been developed [18] which provides a classification of the solutions of the wave equation in terms of ITPC and consequently a computational strategy for the determination of the wave field in complex locally symmetric potential landscapes (see Figure 1). Further very recent extensions of the theory of ITPC include time-dependent periodically driven [20] and parity-time symmetric setups with gain and loss [13,19] where e.g. the ITPC provide an order parameter for the phase diagram of the scattering states [13].…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of local symmetry correlators for interacting many-particle systems

Schmelcher

Krönke

Diakonos

2017

The Journal of Chemical Physics

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Recently (PRL 113, 050403 (2014)) the concept of local symmetries in one-dimensional stationary wave propagation has been shown to lead to a class of invariant two-point currents that allow to generalize the parity and Bloch theorem. In the present work we establish the theoretical framework of local symmetries for higher-dimensional interacting many-body systems. Based on the Bogoliubov-Born-Green-KirkwoodYvon (BBGKY) hierarchy we derive the equations of motion of local symmetry correlators which are offdiagonal elements of the reduced one-body density matrix at symmetry related positions. The natural orbital representation yields equations of motion for the convex sum of the local symmetry correlators of the natural orbitals as well as for the local symmetry correlators of the individual orbitals themselves. An alternative integral representation with a unique interpretation is provided. We discuss special cases, such as the bosonic and fermionic mean field theory and show in particular that the invariant two-point currents are recovered in the case of the non-interacting one-dimensional stationary wave propagation. Finally we derive the equations of motion for anomalous local symmetry correlators which indicate the breaking of a global into a local symmetry in the stationary non-interacting case. * pschmelc@physnet.uni-hamburg.de

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 90%

“…Reducing to a single particle in one dimension which is the case previously treated extensively [11][12][13][14][15][16][17][18][19][20] we obtain…”

Section: Non-interacting Particle Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics of local symmetry correlators for interacting many-particle systems

Schmelcher

Krönke

Diakonos

2017

The Journal of Chemical Physics

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Observation of Local Symmetry in a Photonic System

Schmitt

Weimann

Morfonios

et al. 2020

Laser & Photonics Reviews

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The concept of local symmetry has been shown to be a powerful tool in predicting and designing complex transport phenomena in stationary scattering off aperiodic media, in terms of symmetry‐adapted nonlocal currents. For time‐evolving wavepackets, the spatiotemporal correlations caused by local symmetries are more challenging to reveal. A recent formalism‐based nonlocal continuity equation shows how local symmetries are encoded into the dynamics of light propagation in discrete waveguide arrays governed by a Schrödinger equation. However, the experimental demonstration is elusive so far. Representative examples of locally symmetric, globally symmetric, and fully nonsymmetric configurations are fabricated in fs laser‐written photonic arrays and their dynamics are probed. The approach allows to distinguish all three types of structures.

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Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays

et al. 2017

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We develop a formalism relating nonlocal current continuity to spatial symmetries of subparts in discrete Schrödinger systems. Breaking of such local symmetries hereby generates sources or sinks for the associated nonlocal currents. The framework is applied to locally inversion-(time-) and translation-(time-) symmetric onedimensional photonic waveguide arrays with Hermitian or non-Hermitian effective tight-binding Hamiltonians. For stationary states the nonlocal currents become translationally invariant within symmetric domains, exposing different types of local symmetry. They are further employed to derive a mapping between wave amplitudes of symmetry-related sites, generalizing also the global Bloch and parity mapping to local symmetry in discrete systems. In scattering setups, perfectly transmitting states are characterized by aligned invariant currents in attached symmetry domains, whose vanishing signifies a correspondingly symmetric density. For periodically driven arrays, the invariance of the nonlocal currents is retained on period average for quasi-energy eigenstates. The proposed theory of symmetry-induced continuity and local invariants may contribute to the understanding of wave structure and response in systems with localized spatial order. arXiv:1607.06577v2 [quant-ph]

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Exposing local symmetries in distorted driven lattices via time-averaged invariants

Cited by 8 publications

References 37 publications

Dynamics of local symmetry correlators for interacting many-particle systems

Dynamics of local symmetry correlators for interacting many-particle systems

Observation of Local Symmetry in a Photonic System

Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays

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