Invariant currents in lossy acoustic waveguides with complete local symmetry

Kalozoumis, P. A.; Richoux, Olivier; Diakonos, F. K.; Theocharis, G.; Schmelcher, Peter

doi:10.1103/physrevb.92.014303

Cited by 22 publications

(28 citation statements)

References 47 publications

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“…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%

“…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: 99%

“…The first experimental detection of the ITPC has been achieved in acoustic waveguides [17] where both the phase and magnitude of the pressure field yield a complete reconstruction of the complex ITPC. Here the theory has been extended to include losses and the experiment has also verified the occurence of perfectly transmitting resonances [17].…”

Section: Introductionmentioning

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%

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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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“…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%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamics of local symmetry correlators for interacting many-particle systems

Schmelcher

Krönke

Diakonos

2017

The Journal of Chemical Physics

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“…Besides the familiar global symmetries of parity and particle exchange, infinite barriers induce piecewise-linear local symmetries. Local symmetries have been shown to be useful for wave propagation and scattering in one-dimensional systems with partial symmetry [51,52]. This section also clarifies how this article makes the distinction between systematic and accidental symmetries (following the definitions in [53]).…”

Section: Outline Of Papermentioning

confidence: 99%

Infinite barriers and symmetries for a few trapped particles in one dimension

Harshman

2017

Phys. Rev. A

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This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are dependent on the specific shapes of the traps and the interactions, this article applies symmetry analysis to identify generic features in the spectrum of stationary states of few-particle, few-well systems. Extended attention is given to a simple but flexible threeparameter model of two particles in two wells in one dimension. A key insight is that two limiting cases, hard-core repulsion and no inter-well tunneling, can both be treated as emergent symmetries of the few-particle Hamiltonian. These symmetries are the mathematical consequences of infinite barriers in configuration space. They are necessary to explain the pattern of degeneracies in the energy spectrum, to understand how degeneracies are broken for models away from limiting cases, and to explain separability and integrability. These symmetry methods are extendable to more complicated models and the results have practical consequences for stable state control in fewparticle, few-well systems with ultracold atoms in optical traps.

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Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

Maciá

2017

Annalen der Physik

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A spectral classi…cation of general one-dimensional binary aperiodic crystals (BACs) based on both their di¤raction patterns and energy spectrum measures is introduced along with a systematic comparison of the zeroth-order energy spectrum main features for BACs belonging to di¤erent spectral classes, including Fibonacci-class, precious means, metallic means, mixed means and period doubling based representatives. These systems are described by means of mixed-type Hamiltonians which include both diagonal and o¤-diagonal terms aperiodically distributed. An algebraic approach highlighting chemical correlation e¤ects present in the underlying lattice is introduced.Close analytical expressions are obtained by exploiting some algebraic properties of suitable blocking schemes preserving the atomic order of the original lattice. The existence of a resonance energy which de…nes the basic anatomy of the zeroth-order energy spectra structure for the standard Fibonacci, the precious means and the Fibonacci-class quasicrystals is disclosed. This eigenstate is also found in the energy spectra of BACs belonging to other spectral classes, but for speci…c particular choices of the corresponding model parameters only. The transmission coe¢ cient of these resonant states is always bounded below, although their related Landauer conductance values may range from highly conductive to highly resistive ones, depending on the relative strength of the chemical bonds.

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Invariant currents in lossy acoustic waveguides with complete local symmetry

Cited by 22 publications

References 47 publications

Dynamics of local symmetry correlators for interacting many-particle systems

Dynamics of local symmetry correlators for interacting many-particle systems

Infinite barriers and symmetries for a few trapped particles in one dimension

Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

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