Invariants of Broken Discrete Symmetries

Kalozoumis, P. A.; Morfonios, Christian V.; Fk, Diakonos; Schmelcher, Peter

doi:10.1103/physrevlett.113.050403

Cited by 38 publications

(100 citation statements)

References 14 publications

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“…When the latter is globally symmetric, i.e. n(x) = n * (2a − x) for every x ∈ R, a non-vanishing Q is interpreted as a remnant of the PT -symmetry broken by the asymptotic conditions, typical for a scattering problem, as explained in [17]. Particularly, to obtain Q for a PT -symmetric setup, one multiplies Eq.…”

Section: Derivation Of the Invariant Currentmentioning

confidence: 99%

“…(1) has solutions for all k ∈ R, although n(x) is complex. Employing the method developed in [17] for discrete local symmetries one can derive a spatially invariant nonlocal current Q related to the PT -symmetry of the refraction index n(x). When the latter is globally symmetric, i.e.…”

Section: Derivation Of the Invariant Currentmentioning

confidence: 99%

“…In a recent work [17], by employing a generic wavemechanical framework, we have demonstrated how discrete symmetries such as parity and translation lead to symmetry-induced, non-local currents which are invariant within the spatial domains where the corresponding symmetry is obeyed (local symmetry). These invariants, in turn, led to a mapping which was shown to generalize the parity and Bloch theorems in the case where these symmetries are globally broken, while they are recovered in the limit of a corresponding global symmetry.…”

Section: Introductionmentioning

confidence: 99%

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Systematic pathway toPT-symmetry breaking in scattering systems

et al. 2014

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Recently [Phys. Rev. Lett. 106, 093902 (2011)] it has been shown that PT -symmetric scattering systems with balanced gain and loss, undergo a transition from PT -symmetric scattering eigenstates, which are norm preserving, to symmetry broken pairs of eigenstates exhibiting net amplification and loss. In the present work we derive the existence of an invariant non-local current which can be directly associated with the observed transition playing the role of an "order parameter". The use of this current for the description of the PT -symmetry breaking allows the extension of the known phase diagram to higher dimensions incorporating scattering states which are not eigenstates of the scattering matrix.

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Section: Derivation Of the Invariant Currentmentioning

confidence: 99%

Section: Derivation Of the Invariant Currentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Systematic pathway toPT-symmetry breaking in scattering systems

et al. 2014

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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%

“…Equivalently, configuration space symmetry transformations map stationary state wave functions into other stationary state wave functions with the same energy. Following [51], we further distinguish global and local configuration space symmetries. An example of a global symmetry transformation is a linear transformation of the entire space X that commutes with the Hamiltonian.…”

Section: A Configuration Space Symmetriesmentioning

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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Invariants of Broken Discrete Symmetries

Cited by 38 publications

References 14 publications

Systematic pathway toPT-symmetry breaking in scattering systems

Systematic pathway toPT-symmetry breaking in scattering 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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