2022
DOI: 10.1088/1751-8121/ac6840
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Quantum signatures of chaos in relativistic quantum billiards with shapes of circle- and ellipse-sectors*

Abstract: According to the Berry-Tabor conjecture, the spectral properties of typical nonrelativistic quantum systems with an integrable classical counterpart agree with those of Poissonian random numbers. We investigate to what extend it applies to relativistic neutrino billiards (NBs) consisting of a spin-1/2 particle confined to a bounded planar domain by imposing suitable boundary conditions (BCs). In distinction to nonrelativistic quantum billiards (QBs), NBs do not have a well-defined classical counterpart. Howeve… Show more

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Cited by 7 publications
(18 citation statements)
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“…Furthermore, both the QB and the NB comprise eigenfunctions that are invariant under a discrete rotational symmetry, however, the first and second component of those of the NB transform differently under the respective rotation [16]. We demonstrated in [30] that, as a consequence, the circle NB and circle-sector NBs with inner angle 0 < φ 0 < 2π, constructed by cutting it along the symmetry lines φ = 0 and φ = φ 0 , do not have any common eigenstates and, as a consequence, the spectral properties of the latter may coincide with those of QBs with chaotic classical dynamics. The terms entering the BIE equation ( 24) can be expressed in terms of φ = φ − φ ′ ,…”
Section: Test Of the Bies For Massive Circle Nbsmentioning
confidence: 79%
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“…Furthermore, both the QB and the NB comprise eigenfunctions that are invariant under a discrete rotational symmetry, however, the first and second component of those of the NB transform differently under the respective rotation [16]. We demonstrated in [30] that, as a consequence, the circle NB and circle-sector NBs with inner angle 0 < φ 0 < 2π, constructed by cutting it along the symmetry lines φ = 0 and φ = φ 0 , do not have any common eigenstates and, as a consequence, the spectral properties of the latter may coincide with those of QBs with chaotic classical dynamics. The terms entering the BIE equation ( 24) can be expressed in terms of φ = φ − φ ′ ,…”
Section: Test Of the Bies For Massive Circle Nbsmentioning
confidence: 79%
“…Furthermore, for billiards that possess a discrete rotational symmetry, for both the QB [11][12][13] and the NB the eigenstates can be separated according to the transformation properties under the corresponding rotation, however for the latter they differ for the two spinor eigenfunction components [29]. As a consequence, the circle NB and sectors of it do not have any common eigenstates [30]. Similarly, for billiards with a shape that generates a unidirectional dynamics, the unidirectionality of the current and the relative phase of the spinor components at the boundary resulting from the BC equation (58), which are clockwise for µ = +1 and counterclockwise for µ = −1, leads to the large splittings of the eigenvalues corresponding to clockwise and counterclockwise modes, respectively, and rules out dynamical tunneling; see also [35].…”
Section: Discussionmentioning
confidence: 99%
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“…In sequence, we introduce a perturbation of the C-C 3 B, replacing the circumferences with ellipses. Recently, billiards with elliptical borders have been studied in other contexts, i.e., in singular potentials [30], in relativistic limits [31], and flows that move around chaotic cores [32]. We start the analysis by presenting the billiards, discussing their classical dynamics, showing some mixed phase spaces, and calculating the fraction of the chaotic sea on these phase spaces.…”
Section: Introductionmentioning
confidence: 99%
“…It has been demonstrated in Refs. [51,52] that the spectral properties of GBs and NBs of corresponding shape do not coincide [1,8,24,28,[53][54][55][56][57][58][59]. These discrepancies were attributed to intervalley scattering at the boundary of GBs [55,58,59].…”
Section: Introductionmentioning
confidence: 99%