Quantum chaos effects in the axial channeling of electrons

Шульга, Н.Ф.; Сыщенко, В. В.; Tarnovsky, A. I.; Isupov, A. Yu.

doi:10.1134/s1027451015040199

Cited by 8 publications

(11 citation statements)

References 6 publications

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“…numerically using the so-called spectral method [16], the details of which are described in [7][8][9][10] as applied to the channeling problem.…”

Section: Methodsmentioning

confidence: 99%

“…This difference is due to the fact that the energy levels of the integrable system do not interact with each other, while there is the interaction of energy levels of the nonintegrable (chaotic in the classical limit) system, which leads to their mutual repulsion. The manifestations of dynamic chaos in electron channeling [5,6] were studied in [7][8][9][10][11] for the case of motion near the silicon-crystal [110] direction. In this case, pairs of neighboring atomic chains create a two-well potential, above the saddle point of which the motion of electrons turns out to be almost completely chaotic.…”

Section: Introductionmentioning

confidence: 99%

“…The quantum chaos theory predicts (see, e.g., [3][4][5]) that the energy levels nearest-neighbor distribution of the chaotic system obeys Wigner distribution while the regular system -the exponential one (characteristic to Poisson flow). The level statistics for the electrons channeling near [110] direction in silicon crystal has been studied in [6][7][8]. In that case each pair of the closest parallel atomic strings forms the two-well potential (see, e.g., [1]), in which the motion above the saddle point is chaotic for the major part of the initial conditions.…”

Section: Introductionmentioning

confidence: 99%

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Splitting of the Transverse-Motion Energy Levels of Positrons during Channeling in the [100] Direction of a Silicon Crystal

et al. 2021

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The motion of charged particles in the crystal can be both regular and chaotic. Within the quantum approach, chaos manifests itself in the statistical properties of the set of energy levels. The systems in which regions of regular motion are separated by that of chaotic motion in phase space are of special interest. The statistics of levels of these systems is greatly influenced by the possibility of tunneling between phase-space regions dynamically isolated from each other. Matrix elements for such tunneling transitions are estimated in the present paper. To do this, all transverse-motion energy levels of 20 GeV positrons moving in the axialchanneling mode along the Si crystal [100] direction, as well as the Hamiltonian eigenfunctions corresponding to these states, are calculated numerically. The superposition of these eigenfunctions that correspond to classical orbits localized in symmetric but dynamically isolated regions of phase space are found. The energylevel splitting makes it possible to estimate the tunneling-transition matrix elements.

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“…numerically using the so-called spectral method [16], the details of which are described in [7][8][9][10] as applied to the channeling problem.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Splitting of the Transverse-Motion Energy Levels of Positrons during Channeling in the [100] Direction of a Silicon Crystal

et al. 2021

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“…In [6], the predictions of the theory of quantum chaos were tested for the energy levels of the transverse motion of relativistic electrons moving in the axialchanneling regime [7,8] near the [110] direction of a silicon crystal. In this case, the statistics of energy levels was studied in a narrow interval near the upper edge of the potential well formed by continuous potentials of atomic chains, within which the average density of levels can be considered constant.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the statistical properties of energy levels for each of these classes must be investigated independently [3]. The energy levels of the transverse motion of a charged particle in the field (5) are found numerically using the spectral method [10], which was successfully used in the channeling problem in [6,[11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Statistical Properties of the Transverse-Motion Energy Levels for Channeling Electrons in a Silicon Crystal under Dynamical Chaos Conditions

Сыщенко

Tarnovsky

2021

J. Surf. Investig.

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The classical motion of particles in external fields is frequently chaotic although deterministic within the classical limit. Studying the quantum mechanical behavior of such systems amounts to the problematics of quantum chaos. Quantum chaos manifests itself primarily in the statistical properties of the energy-level arrays of such systems. However, the typical objects under consideration are systems of the type billiards with rigid walls. This paper studies the calculated energy levels of the transverse motion of relativistic electrons in the axial-channeling regime along the [100] direction of the silicon crystal which is described as motion in the smooth potential well. The nearest-level spacing distributions as well as the spectral rigidity are studied for the range of parameters where electron motion is chaotic within the classical limit. Both these characteristics demonstrate agreement with quantum-chaos-theory predictions.

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Regular and chaotic motion domains in the channeling electron's phase space and mean level density for its transverse motion energy

Шульга¹,

Сыщенко²,

Tarnovsky³

et al. 2019

J. Inst.

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A: The motion of charged particles in a crystal in the axial channeling regime can be both regular and chaotic. The chaos in quantum case manifests itself in the statistical properties of the energy levels set. These properties have been studied previously for the electrons channeling along [110] direction of the silicon crystal, in the case when the classical motion was completely chaotic. The case of channeling along [100] direction is of special interest because the classical motion here can be both regular and chaotic for the same energy depending on the initial conditions. The semiclassical energy level density (as well as its part that corresponds to the regular motion domains in the phase space) is computed for the 10 GeV channeling electrons and positrons. It is demonstrated that the level spacing distribution for both electrons and positrons can be better described by Berry-Robnik distribution than by both Wigner (completely chaotic case) or Poisson (completely regular case) distributions. K: Interaction of radiation with matter A X P : 1909.132381Corresponding author.

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Quantum chaos effects in the axial channeling of electrons

Cited by 8 publications

References 6 publications

Splitting of the Transverse-Motion Energy Levels of Positrons during Channeling in the [100] Direction of a Silicon Crystal

Splitting of the Transverse-Motion Energy Levels of Positrons during Channeling in the [100] Direction of a Silicon Crystal

Statistical Properties of the Transverse-Motion Energy Levels for Channeling Electrons in a Silicon Crystal under Dynamical Chaos Conditions

Regular and chaotic motion domains in the channeling electron's phase space and mean level density for its transverse motion energy

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