Structure of the channeling electrons wave functions under dynamical chaos conditions

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

doi:10.1016/j.nimb.2015.12.040

Cited by 15 publications

(18 citation statements)

References 10 publications

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“…Remember two groups of the qualitative distinctions between the wave functions in the regular and chaotic cases discovered and studied by various authors (see, e.g. [4,5,7,11]):…”

Section: Channeling Positrons Wave Functions Structurementioning

confidence: 99%

Positrons vs electrons channeling in silicon crystal: energy levels, wave functions and quantum chaos manifestations

et al. 2018

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A: The motion of fast electrons through the crystal during axial channeling could be regular and chaotic. The dynamical chaos in quantum systems manifests itself in both statistical properties of energy spectra and morphology of wave functions of the individual stationary states. In this report, we investigate the axial channeling of high and low energy electrons and positrons near [100] direction of a silicon crystal. This case is particularly interesting because of the fact that the chaotic motion domain occupies only a small part of the phase space for the channeling electrons whereas the motion of the channeling positrons is substantially chaotic for the almost all initial conditions. The energy levels of transverse motion, as well as the wave functions of the stationary states, have been computed numerically by the method presented at previous RREPS. Note that the potential of the elementary cell in (100) plane of silicon crystal possesses the symmetry of the square. The group theory methods had been used for classification of the computed eigenfunctions and identification of the non-degenerate and doubly degenerate energy levels. The channeling radiation spectrum for the low energy electrons has been also computed. K: Only keywords from JINST's keywords list please A X P : 1234.56789

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“…Remember two groups of the qualitative distinctions between the wave functions in the regular and chaotic cases discovered and studied by various authors (see, e.g. [4,5,7,11]):…”

Section: Channeling Positrons Wave Functions Structurementioning

confidence: 99%

Positrons vs electrons channeling in silicon crystal: energy levels, wave functions and quantum chaos manifestations

et al. 2018

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“…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%

“…In addition to studying the distribution of distances between adjacent levels, the presence of correlations is also checked by calculating the so-called spectral rigidity, or statistics [2][3][4][5]. For a set of unfolded levels in a certain interval (13) a step function is constructed similar to (10), and the variance of the deviation of this function from the straight line, fitted by the least-squares method, is calculated: (14) The average value of this value over a set of consecutive nonoverlapping intervals serves as…”

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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“…Quantum theory is based upon special representation of the scattering amplitude [7] in the form of an integral over the surface surrounding the region of influence of the external crystal field onto the particle (in the considered problem this corresponds to the field of the entire crystal), and upon the development of numeric methods of calculating of the wave function inside the crystal, that is done by using the so-called spectral method of solving wave equations [8][9][10]. The classical theory is based upon the solution of the particle motion equation by numerical methods [11].…”

Section: Introductionmentioning

confidence: 99%

Quantum and classical effects at scattering of high energy charged particles in thin crystals

Шульга¹,

Shulga²

2018

REFFIT

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The present work reviews the results concerning quantum scattering theory of ultrarelativistic electrons in ultrathin crystals and its comparison with analogous classical results. It deals with an intermediate range of thicknesses, large enough for that the particle motion could not be considered as rectilinear but small enough for that the channeling regime of motion was not established. The quantum theory is based both upon the representation of the scattering amplitude as an integral over the surface surrounding the target, and on the so-called operator method of determination of the wave function as a solution of a Schro .. dinger-like equation.The latter method implies a wide use of the Fourier technique, both in calculation of each next step in the wave packet evolution, and in moving from the spatial coordinates to the angular ones. The authors compare the quantum differential scattering cross-sections with the classical ones in the considered range of crystal thicknesses and show their resemblances, distinctions and the evolution of these distinctions with the change of the particle energy. The simplest variant of quantum scattering theory based upon the eikonal approximation of quantum mechanics is considered. In the paper the quantum differential scattering cross-section was calculated and its affinity with the classical one was demonstrated. In the preparation of these lecture notes the material of the paper [4] was used.

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Structure of the channeling electrons wave functions under dynamical chaos conditions

Cited by 15 publications

References 10 publications

Positrons vs electrons channeling in silicon crystal: energy levels, wave functions and quantum chaos manifestations

Positrons vs electrons channeling in silicon crystal: energy levels, wave functions and quantum chaos manifestations

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

Quantum and classical effects at scattering of high energy charged particles in thin crystals

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