6 research outputs found
Π ΠΏΠ΅ΡΠ΅Π½ΠΎΡΠ΅ ΡΡΠ΄Π° ΠΏΠΎΠ½ΡΡΠΈΠΉ ΡΡΠ°ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ°Π΄ΠΈΠΎΡΠΈΠ·ΠΈΠΊΠΈ Π² ΡΠ΅ΠΎΡΠΈΡ ΠΎΠ΄Π½ΠΎΠΌΠ΅ΡΠ½ΡΡ ΡΠΎΡΠ΅ΡΠ½ΡΡ ΠΎΡΠΎΠ±ΡΠ°ΠΆΠ΅Π½ΠΈΠΉ
In the article, the possibility of using a bispectrum under the investigation of regular and chaotic behaviour of one-dimensional point mappings is discussed. The effectiveness of the transfer of this concept to nonlinear dynamics was demonstrated by an example of the Feigenbaum mapping. Also in the work, the application of the Kullback-Leibler entropy in the theory of point mappings is considered. It has been shown that this information-like value is able to describe the behaviour of statistical ensembles of one-dimensional mappings. In the framework of this theory some general properties of its behaviour were found out. Constructivity of the Kullback-Leibler entropy in the theory of point mappings was shown by means of its direct calculation for the βsaw toothβ mapping with linear initial probability density. Moreover, for this mapping the denumerable set of initial probability densities hitting into its stationary probability density after a finite number of steps was pointed out.Β Π ΡΡΠ°ΡΡΠ΅ ΠΎΠ±ΡΡΠΆΠ΄Π°Π΅ΡΡΡ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ Π±ΠΈΡΠΏΠ΅ΠΊΡΡΠ° ΠΏΡΠΈ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ΅Π³ΡΠ»ΡΡΠ½ΠΎΠ³ΠΎ ΠΈ Ρ
Π°ΠΎΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΏΠΎΠ²Π΅Π΄Π΅Π½ΠΈΡ ΠΎΠ΄Π½ΠΎΠΌΠ΅ΡΠ½ΡΡ
ΡΠΎΡΠ΅ΡΠ½ΡΡ
ΠΎΡΠΎΠ±ΡΠ°ΠΆΠ΅Π½ΠΈΠΉ. ΠΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΡ ΡΡΠ°Π½ΡΡΠ΅ΡΠ° ΡΡΠΎΠ³ΠΎ ΠΏΠΎΠ½ΡΡΠΈΡ Π² Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΡΡ Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΡ ΠΏΡΠΎΠ΄Π΅ΠΌΠΎΠ½ΡΡΡΠΈΡΠΎΠ²Π°Π½Π° Π½Π° ΠΏΡΠΈΠΌΠ΅ΡΠ΅ ΠΎΡΠΎΠ±ΡΠ°ΠΆΠ΅Π½ΠΈΡ Π€Π΅ΠΉΠ³Π΅Π½Π±Π°ΡΠΌΠ°. Π’Π°ΠΊΠΆΠ΅ Π² ΡΠ°Π±ΠΎΡΠ΅ ΡΠ°ΡΡΠΌΠΎΡΡΠ΅Π½ΠΎ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ ΡΠ½ΡΡΠΎΠΏΠΈΠΈ ΠΡΠ»ΡΠ±Π°ΠΊΠ°βΠΠ΅ΠΉΠ±Π»Π΅ΡΠ° Π² ΡΠ΅ΠΎΡΠΈΠΈ ΡΠΎΡΠ΅ΡΠ½ΡΡ
ΠΎΡΠΎΠ±ΡΠ°ΠΆΠ΅Π½ΠΈΠΉ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΡΡΠ° Π²Π΅Π»ΠΈΡΠΈΠ½Π° ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠ° ΠΏΡΠΈΠ³ΠΎΠ΄Π½Π° Π΄Π»Ρ ΠΎΠΏΠΈΡΠ°Π½ΠΈΡ ΠΏΠΎΠ²Π΅Π΄Π΅Π½ΠΈΡ ΡΡΠ°ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
Π°Π½ΡΠ°ΠΌΠ±Π»Π΅ΠΉ ΠΎΠ΄Π½ΠΎΠΌΠ΅ΡΠ½ΡΡ
ΠΎΡΠΎΠ±ΡΠ°ΠΆΠ΅Π½ΠΈΠΉ. Π ΡΠ°ΠΌΠΊΠ°Ρ
ΡΡΠΎΠΉ ΡΠ΅ΠΎΡΠΈΠΈ Π²ΡΡΠ²Π»Π΅Π½Ρ Π½Π΅ΠΊΠΎΡΠΎΡΡΠ΅ ΠΎΠ±ΡΠΈΠ΅ ΡΠ²ΠΎΠΉΡΡΠ²Π° Π΅Ρ ΠΏΠΎΠ²Π΅Π΄Π΅Π½ΠΈΡ. ΠΠΎΠ½ΡΡΡΡΠΊΡΠΈΠ²ΠΈΠ·ΠΌ ΡΠ½ΡΡΠΎΠΏΠΈΠΈ ΠΡΠ»ΡΠ±Π°ΠΊΠ°βΠΠ΅ΠΉΠ±Π»Π΅ΡΠ° Π² ΡΠ΅ΠΎΡΠΈΠΈ ΡΠΎΡΠ΅ΡΠ½ΡΡ
ΠΎΡΠΎΠ±ΡΠ°ΠΆΠ΅Π½ΠΈΠΉ ΠΏΠΎΠΊΠ°Π·Π°Π½ ΡΠ°ΠΊΠΆΠ΅ ΠΏΡΡΠΌΡΠΌ Π΅Ρ Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΠ΅ΠΌ Π΄Π»Ρ ΠΎΡΠΎΠ±ΡΠ°ΠΆΠ΅Π½ΠΈΡ Β«Π·ΡΠ± ΠΏΠΈΠ»ΡΒ» Ρ Π»ΠΈΠ½Π΅ΠΉΠ½ΡΠΌ Π½Π°ΡΠ°Π»ΡΠ½ΡΠΌ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ΠΌ Π²Π΅ΡΠΎΡΡΠ½ΠΎΡΡΠ΅ΠΉ. ΠΡΠΎΠΌΠ΅ ΡΠΎΠ³ΠΎ, Π΄Π»Ρ ΡΡΠΎΠ³ΠΎ ΠΎΡΠΎΠ±ΡΠ°ΠΆΠ΅Π½ΠΈΡ ΡΠΊΠ°Π·Π°Π½ΠΎ ΡΡΡΡΠ½ΠΎΠ΅ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²ΠΎ Π½Π°ΡΠ°Π»ΡΠ½ΡΡ
ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠΉ Π²Π΅ΡΠΎΡΡΠ½ΠΎΡΡΠ΅ΠΉ, ΠΏΠΎΠΏΠ°Π΄Π°ΡΡΠΈΡ
Π² Π΅Π³ΠΎ ΡΡΠ°ΡΠΈΠΎΠ½Π°ΡΠ½ΠΎΠ΅ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ Π²Π΅ΡΠΎΡΡΠ½ΠΎΡΡΠ΅ΠΉ Π·Π° ΠΊΠΎΠ½Π΅ΡΠ½ΠΎΠ΅ ΡΠΈΡΠ»ΠΎ ΡΠ°Π³ΠΎΠ².Β
On the Transfer of a Number of Concepts of Statistical Radiophysics to the Theory of One-dimensional Point Mappings
In the article, the possibility of using a bispectrum under the investigation of regular and chaotic behaviour of one-dimensional point mappings is discussed. The effectiveness of the transfer of this concept to nonlinear dynamics was demonstrated by an example of the Feigenbaum mapping. Also in the work, the application of the Kullback-Leibler entropy in the theory of point mappings is considered. It has been shown that this information-like value is able to describe the behaviour of statistical ensembles of one-dimensional mappings. In the framework of this theory some general properties of its behaviour were found out. Constructivity of the Kullback-Leibler entropy in the theory of point mappings was shown by means of its direct calculation for the βsaw toothβ mapping with linear initial probability density. Moreover, for this mapping the denumerable set of initial probability densities hitting into its stationary probability density after a finite number of steps was pointed out
Edge States and Chiral Solitons in Topological Hall and ChernβSimons Fields
The multi-component extension problem of the (2+1)D-gauge topological JackiwβPi model describing the nonlinear quantum dynamics of charged particles in multi-layer Hall systems is considered. By applying the dimensional reduction (2 + 1)D β (1 + 1)D to Lagrangians with the ChernβSimons topologic fields , multi-component nonlinear Schrodinger equations for particles are constructed with allowance for their interaction. With Hirotaβs method, an exact two-soliton solution is obtained, which is of interest in quantum information transmission systems due to the stability of their propagation. An asymptotic analysis t βΒ±β of soliton-soliton interactions shows that there is no backscattering processes. We identify these solutions with the edge (topological protected) states β chiral solitons β in the multi-layer quantum Hall systems. By applying the Hirota bilinear operator algebra and a current theorem, it is shown that, in contrast to the usual vector solitons, the dynamics of new solutions (chiral vector solitons) has exclusively unidirectional motion. The article is published in the authorβs wording
ΠΡΠ°Π΅Π²ΡΠ΅ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ ΠΈ ΠΊΠΈΡΠ°Π»ΡΠ½ΡΠ΅ ΡΠΎΠ»ΠΈΡΠΎΠ½Ρ Π² ΡΠΎΠΏΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ ΠΏΠΎΠ»ΡΡ Π§Π΅ΡΠ½Π°βΠ‘Π°ΠΉΠΌΠΎΠ½ΡΠ°β Π₯ΠΎΠ»Π»Π°
The multi-component extension problem of the (2+1)D-gauge topological JackiwβPi model describing the nonlinear quantum dynamics of charged particles in multi-layer Hall systems is considered. By applying the dimensional reduction (2 + 1)D β (1 + 1)D to Lagrangians with the ChernβSimons topologic fields , multi-component nonlinear Schrodinger equations for particles are constructed with allowance for their interaction. With Hirotaβs method, an exact two-soliton solution is obtained, which is of interest in quantum information transmission systems due to the stability of their propagation. An asymptotic analysis t βΒ±β of soliton-soliton interactions shows that there is no backscattering processes. We identify these solutions with the edge (topological protected) states β chiral solitons β in the multi-layer quantum Hall systems. By applying the Hirota bilinear operator algebra and a current theorem, it is shown that, in contrast to the usual vector solitons, the dynamics of new solutions (chiral vector solitons) has exclusively unidirectional motion. The article is published in the authorβs wording.Β Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ° ΠΌΠ½ΠΎΠ³ΠΎΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠ½ΠΎΠ³ΠΎ ΡΠ°ΡΡΠΈΡΠ΅Π½ΠΈΡ (2+1)D-ΠΊΠ°Π»ΠΈΠ±ΡΠΎΠ²ΠΎΡΠ½ΠΎΠΉ ΡΠΎΠΏΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ JackiwβPi, ΠΎΠΏΠΈΡΡΠ²Π°ΡΡΠ΅ΠΉ Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΡΡ ΠΊΠ²Π°Π½ΡΠΎΠ²ΡΡ Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΡ Π·Π°ΡΡΠΆΠ΅Π½Π½ΡΡ
ΡΠ°ΡΡΠΈΡ Π² ΠΌΠ½ΠΎΠ³ΠΎΡΠ»ΠΎΠΉΠ½ΡΡ
ΡΠΈΡΡΠ΅ΠΌΠ°Ρ
Π₯ΠΎΠ»Π»Π°. ΠΡΠΈΠΌΠ΅Π½ΡΡ ΡΠ°Π·ΠΌΠ΅ΡΠ½ΡΡ ΡΠ΅Π΄ΡΠΊΡΠΈΡ (2 + 1)D β (1+1)D ΠΊ Π»Π°Π³ΡΠ°Π½ΠΆΠΈΠ°Π½Π°ΠΌ Ρ ΡΠΎΠΏΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ ΠΏΠΎΠ»ΡΠΌΠΈ Π§Π΅ΡΠ½Π°βΠ‘Π°ΠΉΠΌΠΎΠ½ΡΠ°, ΠΌΡ ΠΏΠΎΡΡΡΠΎΠΈΠ»ΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠ½ΡΠ΅ Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΡΠ΅ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ Π¨ΡΠ΅Π΄ΠΈΠ½Π³Π΅ΡΠ° Π΄Π»Ρ ΡΠ°ΡΡΠΈΡ Ρ ΡΡΠ΅ΡΠΎΠΌ ΠΈΡ
Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΡ. ΠΡΠΏΠΎΠ»ΡΠ·ΡΡ ΠΌΠ΅ΡΠΎΠ΄ Π₯ΠΈΡΠΎΡΡ, ΠΏΠΎΠ»ΡΡΠΈΠ»ΠΈ ΡΠΎΡΠ½ΠΎΠ΅ Π΄Π²ΡΡ
ΡΠΎΠ»ΠΈΡΠΎΠ½Π½ΠΎΠ΅ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅, ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΡΡΠ΅Π΅ ΠΈΠ½ΡΠ΅ΡΠ΅Ρ Π΄Π»Ρ ΠΊΠ²Π°Π½ΡΠΎΠ²ΡΡ
ΡΠΈΡΡΠ΅ΠΌ ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ Π² ΡΠΈΠ»Ρ ΡΡΡΠΎΠΉΡΠΈΠ²ΠΎΡΡΠΈ ΠΈΡ
ΡΠ°ΡΠΏΡΠΎΡΡΡΠ°Π½Π΅Π½ΠΈΡ. ΠΡΠΈΠΌΠΏΡΠΎΡΠΈΡΠ΅ΡΠΊΠΈΠΉ t βΒ±β Π°Π½Π°Π»ΠΈΠ· ΡΠΎΠ»ΠΈΡΠΎΠ½-ΡΠΎΠ»ΠΈΡΠΎΠ½Π½ΡΡ
Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΠΉ ΠΏΠΎΠΊΠ°Π·ΡΠ²Π°Π΅Ρ, ΡΡΠΎ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ°ΡΠ½ΠΎΠ³ΠΎ ΡΠ°ΡΡΠ΅ΡΠ½ΠΈΡ Π½Π΅Ρ. ΠΡ ΠΎΡΠΎΠΆΠ΄Π΅ΡΡΠ²Π»ΡΠ΅ΠΌ ΡΡΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΡ Ρ ΠΊΡΠ°Π΅Π²ΡΠΌΠΈ (ΡΠΎΠΏΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈ Π·Π°ΡΠΈΡΠ΅Π½Π½ΡΠΌΠΈ) ΡΠΎΡΡΠΎΡΠ½ΠΈΡΠΌΠΈ β ΠΊΠΈΡΠ°Π»ΡΠ½ΡΠΌΠΈ ΡΠΎΠ»ΠΈΡΠΎΠ½Π°ΠΌΠΈ β Π² ΠΌΠ½ΠΎΠ³ΠΎΡΠ»ΠΎΠΉΠ½ΡΡ
ΠΊΠ²Π°Π½ΡΠΎΠ²ΡΡ
ΡΠΈΡΡΠ΅ΠΌΠ°Ρ
Π₯ΠΎΠ»Π»Π°. ΠΡΠΈΠΌΠ΅Π½ΡΡ Π±ΠΈΠ»ΠΈΠ½Π΅ΠΉΠ½ΡΡ ΠΎΠΏΠ΅ΡΠ°ΡΠΎΡΠ½ΡΡ Π°Π»Π³Π΅Π±ΡΡ Π₯ΠΈΡΠΎΡΡ ΠΈ ΡΠ΅ΠΎΡΠ΅ΠΌΡ ΡΠΎΠΊΠ°, ΠΌΡ ΠΏΠΎΠΊΠ°Π·Π°Π»ΠΈ, ΡΡΠΎ Π² ΠΎΡΠ»ΠΈΡΠΈΠ΅ ΠΎΡ ΠΎΠ±ΡΡΠ½ΡΡ
Π²Π΅ΠΊΡΠΎΡΠ½ΡΡ
ΡΠΎΠ»ΠΈΡΠΎΠ½ΠΎΠ² Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠ° Π½ΠΎΠ²ΡΡ
ΡΠ΅ΡΠ΅Π½ΠΈΠΉ (ΠΊΠΈΡΠ°Π»ΡΠ½ΡΡ
Π²Π΅ΠΊΡΠΎΡΠ½ΡΡ
ΡΠΎΠ»ΠΈΡΠΎΠ½ΠΎΠ²) ΠΈΠΌΠ΅Π΅Ρ ΠΈΡΠΊΠ»ΡΡΠΈΡΠ΅Π»ΡΠ½ΠΎ ΠΎΠ΄Π½ΠΎΠ½Π°ΠΏΡΠ°Π²Π»Π΅Π½Π½ΠΎΠ΅ Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΠ΅. Π‘ΡΠ°ΡΡΡ ΠΏΡΠ±Π»ΠΈΠΊΡΠ΅ΡΡΡ Π² Π°Π²ΡΠΎΡΡΠΊΠΎΠΉ ΡΠ΅Π΄Π°ΠΊΡΠΈΠΈ.