2 research outputs found
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.