Perturbation Theory for Nearly Integrable Systems

2006 ◽  
pp. 21-37
Author(s):  
Sadrilla S. Abdullaev
Keyword(s):  
Perturbation Theory ◽  
Integrable Systems ◽  
Nearly Integrable Systems

Normal form construction for nearly-integrable systems with dissipation

2012 ◽  
Vol 17 (3-4) ◽  
pp. 273-292 ◽  
Author(s):  
Aessandra Celletti ◽  
Christoph Lhotka
Keyword(s):  
Normal Form ◽  
Integrable Systems ◽  
Nearly Integrable Systems

Dynamics of solitons in nearly integrable systems

1989 ◽  
Vol 61 (4) ◽  
pp. 763-915 ◽  
Author(s):  
Yuri S. Kivshar ◽  
Boris A. Malomed
Keyword(s):  
Integrable Systems ◽  
Nearly Integrable Systems

scholarly journals One-loop non-planar anomalous dimensions in super Yang-Mills theory

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Tristan McLoughlin ◽  
Raul Pereira ◽  
Anne Spiering
Keyword(s):  
Perturbation Theory ◽  
Integrable Systems ◽  
Chaotic Systems ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Mechanical Perturbation ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Dilatation Operator ◽  
Scalar Products

Abstract We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use non-degenerate quantum-mechanical perturbation theory to compute the leading 1/N2 corrections to operator dimensions and as an example compute the large R-charge limit for two-excitation states through subleading order in the R-charge. Finally, we numerically study the distribution of level spacings for these theories and show that they transition from the Poisson distribution for integrable systems at infinite N to the GOE Wigner-Dyson distribution for quantum chaotic systems at finite N.

scholarly journals Recurrence of fidelity in nearly integrable systems

2003 ◽  
Vol 68 (3) ◽  
Author(s):  
R. Sankaranarayanan ◽  
Arul Lakshminarayan
Keyword(s):  
Integrable Systems ◽  
Nearly Integrable Systems

Addendum: Dynamics of solitons in nearly integrable systems

1991 ◽  
Vol 63 (1) ◽  
pp. 211-211 ◽  
Author(s):  
Yuri S. Kivshar ◽  
Boris A. Malomed
Keyword(s):  
Integrable Systems ◽  
Nearly Integrable Systems

The singularity analysis for nearly integrable systems: homoclinic intersections and local multivaluedness

1995 ◽  
Vol 85 (1-2) ◽  
pp. 93-125 ◽  
Author(s):  
Alain Goriely ◽  
Michael Tabor
Keyword(s):  
Integrable Systems ◽  
Singularity Analysis ◽  
Nearly Integrable Systems

Perturbation Theory for Integrable Systems

1997 ◽  
pp. 138-211
Author(s):  
V. I. Arnold ◽  
V. V. Kozlov ◽  
A. I. Neishtadt
Keyword(s):  
Perturbation Theory ◽  
Integrable Systems

Phase convection and nonequilibrium fluctuations in nearly-integrable systems

1989 ◽  
Vol 135 (2) ◽  
pp. 92-98 ◽  
Author(s):  
A.L. Gerasimov
Keyword(s):  
Integrable Systems ◽  
Nonequilibrium Fluctuations ◽  
Nearly Integrable Systems
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