Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0506300 · Annals of Physics

Wavepacket dynamics, quantum reversibility, and random matrix theory

Moritz Hiller, Doron Cohen, Theo Geisel, Tsampikos Kottos

Published Feb 10, 2006• 19 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2005.12.003

Related papers

Random quantum dynamics

Winton Brown

•Jan 1, 2010•1 citation

Entanglement production in coupled kicked tops

Jayendra N. Bandyopadhyay, Arul Lakshminarayan

Entanglement production in coupled chaotic systems is studied with the help of kicked tops. Deriving the correct classical map, we have introduced and used the reduced Husimi function to visualize the possible behaviors of a wavepacket. We have studied a phase space based measure of the complexity of a state and used random matrix theory (RMT) to model the strongly chaotic cases. Extensive numerical studies have been done for the entanglement production in coupled kicked tops corresponding to different underlying classical dynamics and different coupling strengths. An approximate formula, based on RMT, is derived for the entanglement production in coupled strongly chaotic systems. This formula, applicable for arbitrary coupling strengths and also valid for long time, complements and extends significantly recent perturbation theories for strongly chaotic weakly coupled systems.

•Jul 18, 2003•0 citations

Random matrix theory and higher genus integrability: the quantum chiral Potts model

J-Ch Angl s d Auriac, J.-M. Maillard, C.-M. Viallet

We perform a random matrix theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L = 8. Our analysis gives clear evidence of a Gaussian orthogonal ensemble (GOE) statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore, a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of ‘higher genus integrability’.

arXiv:cond-mat/0205101•Journal of Physics A Mathematical and General•May 31, 2002•11 citations

Quantum Wavepacket Dynamics with Trajectories

Róbert E. Wyatt

APS•Mar 1, 2001•5 citations

Random fields and quantum dynamics

Takeyuki Hida

Foundations of Physics•Nov 1, 1997•2 citations

Scars in quantum chaotic wavefunctions

Lev Kaplan

We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behaviour of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics framework leads to predictions about statistical long-time and stationary properties of quantum systems with chaotic classical analogues. Many long-time quantum properties can be quantitatively understood using only short-time classical dynamics information; these include wavefunction intensity distributions, intensity correlations in phase space and correlations between wavefunctions, and distributions of decay rates and conductance peaks in weakly open systems. Strong deviations from random matrix theory are predicted and observed in the presence of short unstable periodic orbits.

arXiv:chao-dyn/9810013•Nonlinearity•Jan 1, 1999•112 citations
Entanglement production in coupled chaotic systems is studied with the help of kicked tops. Deriving the correct classical map, we have introduced and used the reduced Husimi function to visualize the possible behaviors of a wavepacket. We have studied a phase space based measure of the complexity of a state and used random matrix theory (RMT) to model the strongly chaotic cases. Extensive numerical studies have been done for the entanglement production in coupled kicked tops corresponding to different underlying classical dynamics and different coupling strengths. An approximate formula, based on RMT, is derived for the entanglement production in coupled strongly chaotic systems. This formula, applicable for arbitrary coupling strengths and also valid for long time, complements and extends significantly recent perturbation theories for strongly chaotic weakly coupled systems.
We perform a random matrix theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L = 8. Our analysis gives clear evidence of a Gaussian orthogonal ensemble (GOE) statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore, a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of ‘higher genus integrability’.
We review recent progress in attaining a quantitative understanding of the scarring phenomenon, the non-random behaviour of quantum wavefunctions near unstable periodic orbits of a classically chaotic system. The wavepacket dynamics framework leads to predictions about statistical long-time and stationary properties of quantum systems with chaotic classical analogues. Many long-time quantum properties can be quantitatively understood using only short-time classical dynamics information; these include wavefunction intensity distributions, intensity correlations in phase space and correlations between wavefunctions, and distributions of decay rates and conductance peaks in weakly open systems. Strong deviations from random matrix theory are predicted and observed in the presence of short unstable periodic orbits.