2008/12/31 by Carl T. West, Tomaž Prosen, Tomaz Prosen +1
Computer Science · Mathematics · Physics and Astronomy · #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Dynamics and Pattern Formation #Phase space #Physics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Scaling #Singularity #cond-mat.dis-nn #cond-mat.mes-hall #nlin.CD
paper · pdf · doi:10.1103/physreve.79.050107
published as Phys. Rev. E 79, 050107(R) (2009) · 4 pages, 3 figures
arxiv created 2009/04/27 · openalex publication_date 2009/05/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the Loschmidt echo F(t) for a class of dynamical systems showing critical chaos. Using a kicked rotor with singular potential as a prototype model, we found that the classical echo shows a gap (initial drop) 1\ensuremath-Fg, where Fg scales as Fg(\ensuremathα,ϵ,\ensuremathη)=fcl(\ensuremathχcl\ensuremath≡\ensuremathη^3\ensuremath-\ensuremathα/ϵ); \ensuremathα is the order of singularity of the potential, \ensuremathη is the spread of the initial phase-space density, and ϵ is the perturbation strength. Instead, the quantum echo gap is insensitive to \ensuremathα, described by a scaling law Fg=fq(\ensuremathχq=\ensuremathη2/ϵ) which can be captured by a random matrix theory modeling of critical systems. We trace this quantum-classical discrepancy to strong diffraction effects that dominate the dynamics.