Sensitivity of quantum motion to perturbation in a triangle map

2008/02/29 by Wen-ge Wang
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Exponential decay #Exponential function #Fidelity #Instability #Mathematical analysis #Mathematical physics #Mathematics #Perturbation (astronomy) #Physics #Power law #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #nlin.CD #quant-ph

paper · pdf · doi:10.1103/physreve.77.036206

published as Phys. Rev. E 77, 036206 (2008) · 6 pages, 8 figures, published version

openalex publication_date 2008/03/13 · arxiv created 2008/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study quantum Loschmidt echo, or fidelity, in the triangle map whose classical counterpart has linear instability and weak chaos. Numerically, three regimes of fidelity decay have been found with respect to the perturbation strength epsilon. In the regime of weak perturbation, the fidelity decays as exp(-c epsilon(2)t(gamma)) with gamma approximately 1.7. In the regime of strong perturbation, the fidelity is approximately a function of epsilont(2.5), which is predicted for the classical fidelity [G. Casati, Phys. Rev. Lett. 94, 114101 (2005)], and decays slower than power-law decay for long times. In an intermediate regime, the fidelity has approximately an exponential decay exp(-c' epsilont).

Citations

• Quantum-classical correspondence in perturbed chaotic systems
• Dynamics of Loschmidt echoes and fidelity decay
• Decay of the Loschmidt Echo for Quantum States with Sub-Planck-Scale Structures
• Correspondence in quasiperiodic and chaotic maps: Quantization via the von Neumann equation
• The quantum fidelity for the time-periodic singular harmonic oscillator
• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo