Stability of quantum motion: beyond Fermi-golden-rule and Lyapunov decay.

نویسندگان

  • Wen-ge Wang
  • G Casati
  • Baowen Li
چکیده

We study, analytically and numerically, the stability of quantum motion for a classically chaotic system. We show the existence of different regimes of fidelity decay. In particular, when the underlying classical dynamics is weakly chaotic, deviations from Fermi-golden-rule and Lyapounov regimes are observed and discussed.

منابع مشابه

Quantum corrections to fidelity decay in chaotic systems.

By considering correlations between classical orbits we derive semiclassical expressions for the decay of the quantum fidelity amplitude for classically chaotic quantum systems, as well as for its squared modulus, the fidelity or Loschmidt echo. Our semiclassical results for the fidelity amplitude agree with random matrix theory (RMT) and supersymmetry predictions in the universal Fermi-golden ...

متن کامل

Measuring the Lyapunov exponent using quantum mechanics.

We study the time evolution of two wave packets prepared at the same initial state, but evolving under slightly different Hamiltonians. For chaotic systems, we determine the circumstances that lead to an exponential decay with time of the wave packet overlap function. We show that for sufficiently weak perturbations, the exponential decay follows a Fermi golden rule, while by making the differe...

متن کامل

A Fermi Golden Rule for Quantum Graphs

We present a Fermi golden rule giving rates of decay of states obtained by perturbing embedded eigenvalues of a quantum graph. To illustrate the procedure in a notationally simpler setting we first describe a Fermi golden rule for boundary value problems on surfaces with constant curvature cusps. We also provide a resonance existence result which is uniform on compact sets of energies and metri...

متن کامل

Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo.

The overlap of two wave packets evolving in time with slightly different Hamiltonians decays exponentially approximate to e(-gammat), for perturbation strengths U greater than the level spacing Delta. We present numerical evidence for a dynamical system that the decay rate gamma is given by the smallest of the Lyapunov exponent lambda of the classical chaotic dynamics and the level broadening U...

متن کامل

Crossover of quantum Loschmidt echo from golden-rule decay to perturbation-independent decay.

We study the crossover of the quantum Loschmidt echo (or fidelity) from the golden-rule regime to the perturbation-independent exponential decay regime by using the kicked top model. It is shown that the deviation of the perturbation-independent decay of the averaged fidelity from the Lyapunov decay results from quantum fluctuations in individual fidelity, which are caused by the coherence in t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

متن کامل
عنوان ژورنال:
  • Physical review. E, Statistical, nonlinear, and soft matter physics

دوره 69 2 Pt 2  شماره 

صفحات  -

تاریخ انتشار 2004