Cucchietti F M, Lewenkopf C H, Pastawski H M
T-4, Theory Division, MS B213, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Aug;74(2 Pt 2):026207. doi: 10.1103/PhysRevE.74.026207. Epub 2006 Aug 16.
We study the decay rate of the Loschmidt echo or fidelity in a chaotic system under a time-dependent perturbation V(q,t) with typical strength Planck's/tau(v) . The perturbation represents the action of an uncontrolled environment interacting with the system, and is characterized by a correlation length xi(0) and a correlation time tau(0). For small perturbation strengths or rapid fluctuating perturbations, the Loschmidt echo decays exponentially with a rate predicted by the Fermi "golden rule," 1/approximately tau =tau(c)/tau(v)(2), where tau(c) approximately min[tau(0), xi(0)/upsilon] and upsilon is the typical particle velocity. Whenever the rate 1/approximately tau is larger than the Lyapunov exponent of the system, a perturbation independent Lyapunov decay regime arises. We also find that by speeding up the fluctuations (while keeping the perturbation strength fixed) the fidelity decay becomes slower, and hence one can protect the system against decoherence.
我们研究了在具有典型强度普朗克常数/τ(v)的含时微扰V(q,t)作用下，混沌系统中洛施密特回波或保真度的衰减率。该微扰代表了与系统相互作用的不受控环境的作用，其特征在于关联长度ξ(0)和关联时间τ(0)。对于小的微扰强度或快速波动的微扰，洛施密特回波以费米“黄金规则”预测的速率指数衰减，1/≈τ = τ(c)/τ(v)²，其中τ(c)≈min[τ(0), ξ(0)/υ]，υ是典型粒子速度。只要速率1/≈τ大于系统的李雅普诺夫指数，就会出现与微扰无关的李雅普诺夫衰减 regime。我们还发现，通过加快波动（同时保持微扰强度不变），保真度衰减会变慢，因此可以保护系统免受退相干影响。
