Ares Natalia, Wisniacki Diego A
Departamento de Física J J Giambiagi, FCEN, UBA, Ciudad Universitaria, Buenos Aires, Argentina.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046216. doi: 10.1103/PhysRevE.80.046216. Epub 2009 Oct 26.
Loschmidt echo (LE) is a measure of reversibility and sensitivity to perturbations of quantum evolutions. For weak perturbations its decay rate is given by the width of the local density of states (LDOS). When the perturbation is strong enough, it has been shown in chaotic systems that its decay is dictated by the classical Lyapunov exponent. However, several recent studies have shown an unexpected nonuniform decay rate as a function of the perturbation strength instead of that Lyapunov decay. Here we study the systematic behavior of this regime in perturbed cat maps. We show that some perturbations produce coherent oscillations in the width of LDOS that imprint clear signals of the perturbation in LE decay. We also show that if the perturbation acts in a small region of phase space (local perturbation) the effect is magnified and the decay is given by the width of the LDOS.
洛施密特回波（LE）是对量子演化的可逆性和微扰敏感性的一种度量。对于弱微扰，其衰减率由局域态密度（LDOS）的宽度给出。当微扰足够强时，在混沌系统中已表明其衰减由经典李雅普诺夫指数决定。然而，最近的几项研究表明，作为微扰强度的函数，存在意想不到的非均匀衰减率，而不是李雅普诺夫衰减。在此，我们研究受扰猫映射中该区域的系统行为。我们表明，一些微扰会在LDOS宽度中产生相干振荡，这些振荡在LE衰减中留下清晰的微扰信号。我们还表明，如果微扰作用于相空间的一个小区域（局部微扰），则效果会被放大，衰减由LDOS的宽度给出。
