Overcoming the wall in the semiclassical baker's map

被引：20

作者：

Kaplan, L ^{[1
]}

Heller, EJ ^{[1
]}

机构：

[1] HARVARD SMITHSONIAN CTR ASTROPHYS,CAMBRIDGE,MA 02138

来源：

PHYSICAL REVIEW LETTERS | 1996年 / 76卷 / 09期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1103/PhysRevLett.76.1453

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A major barrier in semiclassical calculations for chaotic systems is the exponential increase in the number of terms at long times. Using an analogy with spin-chain partition functions, we overcome this ''exponential wall'' for the baker's map, reducing to order NT3/2 the number of operations needed to evolve an N-state system for T time steps. This method enables us to obtain semiclassical results up to the Heisenberg time and beyond, providing new insight as to the accuracy of the semiclassical approximation. The semiclassical result is often correct; its breakdown is nonuniform.

引用

页码：1453 / 1456

页数：4

共 16 条

[1] THE QUANTIZED BAKERS TRANSFORMATION [J].