A new tool for quantum chaos could be powerful for other problems:an inspiring application to many-body localization

• 来源期刊: 科学通报（英文版）
• 年，卷（期）: 2017,（10）
• 页码范围: 669-670
• 页数: 2页
• 语种: 英文

摘要

Chaos,popularly referred to as the butterfly effect,widely exists in familiar systems such as fluid and weather.One defining feature of the chaos is the high sensitivity on the initial condition.For example,in classical mechanics,given two close initial conditions in phase space with separation δX(0),the outcome after time evolution could be "exponentially" different |δX(t)|≈eλLt|δX(0)|,where the growth rate λL is often referred to as Lyapunov exponent (see Fig.1 for a carton).This universal phenomenon reveals the nature of a complex system,and even has an impact on the popular culture.However,the generalization of the butterfly effect to the quantum mechanical world is not so simple.1 A naive attempt could be considering two nearby quantum states in Hilbert space |ψ> and |ψ'>,and measuring the distance after time evolution.But this will not work because the distance,if measured by inner product of states,is invariant under time evolution due to the unitarity of the quantum mechanics <ψ(t)|ψ/(t)> =<ψψ|ψ‘>.