Chaotic solutions of the nonlinear Schrodinger equation in classical and quantum systems
msra(1999)
摘要
We discuss stationary solutions of the nonlinear Schrodinger equation (NSE)
applicable to several quantum spin, electron and classical lattice systems. We
show that there may arise chaotic spatial structures in the form of
incommensurate or irregular quantum states and trajectories in space.
As a first (typical) example we consider a single electron which is strongly
coupled with phonons on a 1D chain of atoms. In the adiabatic approximation the
system is conventionally described by a discrete set of NSEs. Another apt
example is that of superconducting states in layered superconductors described
by the same NSE. Amongst many other applications the typical example for a
classical lattice is a system of coupled nonlinear oscillators.
We reformulate this discrete NSE to the form of a 2D mapping. By this we may
investigate a quantum problem by methods conventionally applied to classical
chaotic dynamics. We find three types of solutions: periodic, quasiperiodic and
chaotic. We then develop a procedure which allows us to obtain numerical
solutions of the NSE directly. This procedure may be used to any arbitrary
accuracy and so these solutions are exact to the degree of precision specified.
Both methods give a consistent result. When applied to our typical example we
find that the wave function of an electron on a deformable lattice (and other
quantum or classical discrete systems) may exhibit incommensurate and irregular
structures.
更多查看译文
关键词
mathematical physics,discrete system,superconductors,nonlinear schrodinger equation
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要