Semi-Quantum Chaos

Details Semi-Quantum Chaos Semi-Quantum Chaos

1993-09-13

arxiv.org/abs/chao-dyn/9309004v2

Nonlinear Sciences

Chaotic Dynamics

9 pages, LaTeX, to appear in Phys Rev Letters

Scientific paper

10.1103/PhysRevLett.72.1337

We consider a system in which a classical oscillator is interacting with a purely quantum mechanical oscillator, described by the Lagrangian $ L = \frac{1}{2} \dot{x}^2 + \frac{1}{2} \dot{A}^2 - \frac{1}{2} ( m^2 + e^2 A^2) x^2 \>, $ where $A$ is a classical variable and $x$ is a quantum operator. With $\langle x(t) \rangle = 0$, the relevant variable for the quantum oscillator is $\langle x(t) x(t) \rangle = G(t)$. The classical Hamiltonian dynamics governing the variables $A(t)$, $\Pi_A(t)$, $G(t)$ and $\Pi_G(t)$ is chaotic so that the results of making measurements on the quantum system at later times are sensitive to initial conditions. This system arises as the zero momentum part of the problem of pair production of charged scalar particles by a strong external electric field.

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