Quantum effects in classical systems having complex energy

Understand

On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems extended into the complex domain.

• Three models are examined: the quartic double-well potential $V(x)=x^4-5x^2$, the cubic potential $V(x)=frac{1}{2}x^2-gx^3$, and the periodic potential $V(x)=-\cos x$.
• For the quartic potential a wave packet that is initially localized in one side of the double-well can tunnel to the other side.
• Complex solutions to the classical equations of motion exhibit a remarkably analogous behavior.