2011 Student Scholarship Highlights

Duggins, Peter '13

Non-Monotonic Behavior of the Lyapunov Exponent in the Quantum-Classical Transition

Chaos, a property of certain dynamical systems, is defined as extreme sensitivity to initial conditions -- as the system evolves, a small initial separation between trajectories becomes exponentially larger in time. In this project, we investigated how chaotic behavior is affected as a system transitions in size from that described by classical mechanics to that described by quantum mechanics. Specifically, we calculate the Lyapunov Exponent, a measure of chaos describing a system's sensitivity to initial conditions, as we make the system size smaller and smaller (go deeper into the quantum regime). We find that for a specific system, the damped driven double-well Duffing oscillator, there is a non-monotonic change in the degree of chaos in the quantum-classical transition. This novel result indicates that systems in an intermediate regime can display unique behavior not found in the limiting cases.

Published in Physical Review.

This work was supervised by Arjendu Pattanayak

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